Explore topic-wise InterviewSolutions in .

The correct choice is (a) GAUSS’s Law

Best explanation: Gauss’s Law gives the relation between ELECTRIC flux and charges inside a SURFACE. It states that electric flux coming out from a closed surface is equal to \(\frac {1}{\varepsilon}\) times the charge inside the surface.Coulomb’s Law explains the force between two charges and PASCAL’s Law is related to fluids.

The CORRECT choice is (c) V*m

To explain I would say: Flux is EQUAL to the product of field intensity and area of the surface. But field intensity multiplied by a LENGTH GIVES the unit of electric potential as E=-\(\frac {DV}{dx}\). Therefore, flux also means electric potential multiplied by length. This gives us the unit V*m. There is another unit of flux N*m^2*C^-1.

Correct CHOICE is (a) False

Easiest EXPLANATION: Coulomb’s Law is not valid for inter-atomic distance i.e. distance LESS than 10^-15 m. Besides, if the distance between the TWO bodies is less than the size of any of the bodies, this law is ALSO invalid. We can use this law only in all other cases.

The correct choice is (c) \(\frac {1}{8.85}\)*10^-12

To elaborate: According to GAUSS’s LAW, the total number of electric FIELD lines coming out of a charge q is = \(\frac {q}{\varepsilon_o}\) where εo is the ABSOLUTE permittivity of air. Its value is 8.85*10^-12. THEREFORE the number of lines coming out from a 1C charge = \(\frac {1}{8.85}\)*10^-12.

The correct answer is (a) 0

To explain I would say: DISTANCE of center from each corner point of the SQUARE is = \(\frac {10\sqrt2}{2}\) = 5√2. Therefore FIELD intensity at the center due to a single charge is = \(\frac {20}{(5\sqrt2)^2}\) dyne/esu. But the FIELDS due to the FOUR charges are equal and are at perpendicular to each other. So the fields balance each other and the net electric field at the center will be equal to zero.

Correct answer is (d) 2.38 C/m^3

Best EXPLANATION: Volume of the sphere = \(\frac {4}{3}\)πr^3 where r is the radius of the sphere. THEREFORE, the charge density = \(\frac {TOTAL \, charge}{\frac {4}{3}\PI r^3}\). Now substituting the values, charge density = \(\frac {10}{\frac {4}{3}\pi r^3}\) = 2.38 C/m^3. But if the sphere is conducting, we have to consider the surface charge density.

Right choice is (a) Electric field intensity

Easiest explanation: E=-\(\frac {dV}{DX}\) where E is the field intensity, V is POTENTIAL and x is distance. THEREFORE unit of electric field intensity will be \(\frac {unit \, of \, potential}{unit \, of \, distance} = \frac {V}{m}\). Electric flux has unit V*m, V is the unit of electric potential whereas CHARGE has a unit of Coulomb or esu.

Correct OPTION is (b) 4.5N

Best EXPLANATION: The FORCE will be 9*\(\frac {\sqrt2*\sqrt2}{2^2}\) N=4.5N because the force is proportional to the product of the two CHARGES and inversely proportional to the square of the distance between them. Similarly, if the charges are the same but the distance is doubled, the force between them will be \(\frac {1}{4}\) TIMES the previous value.

The correct answer is (b) Vector quantity

Easiest explanation: A scalar quantity is a quantity with magnitude only but no direction. But a vector quantity possesses both magnitude and direction. An ELECTRIC FIELD has a very specific direction (away from a positive charge or TOWARDS a negative charge). Hence electric field is a vector quantity. MOREOVER, we have to use a vector addition for ADDING two electric fields.

The correct OPTION is (a) For all conductors

Easiest explanation: Charge remains on the OUTER surface of a conductor, irrespective of the shape and size of the conductor and ALSO for hollow and SOLID conductors both. But if there is a sharp edge in the conductor, surface charge DENSITY will be more at that point. The surface charge density is uniform in the case of a sphere.

Right option is (c) C/m^2

The explanation: SURFACE CHARGE density means how much charge is stored in the unit surface area of a CONDUCTOR. So, it’s unit will be=\(\frac{the \, unit \, of \, the \, charge}{the \, unit \, of \, area}\). In SI the unit of charge is Coulomb and the unit of area is m^2. THEREFORE the REQUIRED unit will be C/m^2.

Right answer is (b) 20cm AWAY from the +4Q charge

Explanation: The electric FIELD at a distance of r from a charge q is equal to \(\frac {q}{4\pi\varepsilon_or^2}\). Let the electric field intensity will be zero at a distance of x cm from +4q charge, so the fields DUE to the two CHARGES will balance each other at that point. Therefore \(\frac {4q}{4\pi\varepsilon_ox^2}=\frac {q}{4\pi\varepsilon_o(30-x)^2}\). Solving this we get x=20cm. Therefore the point will be 20cm away from the +4q charge.

