624 + Interview Questions in MAGNETIC-EFFECT-OF-CURRENT IN GENERAL AWARENESS Page 4 InterviewSolution

151.	Statement - 1 : If an electron is not deflected while passing through a certain region of space, then only possibility is that there is no magnetic region. Statement - 2 : Magnetic force is directly proportional to the magnetic field applied.A. If both assertion and reason are true and the reason is the correctexplanation of the assertion.B. If both assertion and reason are true but reason is not the correctexplanation of the assertion.C. If assertion is true but reason is false.D. If assertion is false but reason is true.
Answer» Correct Answer - D

Discussion

152.	If the distance between two parallel current carrying wires is doubled, what is the force between them?
Answer» The force acting on one wire due to currents through two wires is inversely proportional to the distance between them. Thus the force becomes `1//2` times if the distance between the wires is doubled.

Discussion

153.	A beam of well collimated cathode rays travelling with a speed of `5xx10^(6)ms^(-1)` enter a region of mutually perpendicular electric and magnetic fields and emerge undeviated from this region. If `\|B\|=0.02t`, the magnitude of the electric field isA. `10^(5)Vm^(-1)`B. `2.5xx10^(8)Vm^(-1)`C. `1.25xx10^(10)Vm^(-1)`D. `2xx10^(3)Vm^(-1)`
Answer» Correct Answer - A

Discussion

154.	An `alpha`-particle of mass `6.65xx10^-27kg` is travelling at right angles to a magnetic field with a speed of `6xx10^5ms^-1`. The strength of the magnetic field is `0.2T`. Calculate the force on the `alpha`-particle and its acceleration.
Answer» Correct Answer - `5*77xx10^(12)ms^-2` Acceleration, `q=(Bqv)/(m)=(B(2e)v)/(m)` `:.` Charge on `alpha`-particle is twice that of proton.

Discussion

155.	Three long, straight and parallel wires are arranged as shown in Fig. The forces experienced by 10 cm length of wire Q is A. `1.4xx10^(-4)N` towardes the rightB. `1.4xx10^(-4)N` towards the leftC. `2.6xx10^(-4)N` to the rightD. `2.6xx10^(-4)N` to the left
Answer» Correct Answer - A

Discussion

156.	Three long, straight parallel wires carrying current, are arranged as shown in figure. The force experienced by a `25cm` length of wire `C` is A. `10^(-3)N`B. `2.5xx10^(-3)N`C. ZeroD. `1.5xx10^(-3)N`
Answer» Correct Answer - C

Discussion

157.	An electron in an atom revolves around the nucleus in an orbit of radius `053Å`. Calculate the equivalent magnetic moment, if the frequency of revolution of electron is `68xx10^9MHz`.
Answer» Correct Answer - `96xx10^(-24)Am^2` Here, `r=053Å=053xx10^(-10)m` `v=68xx10^9MHz=68xx10^(15)Hz`, `M=?` If e is charge on electron, then the equivalent current, `I=e/T=ev` `M=IA=ev(pir^2)` `=16xx10^(-19)xx68xx10^(15)xx314(053xx10^(-10))^2` `=96xx10^(-24)Am^2`

Discussion

158.	This questions has Statement I and Statement II. Of the four choices given after the Statements, choose the one that best describes into two Statements. Statement-I : Higher the range, greater is the resistance of ammeter. Statement- II : To increase the range of ammeter, additional shunt needs to be used across it.A. Statement-1 is true, Statement-2 is true, Statement-2 is a correct explaination of Statement-1.B. Statement-1 is true, Statement-2 is true, Statement-2 is not a correct explanation of Statement-1.C. Statement-1 is true, Statement-2 is false.D. Statement-1 is false, Statement-2 is true.
Answer» Correct Answer - D In order to increase the range of ammeter, its resistance should be decreased, i.e., additional shunt is connected in parallel. Thus statement-1 is false. Statement-2 is true.

Discussion

159.	What is the basic principle of working of cyclotron? Write two uses of this machine.
Answer» The working of the cyclotron is based on the fact that a heavy positively charged particle can be accelerated to a sufficiently high energy with the help of smaller values of oscillating electric field, by making it to cross the same electric field time and again with the use of strong magnetic field. A cyclotron is used (i) to bombard nuclei with high energy particles and to study the resulting nuclear reaction (ii) to produce radioactive substances which may be used in hospitals for diagnosing the diseases in the body.

Discussion

160.	A body is suspended from the lower end of a vertical spring. What shall be the effect on the position of the body when a current is sent through the spring? Does it depend upon the direction of current in the spring?
Answer» When the current is passed through a vertically suspended spring, the direction of currents in two adjoining parallel turns of wire is the same. Hence a force of attraction will be acting there. Due to it, the spring is compressed and the body attached at the end of spring is lifted upwards. The similar observations are made if the direction of current is reversed.

Discussion

161.	Particles having positive charges occasionally come with high velocity from the sky towards the earth. On account of the magnetic field of earth, they would be deflected towards theA. NorthB. SouthC. EastD. West
Answer» Correct Answer - C

Discussion

162.	An electron entres a magnetic field whose direction is perpendicualr to the velocity of the electron. ThenA. The speed of the electron will increaseB. The speed of the electron will decreaseC. The speed of the electron will remain the sameD. The velocity of the electron will remain the same
Answer» Correct Answer - C

Discussion

163.	Electrons moving with different speeds enter a unifrom magnetic field in a diection perpendicualr filed. They will move along circular paths .A. of same radiusB. with larger radii for the faster electronsC. with smaller radii for the faster electrons .D. either `(B)` or `C ` depending on the magnitude of the magnetic field .
Answer» Correct Answer - B `r = (mv)/(qB) implies r propv`

Discussion

164.	Two particles of charges `+Q` and `-Q` are projected from the same point with a velocity v in a region of unifrom magnetic filed `B` such that the velocity vector makes an angle 0 with the magnetic filed Their masses are `M` and `2M` respectively Then, they will meet again for the first time at a point whose distane from the point of projection is .A. `2piMvcos0//qB`B. `8piMvcos0//qB`C. `piMvcos0//qB`D. `4piMv cos 0//qB`
Answer» Correct Answer - D `T_(1) = (2piM)/(qB) T_(2) = (2pi(2M))/(qB)impliesT_(2)=(4piM)/(qB)` they will meet again when first will complete two revolution and second will complete one revoluation so direction `d =v cos thetat = vcostheta.2 (2piM)/(qB) = (4piMvcostheta)/(qB)` .

