# Objective questions on Electric Potential

## Paragraph Type of Question

(A) Electric potential at any point x, y, z in the space is given $V = 4x^2 - 3x$
Question 1
Find the electric field at any point (x, y, z)
(a) (8x - 3)i
(b) -(8x - 3)i
(c) -8xi
(d) 8xi

Question 2
Equipotential surface in the region are
(a) planes parallel to X-Y plane
(b) planes parallel to Y-Z plane
(c) planes parallel to X-Z plane
(d) none of the above

Question 3
Find the force experienced by a charge particle q at point (1, 1, 1)
(a) -11qi
(b) 11qi
(c) 11qi + j
(d) 11qi – j

Question 4
Find the value of
a. -1 volt
b. 0 volt
c. -2 volt
d. 1 volt

(B) A spherical shell of radius R is carries a uniform surface charge q. Take the reference point at ∞
Question 5
Find the electric field at r>R .Here is the r is the unit vector across radial direction

Question 6
Find the electric field at r<R
a. (1/4πε0) (q/R2)
b. (1/4πε0) (q/r2)
c. zero
d. (1/4πε0) (q/r2 + R2)

Question 7
Find the potential at r>R
a. (1/4πε0) (q/r)
b. (1/4πε0) (q/r +R)
c. (1/4πε0) (q/r - R)
d. none of the above

Question 8
Find the potential at r<R
a. (1/4πε0) (q/r)
b. (1/4πε0) (q/R)
c. (1/4πε0) (q/R - r)
d. none of the above

Question 9
If I placed an second uniformly charge shell (Q) at radius R'>R, will the value of potential change at r<R
a. increases
b. decreases
c. constant
d. none of the above

Question 10
What will the electric field at r<R
a. (1/4πε0) (q/r2)
b. (1/4πε0) (q/R2)
c. zero
d. (1/4πε0) (q/r + R)

Question 11
A point charge q is located at (2, 3, 3) in xyz coordinate. Find the potential differences between A and B
A = (2, 3, 3)
B = (-2, 3, 3)
1. q/ 4πε0
2.  1/16πε0
3.  3q/16πε0
4.  none of the above

Question 12
Two equally charges are placed on the x-axis at (-a, 0) and (a, 0). Charge is q and mass is m. They are released from rest. Find their velocities when they are 4a apart
a. q √(1/πε0m)
b. (q/4) √(1/πε0m)
c. q/πε0m
d. q/4πε0m

Question 13
A point charge q1 = +2µC is placed at the origin of coordinates. A second charge
q2 = -3µC is placed on the y-axis at y = 100cm. At what point on the y-axis, potential is zero
a. y = -200cm
b. y = 40cm
c. y = 200cm
d. none of the above

Question 14
The electric potential at a point (x,y) in (x-y) plane is given by
$V=-xy$.
The Field intensity at a distance r from origin varies as
(a) $r^2$
(b) r
(c) $\frac {1}{r}$
(d) $\frac {1}{r^2}$

Question 15
Charge 2 and -4 C are placed at some distance .The locus of points in the plane of charge where the potential is zero will be
(a) Straight line
(b) Circle
(c) Parabola
(d) Ellipse
Question 16
A spherical conductor has charge Q on its surface. Radius of the conductor is R. Which of the following is correct?
(a) Electric Potential is a non zero constant for 0 R
(b) Electric Potential is a constant for 0 R
(c) Electric Field is zero for 0 R
(d) Electric Field is a non zero constant for 0 R

Question 17
Four equal point charge Q are to be placed at the corner of square ABCD of side 1 m one at a time. Find the energy in the system after each charge is positioned

(a) 0,K,$K(2+\frac{1}{\sqrt {2}})$,$2K(2+\frac{1}{\sqrt2})$
(b) 0,K,$K(2-\frac{1}{\sqrt2})$,$2K(2-\frac{1}{\sqrt2})$
(c) 0,K,2K,4K
(d) 0,K,$K(2+\frac{1}{\sqrt2})$,$4K(2+\frac{1}{\sqrt2})$
Where $K=\frac{Q^2}{4\pi\varepsilon_0}$

Question 18
The electrostatic potential on the surface of a charged conducting sphere is 200V. Two statments are made in this regard:
S1 : At any point inside the sphere, electric intensity is zero.
S2 : At any point inside the sphere, the electrostatic potential is 200V.
Which of the following is a correct statement?
(a) S1 is true but S2 is false.
(b) Both S1 & S2 are false.
(c) S1 is true, S2 is also true and S1 is the cause of S2.
(d) S1 is true, S2 is also true but the statements are independant.

Question 19
Consider a uniform electric field in the $\hat{z}$ direction. The potential is a constant
(a) in all space.
(b) for any x for a given z.
(c) for any y for a given z.
(d) on the x-y plane for a given z.

