1638 + Interview Questions in ELECTROSTATICS IN GENERAL AWARENESS Page 1 InterviewSolution

1.	Two spherical , noncoducting and very tin shells of unifromly distributed jpositive charge `Q` and radiuy d are located a distance ` 10d` from each other . A positive point charge q is placed inside one of the shells at a dustabce ` d//2` from the center, on the line connecting the centers of the two shells , as shown in the figure, What is the net force on the charge `q` ? . A. ` (qQ)/(3 61 pi varepsilon_0 d^2) ` to the leftB. `(qQ)/(36 1 pi varepsilon_0 pi d^2) ` to the rightC. ` ( 362qQ)/(36 1 pi varepsilon_0d^2)` to the leftD. `(36 0qQ)/(36 1 pi varepsilon_0d^2)` to the right
Answer» Correct Answer - A Field at `q` will be due to second spherical shall ` F=qE` `=q xx 1/(4 pi in_0) Q/( 10d -d/2)^2` ` vec F = (qQ)/(36 1 pi in_0d^2)` towatds left.

Discussion

2.	A hollow metal sphere of radius ` 5 cm` is charged such that the potential on its surcace is ` 10V`. The potential at the centre of the centre of the sphere is -A. ` 0 V`B. ` 10 V`C. same as at point ` 5 cm` away from the surface out side sphereD. same as a point ` 25` cm away from the surface
Answer» Correct Answer - B Since there is no electric field inside the inner sphere so potential will remain ` 10V`.

Discussion

3.	A hollow metal sphere of radius 5 cm is charged such that the potential on its surface is `10V`. The potential at the distance `3 cm` from the centre of the sphere is:A. zeroB. 10 VC. same as at a point 5 cm away from the surfaceD. same as at a point 25 cm away from the surface
Answer» Correct Answer - B

Discussion

4.	A hollow metal sphere of radius ` 5 cm` is charged such that the potential on its surface is ` 10V`. The potential at the center of the sphere is -
Answer» 10V, since electric potential si same at all points inside the hollow sphere and at the surface of the sphere.

Discussion

5.	The electric field in the region between two concentric charged spherical shells- (a) is zero (b) increases with distance from centre (c) is constant (d) decreases with distance from centre
Answer» (d) decreases with distance from centre

Discussion

6.	A hollow metallic sphere of radius 10 cm is given a charge of `3.2 xx 10^(-9) C.` The electric intensity at a point 4 cm from the center isA. `9xx10^(-9)NC^(-1)`B. `"288 NC"^(-1)`C. `"2.88 NC"^(-1)`D. zero
Answer» Correct Answer - D Inside the sphere at any point, E = 0 .

Discussion

7.	A hollow metal sphere of radius 10 cm is charged such that the potential on its surface is 80 V. The potential at the centre of the sphere is-(a) 800 V (b) zero (c) 8 V(d) 80 V
Answer» Correct answer is (d) 80 V

Discussion

8.	A hollow metal sphere of radius 10cm is charged such that the potential on its surface is 80 V. The potential at the centre of the sphere isA. zeroB. `80 V`C. `800 V`D. `8V`
Answer» Correct Answer - B

Discussion

9.	The electric field strength in air at NTP is `3 xx 10^(6)V//m`. The maximum charge that can be given to a spherical conductor of radius 3m isA. `3xx 10^(4)C`B. `3 xx 10^(-3)C`C. `3 xx 10^(-2)C`D. `3 xx 10^(-1)C`
Answer» Correct Answer - B

Discussion

10.	Two spherical conductors A and B of radii 1mm and 2mm are separated by a distance of 5 cm and are uniformly charged. If the spheres are connected by a conducting wire then in equilibrium condition, the ratio of the magnitude of the electric fields at the surfaces of spheres A and B isA. `4 :1`B. `1:2`C. `2:1`D. `1:4`
Answer» Correct Answer - A

Discussion

11.	A charge q is placed at the centre of the line joining two equal charges Q. The system of the three charges will be in equilibrium if q is equal to:A. `Q//4`B. `-Q//4`C. `-Q//8`D. `Q//8`
Answer» Correct Answer - B For equilibrium net force must be zero `i.e." "1/(4piin_(0))(Qq)/((r//2)^(2))+1/(4piin_(0))(Q Q)/r^(2)=0` `therefore" "q=(-Q)/4`

Discussion

12.	A charge q is placed at the centre of the line joining two equal charges Q. The system of the three charges will be in equilibrium if q is equal to:A. `-4Q`B. `-(Q)/(4)`C. `-(Q)/(2)`D. `+(Q)/(2)`
Answer» Correct Answer - B For equilibrium, net force on q = 0 `therefore" "(kqQ)/((2x)^(2))+(kqQ)/(x^(2))=0` `therefore" "q=-Q//4`

Discussion

13.	A solid conducting sphere having a charge Q is surrounded by an uncharged concentric conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given a charge of `-3Q`, the new potential difference between the same two surfaces is :A. (a) VB. (b) 2VC. (c) 4VD. (d) `-2V`
Answer» Correct Answer - A The potential inside the shell will be the same everywhere as on its surface. As we added `-3Q` charge on the surface, the potential on the surface changes by the same amount as that inside. Therefore the potential difference remains the same.