Discussion

165.	An electron is projected with velocity `v_(0)` in a unifrom electric field E perpendicular to the field Again it is projectced with velocity `v_(0)` perpendicular to a unifrom magnetic field `B//` if `r_(1)` is initial radius of curvature just after entering in the electric field and `r_(2)` is initial radius of curvature just after entering in magnetic field then the ratio `r_(1)//r_(2)` is equal to .A. `(Bv_(0)^(2))/(E)`B. `(B)/(E)`C. `(Ev_(0))/(B)`D. `(Bv_(0))/(B)`
Answer» Correct Answer - D `eE = (mV_(0)^(2))/(r_(1)) implies r_(1) = (mV_(0)^(2))/(eE) ` `eV_(0)B = (mV_(0)^(2))/(r_(2)) = (mV_(0))/(eB) implies (r_(1))/(r_(2)) =(V_(0)B)/(E)` .

Discussion

166.	An electron is moving along positive x-axis `A` unifrom electric filed exists to wards negative y-axis. What should be the direaction of magnetic field of suitable magnitude so that net force of electrons is zero .A. positivez-axisB. negative z-axisC. positivey-axisD. negative y-axis
Answer» Correct Answer - B `oversetrarr(F_(e)) + oversetrarr(F_(m)) = 0 ` `qoversetrarrE + q (oversetrarrV xx oversetrarrB) =0 implies oversetrarr(E) + oversetrarrV xx oversetrarrB =0` `E (-hatj) + VB (hati xx hatn) =0 implies hati xx hatn` should be in `hatj . So hatn = - hatk` .

Discussion

167.	The scale of galvanometer is divided into `150` equal divisions. The galvanometer has a current sensitivity of `10"divisions"//mA` and the voltage sensitivity of `2"divisions"//mV`. How the galvanometer be designed to read (i) 6A per division and (ii) 1 V per division?
Answer» Correct Answer - (a) `83xx10^-5Omega` in parallel (b) `9995 Omega` in series Galvanometer resistance is `=(I_s)/(V_s)=(nBA//k)/(nBA//kG)=G` So, `G=(I_s)/(V_s)=10/2=5Omega` Current for full scale deflection `I_g=(150)/(10)mA=15mA=15xx10^-3A` (i) The total current to be read, `I=6xx150=900A` As, `S=(I_gG)/(I-I_g)=(15xx10^-3xx5)/(900-15xx10^-3)` `=(15xx5xx10^-3)/(900)` `=83xx10^-5Omega` in parallel (ii) The total voltage to be read, `V=1xx150=150V` As `R=(V)/(I_g)-G=(150)/(15xx10^-3)-5` `=10^4-5=9995Omega` in series

Discussion

168.	A magnetising field of `1500 A//m` produces a flux of `24xx10^-5` weber in a bar of iron of cross-sectional area `05cm^2`. Calculate the permeability and susceptibility of the iron bar used.
Answer» Correct Answer - `255`; `254` Here, `H=1500A//m`, `phi=24xx10^-5weber` `a=05cm^2=05xx10^-4m^2` `mu_r=?`, `chi_m=?` Now `B=phi/a=(2.4xx10^-5)/(05xx10^-4)=48xx10^-1T` `mu=B/H=(48xx10^-1)/(1500)=32xx10^-4` `mu_r=(mu)/(mu_0)=(32xx10^-4)/(4pixx10^-7)=0*255xx10^3=255` As `mu_r=1+chi_m :. chi_m=mu_r-1=255-1=254`

Discussion

169.	Individual atoms/molecules/ions of a diamagnetic substance………….any net………………..on their own.
Answer» Correct Answer - do not posses ; magnetic moment

Discussion

170.	For which of the following magnetic materials, `B=muH` is valid, where B is the magnetic induction and H is the magnetising field and `mu` is nearly a constant for a wide range of H?A. Diamagnetic and ferromagnetic materials onlyB. Diamagnetic and paramagnetic materials onlyC. Paramagnetic and ferromagnetic materials onlyD. Diamagnetic, paramagnetic and ferromagnetic materials
Answer» Correct Answer - D The relation `B=muH` is valid for all Diamagnetic, paramagnetic and ferromagnetic materials.

Discussion

171.	If the magnetising field on a ferromagnetic material is increased, its permeability isA. decreasedB. increasedC. is unaffectedD. may be increased or decreased
Answer» Correct Answer - A Magnetic permeability of a ferromagnetic substance, `mu=B//H` or `muprop1/H`, where H is the magnetising field. If H increases then `mu` decreases.

Discussion

172.	Units of magnetising intensity and intensity of magnetisation are…………………., i.e., ………………… .
Answer» Correct Answer - same; `Am^-1`

Discussion

173.	Name the cgs unit of magnetising intensity. How is it related to SI unit of intensity.
Answer» The cgs unit of manetising intensity H is oersted. `1 =80Am^-1`

Discussion

174.	A charged paricle goes undeflected in a region containing electric and magnetic field. It is possible thatA. `vecE\|\|vecB` but `vecv` is not parallel to `vecE`B. `vecv\|\|vecB` but `vecE` is not parallel to `vecB`C. `vecE\|\|vecB`, `vecv\|\|vecE`D. `vecE` is not parallel to `vecB` and `vecv`.
Answer» A charged particle will go undeflected in the electric field and magnetic field if the direction of force on particle due to electric field only acts in the direction of motion of the particle, i.e., the charged particles moves parallel to the electric field and magnetic field acts parallel to the direction of motion of charged particle. A moving charged particle will also not be deflected while passing through a region if the force on it due to electric field is equal and opposite to the force due to magnetic field. It will be so if magnetic field is `_\|_r` to electric field and both the fields are `_\|_r` to the direction of motion of charged particle.