Question 20
In a region of constant potential
(a) the electric field is uniform
(b) the electric field is zero
(c) there can be no charge inside the region.
(d) the electric field shall necessarily change if a charge is placed outside the region.

## Paragraph Based Questions

(C) Two spherical cavities ( A and B) of radii x and y are hollowed out from the interior of a conducting sphere of radius R. Charge $q_1$ and $q_2$ charges are placed at center of cavities A and B. The situation is depicted in the below fig

Question 21
Find the surface charge densities at A, B and outer surface of the sphere
(a) $\frac{-q_1}{4\pi x^2},\frac{-q_2}{4\pi y^2},\frac{q_1+q_2}{4\pi R^2}$
(b) $\frac{q_1}{4\pi x^2},\frac{q_2}{4\pi y^2},\frac{-(q_1+q_2)}{4\pi R^2}$
(c) $\frac{-q_1}{4\pi y^2},\frac{-q_2}{4\pi x^2},\frac{q_1+q_2}{4\pi R^2}$
(d) None of these

Question 22
What is the electric field outside the conductor at distance r from the center of large sphere
(a) $\frac{1}{4\pi\varepsilon_0}\frac{q_1}{r^2}\mathbf{r}$
(b) $\frac{1}{4\pi\varepsilon_0}\frac{q_1+q_2}{r^2}\mathbf{r}$
(c) $\frac{1}{4\pi\varepsilon_0}\frac{q_2}{r^2}\mathbf{r}$
(d) $\frac{1}{4\pi\varepsilon_0}\frac{q_1-q_2}{r^2}\mathbf{r}$
Where r is the unit vector from center of large sphere

Question 23
What is the field inside the cavity A and cavity?
(a) $\frac{1}{4\pi\varepsilon_0}\frac{q_1}{r_A^2}\mathbf{r_A},\frac{1}{4\pi\varepsilon_0}\frac{q_2}{r_B^2}\mathbf{r_B}$
(b) $\frac{1}{4\pi\varepsilon_0}\frac{q_1}{(r_A-x)^2}\mathbf{r_A},\frac{1}{4\pi\varepsilon_0}\frac{q_2}{(r_B-y)^2}\mathbf{r_B}$
(c) zero, zero
(d) None of these
Where rA and rB are the unit vector from center of cavities respectively

Question 24
What if a third charge is placed near the conductor?
(a) Surface charge on conductor will change
(b) Electric field inside the cavity will change
(c) Electric field inside the conductor will change
(d) Surface charge on cavity will change

Question 25
If the potential of the conductor is 1 V, find the potential at Point N at the distance r from the center of the cavity A ( r < x)
(a) $1+\frac{q_1}{4\pi\varepsilon_0}\left[\frac{1}{r}-\frac{1}{x}\right]$
(b) $1+\frac{q_1}{4\pi\varepsilon_0}\left[\frac{1}{x}-\frac{1}{r}\right]$
(c) $1-\frac{q_1}{4\pi\varepsilon_0}\left[\frac{1}{r}-\frac{1}{x}\right]$
(d) None of these

(D) Three concentric spherical conductors A, B, C are arranged as shown in the figure. The radius of the shell A, B ,C are $R_1$, $R_2$ and $R_3$ respectively. Charge Q, 2Q and 3Q are given the spherical shell A, B and C respectively

Question 26
Find the Surface charge density of the outer surface of shell C
(a) $\frac{3Q}{2\pi\varepsilon_0R_3^2}$
(b) $\frac{Q}{2\pi\varepsilon_0R_3^2}$
(c) $\frac{3Q}{4\pi\varepsilon_0R_3^2}$
(d) $\frac{3Q}{\pi\varepsilon_0R_3^2}$

Question 27
Which of these is true for potential?
(a) Potential at point $R_2 < R < R_3$ is given by
$\frac{Q}{4\pi\varepsilon_0}\left[\frac{3}{R}+\frac{3}{R_3}\right]$
(b) Potential of the outer surface of the shell C is
$\frac{Q}{4\pi\varepsilon_0}\left[\frac{6}{R_3}\right]$
(c) Potential at the center of the system is
$\frac{Q}{4\pi\varepsilon_0}\left[\frac{1}{R_1}+\frac{2}{R_2}+\frac{3}{R_3}\right]$
(d) None of these

Question 28
Find the electric Field at a point $R > R_3$
(a) $\frac{3Q}{2\pi\varepsilon_0R^2}$
(b) $\frac{3Q}{4\pi\varepsilon_0R^2}$
(c) $\frac{3Q}{\pi\varepsilon_0R^2}$
(d) None of these