Discussion

14.	A conducting shell `S_1` having a charge Q is surrounded by an uncharged concentric conducting spherical shell `S_2`. Let the potential difference between `S_1` and that `S_2` be V. If the shell `S_2` is now given a charge `-3Q`, the new potential difference between the same two shells isA. `V`B. `2V`C. `4V`D. `-2V`
Answer» Correct Answer - A According to principle of generator `PD` in this case only depends on the charge on inner shell.

Discussion

15.	Two horizontal parallel conducting plates are kept at a separation `d = 1.5 xx 10^(-2) m` apart one above the other in air as shown in figure. The upper plate is maintained at a positive potential of `1.5 kV`while the other plate is earthed which maintains it at zero potential. Calculate the number of electrons which must be attached to a small oil drop of mass `m =4.9 xx 10^(-15) kg` between the plates to maintain it at rest. Consider density of air is negligible in comparison with that ofoil. If the potential of above plate is suddenly changed to `-l .5kV`, what will be the initial acceleration of the charged drop? Also calculate the terminal velocity of the drop if its radius is `r= 5.0 xx 10^(-6)m` and the coefficient of viscosity of air is `eta = 1.8 x 10--5 N-s//m^(2) [3,2g, 5.7 xx 10^(-5) m//s^(2)]`
Answer» Correct Answer - [3,20`m//s^(2),5.7xx10^(-5)m//s`]

Discussion

16.	A small cork ball A of mass m is suspended by a thread of length I. Another ball B is fixed at a distance I from point of suspension and distance l/2 from thread when is vertical, as shown in figure-1.444. Balls A and B have charges (+ q) each. Ball A is held by an external force such that the thread remains vertical. When ball A is released from rest, thread deflects through a . maximum angle of `beta = 30^(@)`, calculate m in terms of other parameters
Answer» Correct Answer - `[(q^(2))/(2piepsi_(0)gl^(2))((1-sqrt(2-sqrt(3))))/((2-sqrt(3))^(3//2))]`

Discussion

17.	Two small spherical shells a and B are given positive charges of 9 C and 4 C respectively and placed such that their centres are separated by 10 m. If P is a point in between them, where the electric field intensity is zero, then the distance of the point P from the centre of A isA. 5 mB. 6 mC. 7mD. 8 m
Answer» Correct Answer - B

Discussion

18.	An elderly woman went alone to Registrar's office to disburse her property. When she inquired in the office she was asked to get a xerox copy of the document which works under electrostatic induction. The xerox shop was far away and across the road. She took the help of a passer-by and got her xerox done.(a) What values did the passer-by have ?(b) How does a neutral body get charged by electrostatic induction ?
Answer» (a) Helping, sharing and respect for elderly people. (b) For a body to get positively charged, a negatively charged body has to be brought close to the neutral body which after earthing gets charged uniformly.

18.

An elderly woman went alone to Registrar's office to disburse her property. When she inquired in the office she was asked to get a xerox copy of the document which works under electrostatic induction. The xerox shop was far away and across the road. She took the help of a passer-by and got her xerox done.(a) What values did the passer-by have ?(b) How does a neutral body get charged by electrostatic induction ?

Answer»

(a) Helping, sharing and respect for elderly people.

(b) For a body to get positively charged, a negatively charged body has to be brought close to the neutral body which after earthing gets charged uniformly.

Discussion

19.	While travelling back to his residence in car, Dr Pathak was caught up in a thunderstorm. It became very dark. He stopped driving the car and waited for the thunderstorm to stop. Suddenly he noticed a child walking alone on the road. He asked the boy to come inside the car till the thunderstorm stopped. Dr. Pathak dropped the boy at his residence. The boy insisted that Dr. Pathak should meet his parents. The parents expressed their gratitude to Dr. Pathak for his concern for safety of the child. Answer the following questions based on the above information : (a) Why is it safer to sit inside a car during a thunderstorm ? (b) Which two values are displayed by Dr. Pathak in his actions ? (c) Which values are reflected in parent's response to Dr. Pathak ? (d) Give an example of a similar action on your part in the past from everyday life.
Answer» (a) Because during a thunderstorm, a car would act as an electrostatic shield. (Dr. Pathak displayed the values of safety of human life, helpfulness, empathy and scientific emper. (or any other two relevant values) (c) Gratefulness, indebtedness.(or any other relevant values) (d) I once came across a situation where a puppy was struck in the middle f a busy road during rain and was not able to cross due to heavy flow, so I quickly rushed and helped him.

19.