Correct CHOICE is (d) A charge is self-destructive

The BEST EXPLANATION: Electric charge possesses the PROPERTIES of QUANTIZATION, conservation of charge. It cannot be destroyed i.e. it is not self-destructive.

Right option is (b) Both force and TORQUE

The BEST explanation: In the case of a non-uniform ELECTRIC field, the force acting on both the charges of the dipole will be UNEQUAL. So, there will be a net force acting on the dipole in a certain direction. Also, there will be a torque due to two forces acting at two different POINTS. But in case of a uniform electric field, the net force on the dipole will be zero but net torque will be non-zero.

The CORRECT option is (c) 3.7*10^20

To elaborate: 1 AMPERE means 1 Coulomb per second. So the NUMBER of electrons flow per second is \((\FRAC {1}{1.602*10^{-19}})\). Therefore number of electron flow in one MINUTE =\(\frac {1}{1.602*10^{-19}}\)*60 =3.7*10^20.The number will be 60 times more if we have to calculate the number of electron flow in an hour.

The correct option is (b) False

Easiest explanation: Charge is distributed only on the outer surface of a body. As both the SPHERES have the same RADIUS and same surface area, they will CARRY the same amount of charge. But the charge carried by a SPHERE and a cube will be different as their surface areas are different.

The correct option is (a) 6.25*10^21

The best explanation: Electron has the charge of 1.602*10^-19 COULOMB. So, the number of electrons in 1 Coulomb of charge is \(\frac{1}{1.602*10^{-19}}\) = 6.25*10^21. This huge number of electrons can be ACCUMULATED to form 1C of charge. Thus, we can conclude that we NEED Avogadro’s number of electrons (approximately) to GET 100C charges.

Correct OPTION is (b) CHARGE and length of a dipole

Easy explanation: Dipole is defined as two EQUAL but opposite charges, KEPT at a small distance and having a dipole moment. The dipole moment is simply the product of the electric charge and length of the dipole. The dielectric constant of the MEDIUM doesn’t affect the dipole moment i.e. dipole moment of an electric dipole will be the same in water as well as in the air.

Right option is (d) 0 degree

Easiest explanation: We know that the electric field and area both are vector quantity and the electric flux is expressed as \(\VEC{E}.\vec{s}\) (taking dot product). But if the angle between the two vectors is θ then the formula becomes E.s.cosθ.Cosθ will be MAXIMUM if THETA is zero, in all other CASES, the VALUE of Cosθ is less than 1. Therefore flux will be the maximum if the angle is 0 degrees.

Correct option is (a) False

The explanation: In the case of SHM, the force on a body is inversely proportional to the distance of the body from the mean position. But in this case, we know the force ACTING on the body is inversely proportional to the SQUARE of the distance [F =\(\FRAC {QQ}{4\pi\varepsilon_o(2R)^2}\)]. So the motion of the body will be oscillatory but not SHM.

Right option is (b) +210q

For explanation I WOULD say: As charge is ADDITIVE, total charge will be (1+2+3+4+…. +20)*q=\(\frac{20*21}{2}\)*q= 210q. But if the POLARITIES of the charges are different i.e. some of them are positive and some are negative, then the result will be different. We have to ADD separately the positive charges and the negative charges.

The correct choice is (d) The FORCE may increase or decrease depending on whether q3 is positive or negative

Explanation: If both the charges Q1 and Q2 are positive then they will repel each other. Now if the THIRD charge q3 is also positive, the repulsive force will increase. But if q3 is negative, the repulsive force will be reduced by some amount due to the ATTRACTIVE force between q1 and q3.

Correct choice is (d) Don’t ATTRACT or repel

Explanation: The two spheres are oppositely charged by the same amount. So if they come in CONTACT, both of their charges are NEUTRALIZED. So they become UNCHARGED and don’t attract or repel each other.

Correct answer is (d) Spherical

The best EXPLANATION: SPHERE has UNIFORM charge distribution over its ENTIRE surface. It doesn’t have any sharp edges hence very little chance of charge accumulation at those edges and hence very little chance of DISCHARGE of stored charge.

The CORRECT answer is (c) The charges are of opposite POLARITY

Easiest explanation: If both the charges are of the same polarity (maybe of unequal MAGNITUDE), there must be a point in between them where the electric field intensities of the charges are of equal magnitude and in opposite direction. Hence they balance each other and the NET field intensity must be ZERO. But if the charges are of opposite polarities their field intensities aid each other and net field intensity can never be zero.