Discussion

175.	A planar loop of irregular shape encloses an area of `7*5xx10^-4m^2`, and carries a current of `12A`. The sense of flow of current appears to be clockwise to an observer. What is the magnitude and direction of the magnetic moment vector associated with the current loop?
Answer» Here, `A=75xx10^-4m^2, I=12A` As `M=IA` `:. M=12xx75xx10^-4=9xx10^-3Am^2` The direction of `vecM` is perpendicular to the plane of the loop and away from the observer (according to Right hand palm rule).

Discussion

176.	A rectangular loop of sides `27cmxx12cm` carries a current of `12A`. It is placed with its longer side parallel to the long straight conductor `3*0cm` apart and carrying a current of `20A`. Figure. (i) Find the net force on the loop (ii) What will be the net force on the loop if the current in the loop be reversed?
Answer» Correct Answer - (i) `346xx10^-4N`, directed towards long conductor (ii) `346xx10^-4N` directed away from the long conductor Attractive force on side `PQ=(mu_0)/(4pi)(2i_1i_2l)/(r)`, Repulsive force on the side `RS=(mu_0)/(4pi)(2i_1i_2l)/((r+b))`. Net attractive force on the loop `=(mu_0)/(4pi)2i_1i_2[1/r-(1)/(r+b)]l` When current is reversed, then net repulsive force on the loop `=(mu_0)/(4pi)2i_1i_2[1/r-(1)/(r+b)]l`.

Discussion

177.	A uniform magnetic field of `3000G` is established along the positive z-direction. A rectangular loop of sides `10cm` and `5cm` carries a current `12A`. What is the torque on the loop in the different cases shown in the figure. What is the force on each case? Which case corresponds to stable equilibrium?
Answer» Correct Answer - (a) `18xx10^-2Nm` (b) Angle between area vector `vecA` and `vecB` is `0^@` or `180^@` (c) Loop will be in stable equilibrium if area vector `vecA` is parallel to magnetic field `vecB` and in unstable equilibrium when `vecA` is antiparallel to `vecB` Here, `B=3000G=03T`, `I=12A` `A=10xx5=50cm^2=50xx10^-4m^2`. (a) `tau_(max.)=IAB sin 90^@=12xx(50xx10^-4)xx03` `=18xx10^-2Nm` (b) Torque is zero when `sin theta=0` i.e. `theta=0^@` or `180^@` (c) Loop will be in stable equilibrium if `vecA` is parallel to `vecB` and in unstable equilibrium if `vecA` is antiparallel to `vecB`.

Discussion

178.	A uniform magnetic field of `3000G` is established along the positive z-direction. A rectangular loop of sides `10cm` and `5cm` carries a current `12A`. What is the torque on the loop in the different cases shown in the figure. What is the force on each case? Which case corresponds to stable equilibrium?
Answer» Here, `B=3000G=3000xx10^-4T=03T, A=10xx5=50cm^2=50xx10^-4m^2,I=12A` `:. IA=12xx50xx10^-4=060Am^2` (a) Here, `IvecA=006hatiAm^2`, `vecB=03hatkT` Now, torque, `vectau=vec(IA)xxvec(B)=006hatixx03hatk=-18xx10^-2hatjNm` i.e., Torque`=18xx10^-2Nm`. It acts along the negative y direction. (b) Here, `vec(IA)=006hatiAm^2`, `B=03hatkT` Torque, `tau=vec(IA)xxvec(B)=006hatixx03hatk=-18xx10^-2hatjNm` i.e. Torque `=18xx10^-2Nm`. It acts along the negative y-direction. (c) Here, `vec(IA)=-006hatjAm^2, vecB=03hatkT` Torque, `vec(IA)xxvecB=006hatjxx03hatk=-18xx10^-2hatiNm` i.e., Torque `=18xx10^-2Nm`. It acts along the negative x-direction. (d) Here, `IA=006Am^2`, `B=03` Torque, `\|vectau\|=IAB=006xx03T=18xx10^-2Nm` Here, direction of torque is `30^@+90^@=120^@` anticlockwise with negative x direction i.e. `240^@` with positive x-direction. (e) Here, `vec(IA)=006hatkAm^2, vecB=03hatkT` Torque, `vectau=IvecAxxvecB=006hatkxx03hatk=0` (f) Here, `vec(IA)=-006hatkAm^2, vecB=03hatkT` Torque, `vectau=IvecAxxvecB=-006hatkxx0*3hatk=0` The resultant force is zero in all cases. In case (e), `vecIA` and `vecB` are in the same direction, i.e., angle between them `theta=0^@`. Its equilibrium is stable because if loop is distributed a little from this position, it will restore its initial positio. In case (f), `vec(IA)` and `vecB` are in the opposite direction, i.e., angle between them `theta=180^@`. Its equilibrium is unstable because if loop is disturbed a little from this position, it will not restore to its initial position.

Discussion

179.	A coil wrapped around a toroid has inner radius of `15cm` and outer radius of `20cm`. If the toroid has `1000` turns of wire and carries a current of `12A`, find the maximum and minimum values of magnetic field within the toroid.
Answer» Here, `r_1=15cm=015m`, `r_2=20cm=020m`, `N=1000`, `I=12A` `B_(max)=mu_0(N)/(2pir_1)I=((4pixx10^-7)xx1000xx12)/(2pixx015)` `=16xx10^-2T` `B_(min)=mu_0(N)/(2pir_2)I=((4pixx10^-7)xx1000xx12)/(2pixx020)` `=12xx10^-2T`

Discussion

180.	A toroid has a core (non ferromagnetic material) of inner radius `25cm` and outer radius `26cm` around which 3500 turns of wire are wound. If the current in the wire is `11A`, what is the magnetic field (a) outside the toroid (b) inside the core of the toroid (c) in the empty space surrounded by the toroid?
Answer» Here, `r_1=025m`, `r_2=026m`, `N=3500`, `I=11A` (i) Outside the toroid, the magnetic field is zero. (ii) Inside the core of the toroid, the magnetic field induction is, `B=mu_0nI`, where n is the number of turns per unit length of toroid `=N//l`. Here, mean length of toroid, `l=2pi((r_1+r_2)/(2))=pi(r_1+r_2)=pi(025+026)=pixx051m` So `B=(mu_0NI)/(l)=((4pixx10^-7)xx3500xx11)/(pixx051)=3*02xx10^-2T` (iii) In the empty space surrounded by toroid, the magnetic field is zero.