While travelling back to his residence in car, Dr Pathak was caught up in a thunderstorm. It became very dark. He stopped driving the car and waited for the thunderstorm to stop. Suddenly he noticed a child walking alone on the road. He asked the boy to come inside the car till the thunderstorm stopped. Dr. Pathak dropped the boy at his residence. The boy insisted that Dr. Pathak should meet his parents. The parents expressed their gratitude to Dr. Pathak for his concern for safety of the child. Answer the following questions based on the above information : (a) Why is it safer to sit inside a car during a thunderstorm ? (b) Which two values are displayed by Dr. Pathak in his actions ? (c) Which values are reflected in parent's response to Dr. Pathak ? (d) Give an example of a similar action on your part in the past from everyday life.

Answer»

(a) Because during a thunderstorm, a car would act as an electrostatic shield.

(Dr. Pathak displayed the values of safety of human life, helpfulness, empathy and scientific emper. (or any other two relevant values)

(c) Gratefulness, indebtedness.(or any other relevant values)

(d) I once came across a situation where a puppy was struck in the middle f a busy road during rain and was not able to cross due to heavy flow, so I quickly rushed and helped him.

Discussion

20.	Arun had to repaint his car when he was reminded by the car company for his regular car service. He told them to do spray painting of mountain dew colour. The company also replied that they usually perform spray painting only as wastage is minimized and (even) painting uniform is achieved. (a) What values did the car service company have ? (b) If spray painting is done by electrostatic induction, how is even painting achieved ?
Answer» (a) Customer care, commitment, concern and truthfulness. (b) The droplets of paint are charged particles which get attracted to any metallic objects by electrostatic forces.

20.

Arun had to repaint his car when he was reminded by the car company for his regular car service. He told them to do spray painting of mountain dew colour. The company also replied that they usually perform spray painting only as wastage is minimized and (even) painting uniform is achieved. (a) What values did the car service company have ? (b) If spray painting is done by electrostatic induction, how is even painting achieved ?

Answer»

(a) Customer care, commitment, concern and truthfulness.

(b) The droplets of paint are charged particles which get attracted to any metallic objects by electrostatic forces.

Discussion

21.	'A and 'B'are two students in a class who have been assigned to organize Republic Day function. They have also been instructed to invite personally more than 60 members from all the nearby cultural organizations and VIPs in their area. While student A arranged invitations using a photocopy/fax, student 'B' arranges invitations by writing to them individually.(a) Which student's method would you adopt and why ?(b) State the principle behind the source used by student 'A'.
Answer» (a) Student A because, he is aware of the latest technology and its applications. (b) Electrostatic force.

21.

'A and 'B'are two students in a class who have been assigned to organize Republic Day function. They have also been instructed to invite personally more than 60 members from all the nearby cultural organizations and VIPs in their area. While student A arranged invitations using a photocopy/fax, student 'B' arranges invitations by writing to them individually.(a) Which student's method would you adopt and why ?(b) State the principle behind the source used by student 'A'.

Answer»

(a) Student A because, he is aware of the latest technology and its applications.

(b) Electrostatic force.

Discussion

22.	A thread having linear charge density `lamda` is in the shape of a circular arc of radius R subtending an angle `theta` at the centre. (a). Find the electric field at the centre. (b). Using the epression obtained in part (a) find the field at the centre if the thread were emicircular (c). Find the field at centre using the expression obtained in part (a) for the case `thetato`0. Is the result justified? (d). A thread having total charge Q (uniformly distributed is in the shape of a circular arc of radius R subtending an angle `theta` at centre. write the expression for the field at the center. Obtain the field when` thetato0`. Make sure you understand the difference in case. (c) and (d).
Answer» Correct Answer - (a). `E=(2Klamda)/(R)sin((theta)/(2))` (b). `E=(2Klamda)/(R)` (c) `E=0` (d). `E=(KQ)/(R^(2))`

Discussion

23.	Electric charges `q, q, –2q` are placed at the corners of an equilateral triangle ABC of side l. The magnitude of electric dipole moment of the system isA. `ql`B. `2ql`C. `sqrt(3ql)`D. `4ql`
Answer» Correct Answer - C

Discussion

24.	Charges `+2Q` and `-Q` are placed as shown in figure. The point at which electric field intensity is zero, will be A. Somewhere between `-Q and +2Q`B. somewher on the left of `-Q`C. somewhere on the right of `+2Q`D. somewhere on the right bisector of line joining `-q` and `+2Q`
Answer» Correct Answer - B Electric field between `-Q` and `+2Q` is added due to both the charges. The point near to `-Q` and on left of it can have zero field for a large distance.