Right option is (c) 2^nd sphere

For EXPLANATION I would say: The electric field LINE is directly proportional to the charge bound inside a sphere. We know that, field lines are the measure of electric flux i.e. NUMBER of field lines CROSSING through a surface are know an electric flux. THEREFORE flux will be lesser in the case of q charge and will be 10 times in case of a 10q charge.

The correct ANSWER is (d) Depends on the nature of the charges

The best explanation: DEPENDING on the nature and quantity of charges, the net force on the central charge MAY vary its MAGNITUDE and direction. If all the charges are the same the net force will be zero.

Right option is (a) An INFINITE positive and negative charge

For explanation I would say: Earth can be considered as an infinite source of positive and negative charges. This can be JUSTIFIED by the FACT that if we connect any positive or NEGATIVELY charged body to the ground, all of its charges will go to earth.

Correct option is (a) [M^-1L^-3T^4I^2]

Explanation: εo is the absolute permittivity of AIR medium and has VALUE 8.854*10^-12C^2N^-1m^-2. Its dimension is [M^-1L^-3T^4I^2]. The permittivity of a medium is the product of this TERM with the dielectric constant or RELATIVE permittivity of that medium.

The correct answer is (c) House with lightning arrester

Best explanation: Lightning arrester arrests lightning and allows a safe path of electricity to ground. Thus it is a safe place inside a house that has a lightning arrester on the TOP of it. ELSE, electricity finds a high tower or TREE or WALL and travels through them to ground. Therefore these are not safe places to TAKE shelter during lightning.

The correct answer is (a) Almost zero resistivity

The explanation: SEMICONDUCTORS are those which CARRY CURRENT with almost zero resistivity at a very low temperature (EXAMPLE: Lead at -272-degree centigrade). So, they have a very HUGE amount of current flow through them.

Correct answer is (b) False

The BEST I can explain: If an OBJECT is attracted by another charged body, the first object MAY be oppositely charged or not charged because we know both an uncharged object and an oppositely charged object are attracted by another charged object.

Correct answer is (b) False

To elaborate: Though GAUSS GAVE his LAW for the electric field only, this rule is applicable in the CASE of the magnetic field also. In that case, magnetic flux lines are counted and the permittivity of the medium is REPLACED by the permeability of the medium. This law is also applicable in the gravitational field.

The correct ANSWER is (d) Unbounded surface

Explanation: Gauss’s Law is VALID only in case of a closed surface. Solid or hollow sphere, CUBE are closed surface and so Gauss’s Law can be applied in those cases. But in case of unbounded surface, there is no MEANING of charge BOUNDED by the surface and so Gauss’s Law cannot be applied in those cases.

The correct option is (a) Zero

To explain I would say: Electric DIPOLE is the combination of a couple of positive and negative charges having the same MAGNITUDE. THEREFORE, the total charge of an electric dipole is 0. That means the total charge INSIDE the cube is zero and ACCORDING to Gauss’s Law, the net electric flux coming out of the cube is zero.

Right option is (a) [I T L^-1]

To explain I would say: Linear charge DENSITY λ=\(\FRAC {Amount \, of\, charge}{Total \, length}\). The dimension of ELECTRIC charge = [I T] and the dimension of length is [L]. Hence the dimension of linear-charge-density = [I T L^-1]. In the CASE of surface charge density, the dimension is [I T L^-2] because it means charge stored on the unit surface AREA.

The correct choice is (c) \(\vec{p} \times \vec{E}\)

To explain: Forces on +q and –q charges ACT along two opposite direction and the PERPENDICULAR distance between the two forces is equal to 2lsinθ (as the distance between the two point charges is 2l). Therefore the torque = force*distance=qE*2lsinθ=(q*2l)*E*sinθ. But q*2l is defined as the DIPOLE moment \(\vec{p}\) of the dipole. So the expression of torque becomes \(\vec{p} \times \vec{E}\) according to cross PRODUCT rule.

Right option is (a) True

To elaborate: Coulomb force acts ALONG the center-joining-line of the two CHARGES. So this force is called the central force. GRAVITATIONAL force is ALSO the central force.

The correct ANSWER is (a) ∫ \(\vec{E}.d\vec{s}\)

EXPLANATION: Electric flux is defined as the number of field lines CROSSING PERPENDICULARLY through a surface area. The number of electric field lines crossing through the unit cross-section area is known as electric field intensity (E). Therefore field lines crossing through small area ds are E.ds. Taking the integral gives the flux in the entire surface.