Discussion

181.	A toroid has a core of inner radius `20cm` and outer radius `22cm` around which `4200` turns of a wire are wound. If the current in the wire is `10A`, what is the magnetic field (a) inside the core of toroid (b) outside the toroid (c) in the empty space surrounded by toroid?
Answer» Here, inner radius, `r_1=20cm`. Outer radius, `r_2=22cm`, `I=10A` `:.` Mean radius of toroid, `r=(r_1+r_2)/(2)=(20+22)/(2)=21cm=021m` Total length of toroid=circumference of toroid `=2pir=2pixx021` `=042pim` Total number of turns, `N=4200` `:.` Number of turns per unit length will be, `n=(4200)/(042pi)=(10000)/(pi)m^-1` (a) Magnetic field induction inside the core of toroid, `B=mu_0nI=4pixx10^-7x(10000)/(pi)xx10=0*04T` (b) Magnetic field induction outside the toroid is zero, since the field is only confined inside the core of the toroid on which winding has been made. (c) Magnetic field induction in the empty space surrounded by toroid is also zero.

Discussion

182.	A toroid has `2000` turns. The inner & outer radii of its core are `11cm` and `12cm` respectively. The magnetic field in the core for a current of `07A` is `25T`. What is relative permeability of core?
Answer» Correct Answer - `10269` Mean radius `=r=(11+12)/(2)=115cm` `=115xx10^-2m` `:.` No of turns/length `n=(N)/(2pir)=(2000)/(2pixx115xx10^-2)` As `B=munI`, where `B=25T` and `I=07A` `:. mu=(B)/(nI)=(25xx2pixx115xx10^-2)/(07xx2000)` `=1291xx10^-4TmA^-1` `mu_r=(mu)/(mu_0)=(1291xx10^-4)/(4pixx10^-7)=10269`

Discussion

183.	A circular coil of wire consisting of 100 turns, each of radius `80cm` carries a current of `040A`. What is the magnetude of the magnetic field `vecB` at the centre of the coil?
Answer» Here, `n=100`, `r=80xx10^-2m`, `I=040A`, `B=?` `B=(mu_0)/(4pi)(2pinI)/(r)=10^-7xx2xx(22)/(7)xx(100xx04)/(8xx10^-2)=31xx10^-4T`

Discussion

184.	A coil wrapped around a toroid has inner radius of `100cm` and an outer radius of `200cm`. If the wire wrapped makes 600 turns and carries a current of `10*0A`, what are the maximum and minimum values of magnetic field within the toroid?
Answer» Correct Answer - `12mT, 6mT` Here inner radius of toroid, `r_1=10xx10^-2m` Outer radius of toroid, `r_2=20xx10^-2m` `B_(max)=mu_0(N)/(2pir_1)I=((4pixx10^-7)xx600xx10)/(2pixx(10xx10^-2))` `=12xx10^-3T=12mT` `B_(min)=mu_0(N)/(2pir_2)I=((4pixx10^-7)xx600xx10)/(2pixx(20xx10^-2))` `=6xx10^-3T=6mT`

Discussion

185.	A current of `70A` is flowing in a plane circular coil of radius `10cm` having 100 turns. The coil is placed in a uniform magnetic field of `0*2Wb//m^2`. If the coil is free to rotate, what orientation would correspond to its (i) stable equilibrium and (ii) unstable equilibrium? Calculate potential energy of the coil in the two cases.
Answer» Here, `I=70A, r=10cm=10^-2m`, `N=100, B=02Wb//m^2` `M=NIA=Nipir^2` `=100xx70xx22/7(10^-2)^2=022Am^2` (i) Stable equilibrium corresponds to `theta=0^@` i.e. `vecM` parallel to `vecB`. `u_(min)=-MBcos 0^@=022xx02xx1` `=-0044J` (ii) unstable equilibrium corresponds to `vecM` antiparallel to `vecB`. P.E. is maximum `u_(max.)=-MB cos 180^@=-022xx02xx(-1)` `=0*044J`

Discussion

186.	A closely wound solenoid of 2000 turns and area of cross section `16xx10^-4m^2`, carrying a current of `40A` is suspended through its centre allowing it to turn in a horizontal plane. What is the magetic moment associated with the solenoid? What are the force and torque on the solenoid if a uniform horizontal field of `7*5xx10^-2T` is set up at an angle of `30^@` with the axis of the solenoid?
Answer» Correct Answer - `128Am^2`; `F=0`, `tau=0048Nm` Here, `N=2000`, `A=16xx10^-4m^2`, `I=40A` `M=NIA=2000xx40xx16xx10^-4` `=128Am^2` Net force experienced by the magnetic dipole in uniform horizontal field, `F=0` The magnitude of torque exerted by the magnetic field `vecB` on the solenoid is `tau=MBsintheta` `=128xx75xx10^-2xxsin30^@=0048Nm` The torque tends to align the axis of the solenoid, i.e., its magnetic moment `vecM` along the field `vecB`.