Discussion

25.	`100` capacitors each having a capacity of `10 muF` are connected in parallel and are charged by a potential difference of `100 kV`. The energy stored in the capacitors and the cost of charging them, if electrical energy costs `108` paise per `kWh`, will beA. `10^(7)` and 300 paiseB. `5xx10^(6)J` and 300 paiseC. `5xx10^(6)J` and 150 paiseD. `10^(7)J` and 750 paise
Answer» Correct Answer - C Equivalence capacitance of n. Capacitor in parallel, `C=nc_(1)=100xx10muF =1000muF=10^(-3)F` Energy stored, `U=(1)/(2)CV^(2)=(1)/(2)xx10^(-3)xx(10^(5))^(2)` `=5xx10^(8)J=(5xx10^(6))/(3.6xx10^(6))kWJ` Net cost `=(5xx10^(6))/(3.6xx10^(6))xx10^(6)="150 paise"`

Discussion

26.	A circuit is shown in figure for which `C_(1)=(3pm 0.011)muF, C_(2)=(5pm 0.01)muF and C_(3)=(1pm 0.01)muF.` If C is the equivalent capacitance across AB, then C is given by A. `(0.9 pm 0.114)muF`B. `(0.9 pm 0.01)muF`C. `(0.9 mu 0.023)muF`D. `(0.9 mu 0.09) muF`
Answer» Correct Answer - C The capacitor `C_(2)` is shorted, so it is not playing any role in circuit and can be removed. The 3 capacitors each of `C_(1)` are connected in parallel and this is connected to `C_(3)` in series. `C_(eq)=(3C_(1)C_(3))/(3C_(1)+C_(3))=C` `=(3xx3xx1)/(3xx3+1)=0.9muF` So,`" "(DeltaC)/(C)=(3DeltaC_(1))/(C_(1))+(DeltaC_(3))/(C_(3))+(3DeltaC_(1)+DeltaC_(3))/(3C_(1)+C_(3))` [For computaion of errors worst has to be taken] `rArr" "(DeltaC)/(0.9)=(3xx0.011)/(3)+(0.01)/(1)+((0.033+0.01))/(10)` `rArr" "DeltaC=pm 0.023muF`

Discussion

27.	A charged particle having a charge of `-2.0 xx 10^(-6) C` is placed close to a non-conducting plate having a surface charge density `4.0 xx 10^(-6) C m^(-2)`. Find the force of attraction between the particle and the plate.
Answer» Correct Answer - `0.45 N` Here, `q = -2xx10^(-6) C, sigma = 4xx10^(-6) Cm^(-2)` Field of attraction between the charged particle and the plate, `F = qE = (sigma q)/(2 in_(0)) = (4xx10^(-6) xx2xx10^(-6))/(2xx8.845xx10^(-12))` `= 0.45 N`

Discussion

28.	An infinite line charge produces a field of `9xx10^(-4)N" "C^(-1)` at a distance of 2 cm. calculate the linear charge density.A. `10^(-3)Cm^(2)`B. `10^(-4)Cm^(2)`C. `10^(-5)Cm^(2)`D. `10^(-7)Cm^(2)`
Answer» Correct Answer - D Let `lambda` be the linear charge density. Electric field due to infinite line charge, `E=(lambda)/(2pi epsilon_(0)r)`. Dividing and multiplying by 2 to get `(1)/(4pi epsilon_(0))`, because we have the value of `(1)/(4pi epsilon)` `rArr" "E=(2)/(2)xx(lambda)/(2pi epsilon_(0)r)=(2lambda)/(4pi epsilon_(0)r)` Putting the values, we get `9xx10^(4)=(2xx9xx10^(9)xxlambda)/(2xx10^(-2))` `therefore" Linear charge density, "lambda=(9xx10^(4)xx2xx10^(-2))/(2xx9xx10^(9))` `=10^(-7)Cm^(-1)` Thus, the linear charge density is `10^(-7)Cm^(-1).`

Discussion

29.	An infinite line charge produces a field of `9xx10^(4) NC` at a distance of 2cm. Calculate the linear charge density.A. `2 xx 10^(-7) C//m`B. `10^(-8) C//m`C. `10^(7) C//m`D. `10^(-4) C//m`
Answer» Correct Answer - A

Discussion

30.	An infinite line charge produces a field of `9xx10^(4) NC^(-1)` at a distance of `4 cm`. Calculate the linear charge density.
Answer» Correct Answer - `2xx10^(-7) cm^(-1)` Here, `E = 9xx10^(4) NC^(-1), r = 4 cm = 4xx10^(-2)m` `lambda = ?` As `E = (lambda)/(2pi in_(0) r)` `:. lambda = 2pi in_(0) r E = 4pi in_(0) (r )/(2) E` `= (1)/(9xx10^(9)) xx (4xx10^(-2))/(2) xx 9xx10^(4)` `E = 2xx10^(-7) Cm^(-1)`

Discussion

31.	To what potential, must we charge an insulated sphere of radius 14 cm so that its surface charge density of `1 muC m^(-2)` ?
Answer» Here `V = ?, r = 14 cm = 14xx10^(-2) m ` `sigma = 1 muC m^(-2) = 10^(-6) Cm^(-2)` `V = (q)/(4pi in_(0) r) = (1)/(4 pi in_(0)) ((sigma.4 pi r^(2))/(r ))` `= (1)/(4pi in_(0)) (4pi r sigma)` `=9xx10^(9)xx4xx(22)/(7)xx14xx10^(-2)xx10^(-6)` `V = 15840 v`

Discussion

32.	An infinite line charge produce a field of `7.182xx10^(8)NC^(-1)` at a distance of 2 cm. The linear charge density isA. `7.27xx10^(-4)Cm^(-1)`B. `7.98xx10^(-4)Cm^(-1)`C. `7.11xx10^(-4)Cm^(-1)`D. `7.04xx10^(-4)Cm^(-1)`
Answer» Correct Answer - B Electric field intensity due to infinite line charge is `E=(lambda)/(2pi epsilon_(0)r)` `rArr "The linear charge density, "lambda=2pi epsilon_(0)rE=(2xx2pi epsilon_(0)rE)/(2)` `=(2xx10^(-2)xx7.182xx10^(8))/(2xx9xx10^(9))=7.98xx10^(-4)"Cm"^(-1)`.

Discussion

33.	To what potential we must charge an insulate sphere of radius 14 cm, so that the surface charge density is equal to `2 muC m^(-2)` ?
Answer» Correct Answer - 31680 V Here `r = 14 cm = 14xx10^(-2) m`, `sigma = 2 muC m^(-2) = 2xx10^(-6) Cm^(-2)` `:. V = (1)/(4pi in_(0)) (q)/(r ) = (1)/(4pi in_(0)) (4pi r^(2) sigma)/(r ) = (4pi r sigma)/(4pi in_(0))` `= 9xx10^(9)xx4xx (22)/(7) xx14xx10^(-2)xx2xx10^(-6)` = 31680 V

Discussion

34.	Unit of electric flux isA. VmB. N-m/CC. V/mD. C/N-m
Answer» Correct Answer - A The electric flux through an element is `dphi_(E)=(dS)(E cos theta)` `=E ds cos theta =E.dS` Hence, `" "phi_(E)=E.S=(V)/(d).S` `therefore" Unit of "phi_(E)=("volt"xx"metre"^(2))/("metre")="volt-metre"`

Discussion

35.	A parallel plate condenser has a capacitance `50 muF` in air and `100 muF` when immersed in an oil. The dielectric constant `k` of the oil isA. 0.2B. 1.5C. 2.2D. 2.5
Answer» Correct Answer - C `C_(m)=C_("air")xxk` `therefore" "k=C_(m)/C_("air")=110/50=2.2`

Discussion

36.	Find out electric field intensity at point A (0, 1m, 2m) due to a point charge `-20 muC` situated at point `B (sqrt(2)m, 0, 1m)`.
Answer» `E=(KQ)/(\|vec(r)\|^(3))vec(r)=(KQ)/(\|vec(r)\|^(2))vec(r) implies vec(r)=P.V.` of `A-P.V.` of B (P.V. = Position vector) `=(-sqrt(2)hat(i)+hat(j)+hat(k))\|vec(r)\|=sqrt((sqrt(2))^(2)+(1)^(2)+(1)^(2))=2` `E=(9xx10^(9)xx(-20xx10^(-6)))/8(-sqrt(2)hat(i)+hat(j)+hat(k))=-22.5xx10^(3) (-sqrt(2)hat(i)+hat(j)+hat(k))N//C`

Discussion

37.	A charge of `24 muC ` is given to a hollow metallic sphere of radius 0.2m. Find the potential (i) at the surface of sphere (ii) at a distance of 0.1 cm from the center of sphere.
Answer» Correct Answer - `1.08xx10^(6) V, 1.08xx10^(6) V` (i) `q = 24 muC = 24xx10^(-6) C, r = 0.2m`. At the surface of the sphere. `V = (1)/(4pi in_(0)) (q)/(r ) = (9xx10^(9)xx24xx10^(-6))/(0.2)` `= 1.08xx10^(6) V` (ii) Potential at any point inside the sphere = potential on the surface `:.` potential at a distance of 0.1 cm from the cenre `= 1.08xx10^(6) V`

Discussion

38.	A parallel plate condenser with oil (dielectric constant 2) between the plates has capacitance C. If oil is removed, the capacitance of capacitor becomesA. `sqrt(2C`B. 2CC. `(C)/(sqrt2)`D. `(C)/(2)`
Answer» Correct Answer - D The capacitance of a parallel plate capacitor with dielectric (oil) between its plates is. `C=(Kepsilon_(0)d)/(d)" …(i)"` when dielectric (oil) is removed, so capacitance `C_(0)=(epsilon_(0)A)/(d)" …(ii)"` Comparing Eqs. (i) and (ii), we get `C=KC_(0)` `rArr" "C_(0)=(C)/(K)=(C)/(2)" "(because K=2)`

Discussion

39.	two point charges `2 muC` and `-4 muC` are situated at points `(-2m, 0m)` and `(2m, 0m)` respectively. Find out potential at point `C( 4m, 0m)` and `D (0 m, sqrt(5) m)`.
Answer» Potential at point C `V_(C)=V_(q_(1))+V_(q_(2))=(K(2muC))/6+(K(-4muC))/2=(9xx10^(9)xx2xx10^(-6))/6-(9xx10^(9)xx4xx10^(-6))/2=-15000 V`. Similarly, `V_(D)=V_(q_(1))+V_(q_(2))=(K(2muC))/sqrt((sqrt(5))^(2)+2^(2))+(K(-4muC))/sqrt((sqrt(5))^(2)+2^(2))=(K(2 muC))/3+(K(-4muC))/3=-6000 V`.