Discussion

187.	The straight long conductors AOB and COD are perpendicular to each other and carry current `i_(1)` and `i_(2)`. The magnitude of the magnetic induction at point P at a distance a from the point O in a direction perpendicular to the plane ACBD is A. `(mu_(0))/(2pia)(i_(1)+i_(2))`B. `(mu_(0))/(2pia)(i_(1)-i_(2))`C. `(mu_(0))(2pia)(i_(1)^(2)+i_(2)^(2))^(1//2)`D. `(mu_(0))/(2pia)(i_(1)i_(2))/((i_(1)+i_(2)))`
Answer» Correct Answer - C

Discussion

188.	A short conductor of length `50cm` is placed parallel to a long conductor of length `15cm` near its centre. The conductors carry currents `40A` and `30A` respectively in the same direction. What is the total force experienced by the long conductor, when they are `3*0cm` apart?
Answer» Correct Answer - `4xx10^-6N`; attractive Force on long conductor is equal and opposite to the force on small conductor `=(mu_0)/(4pi)(2I_1I_2l)/(r)` Here, `I_1=40A`, `I_2=30A`, `r=30xx10^-2m`, `l=50xx10^-2m`.

Discussion

189.	(a) A circular coil of 30 turns and radius `8.0cm`. Carrying a current of `6.0A` is suspended vertically in a uniform horizontal magnetic field of magnitude `1.0T`. The field lines make an angle of `60^@` with the normal to the coil. Calculate the magnitude of the counter torque that must be applied to prevent the coil from turning. (b) Would your answer change if the circular coil in (a) were replaced by a planar coil of some irregular shape that encloses the same area? (All other particulars are also unaltered).
Answer» Here, `n=30`, `I=6.0A`, `B=1.0T`, `alpha=60^@`, `r=8.0cm=8xx10^-2m`. `:.` Area of the coil, `A=pir^2=(22)/(7)xx(8xx10^-2)^2=2.01xx10^-2m^2` (a) Now, `tau=nIBA sin alpha=30xx6.0xx1.0xx(2.01xx10^-2)xxsin60^@` `=30xx6.0xx2.01xx10^-2xxsqrt3//2=3.133N-m` (b) Since the torque on the planar loop does not depend upon the shape, in case the area of the loop is the same, the torque will remain unchanged.

Discussion

190.	A solenoid `50cm` long has 4 layers of windings of `350` turns each. The radius of the lowest layer is `14cm`. If the current carried is `60A`, estimate the magnitude of magnetic flux density (i) near the centre of the solenoid on its axis, (ii) near the ends on its axis, (iii) outside the solenoid near its centre.
Answer» Here, `l=50cm=0.50m, r=1.4cm=1.4xx10^-2m, I=6.0A`, No. of turns per unit length, `n=(4xx350)/(0.50)=2800m^-1` (i) The magnitude of `vecB` near the centre of solenoid on the axis is `B=mu_0n I=4pixx10^-7xx2800xx6.0=2.11xx10^-2T` (ii) The magnitude of `vecB` near the end of solenoid on the axis is `B=(mu_0nI)/(2)=(2.11xx10^-2)/(2)=1.05xx10^-2T` (iii) Outside the solenoid, the magnetic field is negligibly small as compared to that inside the solenoid.

Discussion

191.	Two straight long conductors AOB and COD are perpendicular to each other and carry currents `I_1` and `I_2`. Find the magnitude of magnetic field induction at a point P at a distance a from the point O in a direction perpendicular to the plane ABCD
Answer» Correct Answer - `(mu_0)/(2pia)(I_1^2+I_2^2)^(1//2)` Magnetic field induction at P due to current through AOB and COD will be `B_1=(mu_0)/(4pi)(2I_1)/(a)` and `B_2=(mu_0)/(4pi)(2I_2)/(a)` Here `vecB_1` and `vecB_2` are perpendicular to each other. The magnitude of resultant magnetic field induction will be `B=sqrt(B_1^2+B_2^2)=[((mu_0)/(4pi)(2I_1)/(a))^2+((mu_0)/(4pi)(2I_2)/(a))^2]^(1//2)` `=(mu_0)/(2pia)(I_1^2+I_2^2)^(1//2)`

Discussion

192.	Two long and parallel straight wires A and B carrying currents of `80A` and `50A` in the same direction are separated by a distance of `4*0cm`. Estimate the force on a `10cm` section of wire A.
Answer» Here, `I_1=80A`, `I_2=50A`, `r=40xx10^-2m`, `l=10cm=01m`, `F=?` `F=(mu_0)/(4pi)(2I_1I_2)/(r)l=10^-7xx(2xx8xx5xx01)/((40xx10^-2))=2xx10^-5N` This force is attractive force normal to A towards B.

Discussion

193.	Two long parallel wires, AB and CD, carry equal currents in opposite directions. They lie in the x-y plane, parallel to the x-axis, and pass through the points (0,-a,0) and (0,a,0) respectively, Figure. The resultant magnetic field is: A. zero on the x-axisB. maximum on the x-axisC. directed along the z-axis at the origin, but not at other points on the z-axisD. directed along the z-axis at all points on the z-axis.
Answer» Correct Answer - B::D The magnetic field at a point on x-axis due to currents through AB and CD will be maximum, given by `B=B_1+B_2=(mu_0)/(4pi)(2I)/(a)+(mu_0)/(4pi)(2I)/(a)=(mu_0I)/(a)` acting along z-axis The resultant magnetic field will be directed along the z-axis at all points on the z-axis.

Discussion

194.	Two long wires carrying current `I_1` and `I_2` are arranged as shown in figure. The one carrying current `I_1` is along the x-axis. The other carrying current `I_2` is along a line parallel to the y-axis given by `x=0` and `z=d`. Find the force exerted at `O_2` because of the wire along the x-axis.
Answer» Magnetic field at point `O_2` due to current `I_1` in long wire along x-axis is `B_(O_2)=(mu_0)/(4pi)(2I)/(d)`, It will be acting along the y-axis. As second wire is along y-axis, so the angle between the directions of `I_2vecl` and `vecB_(O_2)` is zero, i.e., `theta=0^@`. Force on wire lying along y-axis is, `f=I_2\|veclxxvecB_(O_2)\|=I_2lB_(O_2)sin0^@=0`