Discussion

40.	Three Charges of magnitude `100 muC` are placed at the corners A, Band C ofan equilateral triangle of side 4m. If the charge at A and Care positive and the one at point B is negative, what is the magnitude and direction of total force acting on charge at C? `[5.625N]`
Answer» Correct Answer - `[5.625N]`

Discussion

41.	Which one of the following graphs represents the variation of electric field with distance r from the centre of a charged spherical conductor of radius R?A. B. C. D.
Answer» Correct Answer - A

Discussion

42.	A hollow insulated conducting sphere is given a positive charge of `10 mu C` . What will be the electric field at the centre of the sphere it is radius is `2` metres ?A. ZeroB. `55 mu Cm^(-2)`C. `20 muCm^(-2)`D. `8 mu Cm^(-2)`
Answer» Correct Answer - A

Discussion

43.	Two metal spheres `A` and `B` of different sizes are charged such that the electric potential is the same at the surface of each. Sphere A has a radius three times that of sphere `B`. If `E_(A)` and `E_(B)` be the electric field magnitudes at the surface of each sphere, then `E_(B)//E_(A)` is
Answer» Correct Answer - 3 As `V_(A) = V_(B) implies (K Q_(B))/(R_(B)) = (K Q_(A))/(R_(A))` `= (K Q_(B))/(3R_(A)//3) = (KQ_(A))/(R_(A))` or `Q_(A) = 3Q_(B)` or `(Q_(A))/(Q_(B)) = (1)/(3)` Further, `(E_(B))/(E_(A)) = (Q_(B)//R_(B)^(2))/(Q_(A)//R_(A)^(2)) = (1)/(3) (3)^(2) = 3`

Discussion

44.	An infinity long solid cylinder of radius R has a uniform volume charge density `rho`. It has a spherical cavity of radius `R//2` with its centre on the axis of the cylinder, as shown in the figure. The magnitude of the electric field at the point P, which is at a distance 2R from the axis of the cylinder, is given by the expression `(23rhoR)/(16Kepsilon_0)`. The value of k is
Answer» We suppose that the cavity is filled up by a positive as well as negative volume charge of `rho`. So the electric field now produced at P is the superposition of two electric fields (a) The electric field created due to the infinitely long solid cylinder is `E_1=(rhoR)/(4epsilon_0)` directed towards the `+Y` direction (b) The electric field created due to the spherical negative charge density `E_2=(rhoR)/(96epsilon_0)` directed towards the `-Y` direction. `:.` The net electric field is `E=E_1-E_2=1/6[(23rhoR)/(16epsilon_0)]`

Discussion

45.	The capacity of a condenser increases both, when a conducting slab or an insulating slab is introduced between the plates of the condenser. In the former case, electric field `E = 0` inside the conductor and in the latter case, `E lt E_(0)`, inside the insulator. Thus, potentai difference `V = E xx d` decreases and hence capacity `C = Q//V` increases. It should be clearly understood that when a dielectric slab is introduced inbetween the plates of a charged capacitor with battery connected across the plates, (i) Capacity `C` increases, (ii) Potential `V` remains constant, (iii) Charge `Q = CV`, increases, (iv) Electric field `E` decreases, (v) Energy stored `U = (1)/(2) CV^(2)` increases. However, when battery across the plates of charged capacitor is put off and dielectric slab is introduced inbetween th plates of the capacitor, (i) Capacity `C` increases, (ii) charge `Q` remains constant, (iii) Potential `V = (Q)/(C )` decreases, (iv) Electric field. `E = V xx d` decreases, (v) Energy stored `U = (Q^(2))/(2C)` decreases. Consider a parallel plate air capacitor with area of each plate `= 150 cm^(2)` and distance between its plates `= 0.8mm`. With the help of the passage given above, choose the most appropriate for each of the following questions : The air capacitor is charged to `1200 V` and then filled with dielectric of `K = 3`. The charge on the plates will beA. `1.66xx10^(2) C`B. `1.66xx10^(-10) C`C. `1.99xx10^(7)C`D. `1.99xx10^(-7)C`
Answer» Correct Answer - D `Q = C_(0) V_(0) = 1.66xx10^(-10)xx1200` `= 1.99xx10^(7) C` On filling with dielectric after charging, the charge does not change. It remains the same.