Discussion

195.	Two long thin parallel conductors C and D of the shape as shown in figure. Carry currents `I_1` and `I_2`. The separation between the conductors is a, the width of the right hand conductor is equal to b. Both the conductors are lying in one plane. Find the magnetic interaction force between them reduced to a unit length.
Answer» Consider an elementary strip `dx` of conductor D at a distance x from conductor C. Mangnetic field induction at a point on this strip due to current through the conductor C is `B=(mu_0)/(4pi)(2I_1)/(x)` acting perpendicular to the plane, downwards Current through the elementary strip, `dI=(I_2dx)/(b)` Force on unit length of this elementary strip. `dF=dIxxdlBsin90^@` `:. dF=(I_2dx)/(b)xx1xx(mu_0)/(4pi)(2I_1)/(x)=(mu_0)/(4pi)(2I_1I_2)/(b)(dx)/(x)` Total force per unit length of interaction is `F=int dF=(mu_0)/(4pi)(2I_1I_2)/(b)int_(a)^((a+b))` `=(mu_0)/(4pi)(2I_1I_2)/(b)log_e(((a+b))/(a))`

Discussion

196.	Two straight wires A and B of lengths `10m` and `16m` and carrying currents `40A` and `50A` respectively in opposite directiions, lie parallel to each other `4*0cm` apart, Comute the force on a `10cm` long section of the wire B near its centre.
Answer» The magnitude of repulsive force per unit length on each wire is `F/l=(mu_0)/(4pi)(2I_1I_2)/(r)=10^-7xx(2xx40xx50)/((4xx10^-2))=10^-4Nm^-1` `:.` Force on a `10cm` length of the wire `B=10^-4xx0*1=10^-5N`

Discussion

197.	Two parallel wires P and Q placed distance r apart. They are carrying currents `I_1` and `I_2` where `I_1gtI_2`, but in opposite directions as shown in figure. Find the point on the line PQ where the resultant magnetic field is zero.
Answer» The resultant magnetic field will be zero at a point where the magnetic fields due to the currents in two wires are equal nad opposite. Such point R will lie to the right of Q at distance (x say) from Q. Magnetic field at point R due to current `I_1` is `B_1=(mu_0I_1)/(2pi(r+x))` It is acting downwards in the plane of paper. Magnetic field at point R due to current `I_2` is `B_2=(mu_0I)/(2pix)` It is acting upwards in the plane of paper. For zero magnetic field at R, `B_1=B_2` or `(mu_0I)/(2pi(r+x))=(mu_0I_2)/(2pix)` or `(I_1)/(r+x)=(I_2)/(x)` or `x=(I_2r)/(I_1-I_2)`

Discussion

198.	Figure shows two long parallel straight wires distance 5cm apart carrying currents `4A` and `10A` in opposite directions. Find the position of a point where the resultant magnetic field due to current in two wires in zero.
Answer» Correct Answer - `333cm` on the left hand side of wire X The resultant magnetic field will be zero at a point P on the left hand side of wire X. Let x be the distance of point P from wire x. Distance of point P from wire Y is (x+r). Magnetic field at P due to current in wire X is `B_1=(mu_0)/(4pi)(2I_1)/(x)=(10^-7xx2xx4)/(x)` acting perpendicular upwards. Magnetic field at P due to current in wire Y is `B_2=(mu_0)/(4pi)(2I_2)/((x+r))=(10^-7xx2xx10)/((x+5xx10^-2))` acting perpendicular downwards Resultant magnetic field will be zero at P if `B_1=B_2` or `(10^-7xx2xx4)/(x)=(10^-7xx2x10)/((x+5xx10^-2))` or `4/x=(10)/((x+5xx10^-2))` or `4x+20xx10^-2=10x` or `6x=20xx10^-2` or `x=(20xx10^-2)/(6)m=20/6cm=10/3cm=333cm`

Discussion

199.	Quite often, connecting wires carrying currents in opposite directions are twisted together in using electrical appliances. Explain how it avoids unwanted magnetic fields.
Answer» It is so because the magnetic field `vecB` at a point is a function of distance and direction of current. Twisting of wires eliminates the magnetic effects at a distant point because of the following reasons: (i) average distance is practically the same and (ii) current flows in the two wires in opposite directions.

Discussion

200.	Two free paralell wires carrying currents in opposite directionA. Attract each otherB. Repel each otherC. Neither attract nor repelD. Get rotated to be perpendicular to each other
Answer» Correct Answer - B

Discussion

Explore topic-wise InterviewSolutions in .

If the distance between two parallel current carrying wires is doubled, what is the force between them?

An `alpha`-particle of mass `6.65xx10^-27kg` is travelling at right angles to a magnetic field with a speed of `6xx10^5ms^-1`. The strength of the magnetic field is `0.2T`. Calculate the force on the `alpha`-particle and its acceleration.

Three long, straight and parallel wires are arranged as shown in Fig. The forces experienced by 10 cm length of wire Q is A. `1.4xx10^(-4)N` towardes the rightB. `1.4xx10^(-4)N` towards the leftC. `2.6xx10^(-4)N` to the rightD. `2.6xx10^(-4)N` to the left

Three long, straight parallel wires carrying current, are arranged as shown in figure. The force experienced by a `25cm` length of wire `C` is A. `10^(-3)N`B. `2.5xx10^(-3)N`C. ZeroD. `1.5xx10^(-3)N`

An electron in an atom revolves around the nucleus in an orbit of radius `053Å`. Calculate the equivalent magnetic moment, if the frequency of revolution of electron is `68xx10^9MHz`.

What is the basic principle of working of cyclotron? Write two uses of this machine.

A body is suspended from the lower end of a vertical spring. What shall be the effect on the position of the body when a current is sent through the spring? Does it depend upon the direction of current in the spring?

Particles having positive charges occasionally come with high velocity from the sky towards the earth. On account of the magnetic field of earth, they would be deflected towards theA. NorthB. SouthC. EastD. West

An electron entres a magnetic field whose direction is perpendicualr to the velocity of the electron. ThenA. The speed of the electron will increaseB. The speed of the electron will decreaseC. The speed of the electron will remain the sameD. The velocity of the electron will remain the same

An electron is moving along positive x-axis `A` unifrom electric filed exists to wards negative y-axis. What should be the direaction of magnetic field of suitable magnitude so that net force of electrons is zero .A. positivez-axisB. negative z-axisC. positivey-axisD. negative y-axis

The scale of galvanometer is divided into `150` equal divisions. The galvanometer has a current sensitivity of `10"divisions"//mA` and the voltage sensitivity of `2"divisions"//mV`. How the galvanometer be designed to read (i) 6A per division and (ii) 1 V per division?