Discussion

46.	The capacity of a condenser increases both, when a conducting slab or an insulating slab is introduced between the plates of the condenser. In the former case, electric field `E = 0` inside the conductor and in the latter case, `E lt E_(0)`, inside the insulator. Thus, potentai difference `V = E xx d` decreases and hence capacity `C = Q//V` increases. It should be clearly understood that when a dielectric slab is introduced inbetween the plates of a charged capacitor with battery connected across the plates, (i) Capacity `C` increases, (ii) Potential `V` remains constant, (iii) Charge `Q = CV`, increases, (iv) Electric field `E` decreases, (v) Energy stored `U = (1)/(2) CV^(2)` increases. However, when battery across the plates of charged capacitor is put off and dielectric slab is introduced inbetween th plates of the capacitor, (i) Capacity `C` increases, (ii) charge `Q` remains constant, (iii) Potential `V = (Q)/(C )` decreases, (iv) Electric field. `E = V xx d` decreases, (v) Energy stored `U = (Q^(2))/(2C)` decreases. Consider a parallel plate air capacitor with area of each plate `= 150 cm^(2)` and distance between its plates `= 0.8mm`. With the help of the passage given above, choose the most appropriate for each of the following questions : What will be the potential of the capacitor when filled with dielectric after charging as air capacitor ?A. `1200 V`B. `400 V`C. `3600 V`D. `300 V`
Answer» Correct Answer - B `V = (V_(0))/(K) = (1200)/(3) = 400`

Discussion

47.	Assertion. Capacity of a parllel plate condenser remains unaffected on introduced a conducting or insulating slab between the plates. Reason. In both the cases, electric field intensity between the plates increases.A. both, Assertion and Reason are true and the Reason is correct explanation of the Assertion.B. both, Assertion and Reason are true, but Reason is not the correct explanation of the Asserrtion.C. Assertion is true, but the Reason is false.D. both, Assertion and Reason are false.
Answer» Correct Answer - d Electric field inside a conductor is zero. And electric field inside an insulator is reduced to `E = E_(0)//K`./ Both, the assertion and reason are false.

Discussion

48.	Which of the following is deflected by electric field ?A. X-raysB. `gamma-`raysC. NeutronsD. `alpha-`particles
Answer» Correct Answer - D

Discussion

49.	The charge on `4muF` capacitor in the given circuit (in `muC`) is A. 12B. 24C. 36D. 42
Answer» Correct Answer - B In given figure, `C_(1)=4muF and C_(2)=C_(P)=6muF` are in series. `V_(1)=(C_(2)/(C_(1)+C_(2)))V=(6/(4+6))10=6V` Now`" "Q=CV=4xx10^(-6)xx6=24xx10^(-6)C` `=24muC`

Discussion

50.	Two identical conducting sphere carrying different charges attact each other with a force F when placed in air medium at a distance `d` apart. The spheres are brought into contact and then taken to their original positions. Now, the two sphere repel each other with a force whole magnitude is equal to the initial attractive force. The ratio between initial charges on the spheres isA. `- (3 + sqrt8)` onlyB. `-3 + sqrt8` onlyC. `-(3 + sqrt8)` or `(-3 + sqrt8)`D. `+ sqrt3`
Answer» Correct Answer - C

Discussion

Explore topic-wise InterviewSolutions in .

A hollow metal sphere of radius ` 5 cm` is charged such that the potential on its surcace is ` 10V`. The potential at the centre of the centre of the sphere is -A. ` 0 V`B. ` 10 V`C. same as at point ` 5 cm` away from the surface out side sphereD. same as a point ` 25` cm away from the surface

A hollow metal sphere of radius 5 cm is charged such that the potential on its surface is `10V`. The potential at the distance `3 cm` from the centre of the sphere is:A. zeroB. 10 VC. same as at a point 5 cm away from the surfaceD. same as at a point 25 cm away from the surface

A hollow metal sphere of radius ` 5 cm` is charged such that the potential on its surface is ` 10V`. The potential at the center of the sphere is -

The electric field in the region between two concentric charged spherical shells- (a) is zero (b) increases with distance from centre (c) is constant (d) decreases with distance from centre

A hollow metallic sphere of radius 10 cm is given a charge of `3.2 xx 10^(-9) C.` The electric intensity at a point 4 cm from the center isA. `9xx10^(-9)NC^(-1)`B. `"288 NC"^(-1)`C. `"2.88 NC"^(-1)`D. zero

A hollow metal sphere of radius 10 cm is charged such that the potential on its surface is 80 V. The potential at the centre of the sphere is-(a) 800 V (b) zero (c) 8 V(d) 80 V

A hollow metal sphere of radius 10cm is charged such that the potential on its surface is 80 V. The potential at the centre of the sphere isA. zeroB. `80 V`C. `800 V`D. `8V`

The electric field strength in air at NTP is `3 xx 10^(6)V//m`. The maximum charge that can be given to a spherical conductor of radius 3m isA. `3xx 10^(4)C`B. `3 xx 10^(-3)C`C. `3 xx 10^(-2)C`D. `3 xx 10^(-1)C`

A charge q is placed at the centre of the line joining two equal charges Q. The system of the three charges will be in equilibrium if q is equal to:A. `Q//4`B. `-Q//4`C. `-Q//8`D. `Q//8`