A magnetising field of `1500 A//m` produces a flux of `24xx10^-5` weber in a bar of iron of cross-sectional area `05cm^2`. Calculate the permeability and susceptibility of the iron bar used.

Individual atoms/molecules/ions of a diamagnetic substance………….any net………………..on their own.

If the magnetising field on a ferromagnetic material is increased, its permeability isA. decreasedB. increasedC. is unaffectedD. may be increased or decreased

Units of magnetising intensity and intensity of magnetisation are…………………., i.e., ………………… .

Name the cgs unit of magnetising intensity. How is it related to SI unit of intensity.

A charged paricle goes undeflected in a region containing electric and magnetic field. It is possible thatA. `vecE||vecB` but `vecv` is not parallel to `vecE`B. `vecv||vecB` but `vecE` is not parallel to `vecB`C. `vecE||vecB`, `vecv||vecE`D. `vecE` is not parallel to `vecB` and `vecv`.

A planar loop of irregular shape encloses an area of `7*5xx10^-4m^2`, and carries a current of `12A`. The sense of flow of current appears to be clockwise to an observer. What is the magnitude and direction of the magnetic moment vector associated with the current loop?

A coil wrapped around a toroid has inner radius of `15cm` and outer radius of `20cm`. If the toroid has `1000` turns of wire and carries a current of `12A`, find the maximum and minimum values of magnetic field within the toroid.

A toroid has a core of inner radius `20cm` and outer radius `22cm` around which `4200` turns of a wire are wound. If the current in the wire is `10A`, what is the magnetic field (a) inside the core of toroid (b) outside the toroid (c) in the empty space surrounded by toroid?

A toroid has `2000` turns. The inner & outer radii of its core are `11cm` and `12cm` respectively. The magnetic field in the core for a current of `07A` is `25T`. What is relative permeability of core?

A circular coil of wire consisting of 100 turns, each of radius `80cm` carries a current of `040A`. What is the magnetude of the magnetic field `vecB` at the centre of the coil?

A coil wrapped around a toroid has inner radius of `100cm` and an outer radius of `200cm`. If the wire wrapped makes 600 turns and carries a current of `10*0A`, what are the maximum and minimum values of magnetic field within the toroid?

A short conductor of length `50cm` is placed parallel to a long conductor of length `15cm` near its centre. The conductors carry currents `40A` and `30A` respectively in the same direction. What is the total force experienced by the long conductor, when they are `3*0cm` apart?

Two straight long conductors AOB and COD are perpendicular to each other and carry currents `I_1` and `I_2`. Find the magnitude of magnetic field induction at a point P at a distance a from the point O in a direction perpendicular to the plane ABCD

Two long and parallel straight wires A and B carrying currents of `80A` and `50A` in the same direction are separated by a distance of `4*0cm`. Estimate the force on a `10cm` section of wire A.

Two long wires carrying current `I_1` and `I_2` are arranged as shown in figure. The one carrying current `I_1` is along the x-axis. The other carrying current `I_2` is along a line parallel to the y-axis given by `x=0` and `z=d`. Find the force exerted at `O_2` because of the wire along the x-axis.

Two straight wires A and B of lengths `10m` and `16m` and carrying currents `40A` and `50A` respectively in opposite directiions, lie parallel to each other `4*0cm` apart, Comute the force on a `10cm` long section of the wire B near its centre.

Two parallel wires P and Q placed distance r apart. They are carrying currents `I_1` and `I_2` where `I_1gtI_2`, but in opposite directions as shown in figure. Find the point on the line PQ where the resultant magnetic field is zero.

Figure shows two long parallel straight wires distance 5cm apart carrying currents `4A` and `10A` in opposite directions. Find the position of a point where the resultant magnetic field due to current in two wires in zero.

Quite often, connecting wires carrying currents in opposite directions are twisted together in using electrical appliances. Explain how it avoids unwanted magnetic fields.

Two free paralell wires carrying currents in opposite directionA. Attract each otherB. Repel each otherC. Neither attract nor repelD. Get rotated to be perpendicular to each other

Explore topic-wise InterviewSolutions in .

If the distance between two parallel current carrying wires is doubled, what is the force between them?

An `alpha`-particle of mass `6.65xx10^-27kg` is travelling at right angles to a magnetic field with a speed of `6xx10^5ms^-1`. The strength of the magnetic field is `0.2T`. Calculate the force on the `alpha`-particle and its acceleration.

Three long, straight and parallel wires are arranged as shown in Fig. The forces experienced by 10 cm length of wire Q is A. `1.4xx10^(-4)N` towardes the rightB. `1.4xx10^(-4)N` towards the leftC. `2.6xx10^(-4)N` to the rightD. `2.6xx10^(-4)N` to the left

Three long, straight parallel wires carrying current, are arranged as shown in figure. The force experienced by a `25cm` length of wire `C` is A. `10^(-3)N`B. `2.5xx10^(-3)N`C. ZeroD. `1.5xx10^(-3)N`

An electron in an atom revolves around the nucleus in an orbit of radius `0*53Å`. Calculate the equivalent magnetic moment, if the frequency of revolution of electron is `6*8xx10^9MHz`.

What is the basic principle of working of cyclotron? Write two uses of this machine.

A body is suspended from the lower end of a vertical spring. What shall be the effect on the position of the body when a current is sent through the spring? Does it depend upon the direction of current in the spring?

Particles having positive charges occasionally come with high velocity from the sky towards the earth. On account of the magnetic field of earth, they would be deflected towards theA. NorthB. SouthC. EastD. West

An electron entres a magnetic field whose direction is perpendicualr to the velocity of the electron. ThenA. The speed of the electron will increaseB. The speed of the electron will decreaseC. The speed of the electron will remain the sameD. The velocity of the electron will remain the same

An electron is moving along positive x-axis `A` unifrom electric filed exists to wards negative y-axis. What should be the direaction of magnetic field of suitable magnitude so that net force of electrons is zero .A. positivez-axisB. negative z-axisC. positivey-axisD. negative y-axis

The scale of galvanometer is divided into `150` equal divisions. The galvanometer has a current sensitivity of `10"divisions"//mA` and the voltage sensitivity of `2"divisions"//mV`. How the galvanometer be designed to read (i) 6A per division and (ii) 1 V per division?

A magnetising field of `1500 A//m` produces a flux of `2*4xx10^-5` weber in a bar of iron of cross-sectional area `0*5cm^2`. Calculate the permeability and susceptibility of the iron bar used.

Individual atoms/molecules/ions of a diamagnetic substance………….any net………………..on their own.

If the magnetising field on a ferromagnetic material is increased, its permeability isA. decreasedB. increasedC. is unaffectedD. may be increased or decreased

Units of magnetising intensity and intensity of magnetisation are…………………., i.e., ………………… .

Name the cgs unit of magnetising intensity. How is it related to SI unit of intensity.

A charged paricle goes undeflected in a region containing electric and magnetic field. It is possible thatA. `vecE||vecB` but `vecv` is not parallel to `vecE`B. `vecv||vecB` but `vecE` is not parallel to `vecB`C. `vecE||vecB`, `vecv||vecE`D. `vecE` is not parallel to `vecB` and `vecv`.

A planar loop of irregular shape encloses an area of `7*5xx10^-4m^2`, and carries a current of `12A`. The sense of flow of current appears to be clockwise to an observer. What is the magnitude and direction of the magnetic moment vector associated with the current loop?

A coil wrapped around a toroid has inner radius of `15cm` and outer radius of `20cm`. If the toroid has `1000` turns of wire and carries a current of `12A`, find the maximum and minimum values of magnetic field within the toroid.

A toroid has a core of inner radius `20cm` and outer radius `22cm` around which `4200` turns of a wire are wound. If the current in the wire is `10A`, what is the magnetic field (a) inside the core of toroid (b) outside the toroid (c) in the empty space surrounded by toroid?

A toroid has `2000` turns. The inner & outer radii of its core are `11cm` and `12cm` respectively. The magnetic field in the core for a current of `0*7A` is `2*5T`. What is relative permeability of core?

A circular coil of wire consisting of 100 turns, each of radius `8*0cm` carries a current of `0*40A`. What is the magnetude of the magnetic field `vecB` at the centre of the coil?

A coil wrapped around a toroid has inner radius of `10*0cm` and an outer radius of `20*0cm`. If the wire wrapped makes 600 turns and carries a current of `10*0A`, what are the maximum and minimum values of magnetic field within the toroid?

A short conductor of length `5*0cm` is placed parallel to a long conductor of length `1*5cm` near its centre. The conductors carry currents `4*0A` and `3*0A` respectively in the same direction. What is the total force experienced by the long conductor, when they are `3*0cm` apart?

Two straight long conductors AOB and COD are perpendicular to each other and carry currents `I_1` and `I_2`. Find the magnitude of magnetic field induction at a point P at a distance a from the point O in a direction perpendicular to the plane ABCD

Two long and parallel straight wires A and B carrying currents of `8*0A` and `5*0A` in the same direction are separated by a distance of `4*0cm`. Estimate the force on a `10cm` section of wire A.

Two straight wires A and B of lengths `10m` and `16m` and carrying currents `4*0A` and `5*0A` respectively in opposite directiions, lie parallel to each other `4*0cm` apart, Comute the force on a `10cm` long section of the wire B near its centre.

Two parallel wires P and Q placed distance r apart. They are carrying currents `I_1` and `I_2` where `I_1gtI_2`, but in opposite directions as shown in figure. Find the point on the line PQ where the resultant magnetic field is zero.

Figure shows two long parallel straight wires distance 5cm apart carrying currents `4A` and `10A` in opposite directions. Find the position of a point where the resultant magnetic field due to current in two wires in zero.

Quite often, connecting wires carrying currents in opposite directions are twisted together in using electrical appliances. Explain how it avoids unwanted magnetic fields.

Two free paralell wires carrying currents in opposite directionA. Attract each otherB. Repel each otherC. Neither attract nor repelD. Get rotated to be perpendicular to each other

An electron in an atom revolves around the nucleus in an orbit of radius `053Å`. Calculate the equivalent magnetic moment, if the frequency of revolution of electron is `68xx10^9MHz`.

A magnetising field of `1500 A//m` produces a flux of `24xx10^-5` weber in a bar of iron of cross-sectional area `05cm^2`. Calculate the permeability and susceptibility of the iron bar used.

A toroid has `2000` turns. The inner & outer radii of its core are `11cm` and `12cm` respectively. The magnetic field in the core for a current of `07A` is `25T`. What is relative permeability of core?

A circular coil of wire consisting of 100 turns, each of radius `80cm` carries a current of `040A`. What is the magnetude of the magnetic field `vecB` at the centre of the coil?

A coil wrapped around a toroid has inner radius of `100cm` and an outer radius of `200cm`. If the wire wrapped makes 600 turns and carries a current of `10*0A`, what are the maximum and minimum values of magnetic field within the toroid?

A short conductor of length `50cm` is placed parallel to a long conductor of length `15cm` near its centre. The conductors carry currents `40A` and `30A` respectively in the same direction. What is the total force experienced by the long conductor, when they are `3*0cm` apart?

Two long and parallel straight wires A and B carrying currents of `80A` and `50A` in the same direction are separated by a distance of `4*0cm`. Estimate the force on a `10cm` section of wire A.

Two straight wires A and B of lengths `10m` and `16m` and carrying currents `40A` and `50A` respectively in opposite directiions, lie parallel to each other `4*0cm` apart, Comute the force on a `10cm` long section of the wire B near its centre.