A charge q is placed at the centre of the line joining two equal charges Q. The system of the three charges will be in equilibrium if q is equal to:A. `-4Q`B. `-(Q)/(4)`C. `-(Q)/(2)`D. `+(Q)/(2)`

Electric charges `q, q, –2q` are placed at the corners of an equilateral triangle ABC of side l. The magnitude of electric dipole moment of the system isA. `ql`B. `2ql`C. `sqrt(3ql)`D. `4ql`

Charges `+2Q` and `-Q` are placed as shown in figure. The point at which electric field intensity is zero, will be A. Somewhere between `-Q and +2Q`B. somewher on the left of `-Q`C. somewhere on the right of `+2Q`D. somewhere on the right bisector of line joining `-q` and `+2Q`

A circuit is shown in figure for which `C_(1)=(3pm 0.011)muF, C_(2)=(5pm 0.01)muF and C_(3)=(1pm 0.01)muF.` If C is the equivalent capacitance across AB, then C is given by A. `(0.9 pm 0.114)muF`B. `(0.9 pm 0.01)muF`C. `(0.9 mu 0.023)muF`D. `(0.9 mu 0.09) muF`

A charged particle having a charge of `-2.0 xx 10^(-6) C` is placed close to a non-conducting plate having a surface charge density `4.0 xx 10^(-6) C m^(-2)`. Find the force of attraction between the particle and the plate.

An infinite line charge produces a field of `9xx10^(-4)N" "C^(-1)` at a distance of 2 cm. calculate the linear charge density.A. `10^(-3)Cm^(2)`B. `10^(-4)Cm^(2)`C. `10^(-5)Cm^(2)`D. `10^(-7)Cm^(2)`

An infinite line charge produces a field of `9xx10^(4) NC` at a distance of 2cm. Calculate the linear charge density.A. `2 xx 10^(-7) C//m`B. `10^(-8) C//m`C. `10^(7) C//m`D. `10^(-4) C//m`

An infinite line charge produces a field of `9xx10^(4) NC^(-1)` at a distance of `4 cm`. Calculate the linear charge density.

To what potential, must we charge an insulated sphere of radius 14 cm so that its surface charge density of `1 muC m^(-2)` ?

An infinite line charge produce a field of `7.182xx10^(8)NC^(-1)` at a distance of 2 cm. The linear charge density isA. `7.27xx10^(-4)Cm^(-1)`B. `7.98xx10^(-4)Cm^(-1)`C. `7.11xx10^(-4)Cm^(-1)`D. `7.04xx10^(-4)Cm^(-1)`

To what potential we must charge an insulate sphere of radius 14 cm, so that the surface charge density is equal to `2 muC m^(-2)` ?

Unit of electric flux isA. VmB. N-m/CC. V/mD. C/N-m

A parallel plate condenser has a capacitance `50 muF` in air and `100 muF` when immersed in an oil. The dielectric constant `k` of the oil isA. 0.2B. 1.5C. 2.2D. 2.5

Find out electric field intensity at point A (0, 1m, 2m) due to a point charge `-20 muC` situated at point `B (sqrt(2)m, 0, 1m)`.

A charge of `24 muC ` is given to a hollow metallic sphere of radius 0.2m. Find the potential (i) at the surface of sphere (ii) at a distance of 0.1 cm from the center of sphere.

A parallel plate condenser with oil (dielectric constant 2) between the plates has capacitance C. If oil is removed, the capacitance of capacitor becomesA. `sqrt(2C`B. 2CC. `(C)/(sqrt2)`D. `(C)/(2)`

two point charges `2 muC` and `-4 muC` are situated at points `(-2m, 0m)` and `(2m, 0m)` respectively. Find out potential at point `C( 4m, 0m)` and `D (0 m, sqrt(5) m)`.

Three Charges of magnitude `100 muC` are placed at the corners A, Band C ofan equilateral triangle of side 4m. If the charge at A and Care positive and the one at point B is negative, what is the magnitude and direction of total force acting on charge at C? `[5.625N]`

Which one of the following graphs represents the variation of electric field with distance r from the centre of a charged spherical conductor of radius R?A. B. C. D.

A hollow insulated conducting sphere is given a positive charge of `10 mu C` . What will be the electric field at the centre of the sphere it is radius is `2` metres ?A. ZeroB. `55 mu Cm^(-2)`C. `20 muCm^(-2)`D. `8 mu Cm^(-2)`

Two metal spheres `A` and `B` of different sizes are charged such that the electric potential is the same at the surface of each. Sphere A has a radius three times that of sphere `B`. If `E_(A)` and `E_(B)` be the electric field magnitudes at the surface of each sphere, then `E_(B)//E_(A)` is

Which of the following is deflected by electric field ?A. X-raysB. `gamma-`raysC. NeutronsD. `alpha-`particles

The charge on `4muF` capacitor in the given circuit (in `muC`) is A. 12B. 24C. 36D. 42