Free Printable electrostatics and capacitors

1.

There is a non-spherical cavity inside a solid conducting neutral sphere of radius R and a charge +Q is placed

inside the cavity as shown in figure. Consider a point P which is inside the sphere and at a distance of R/2

from point charge Q as shown in figure. Potential at P due to charge on the inner surface of the cavity will

be ( $\frac{1}{4\pi\epsilon_0}$ )

a)

$-\frac{KQ}{2R}$

b)

$\frac{2kQ}{R}$

c)

$-\frac{2KQ}{3R}$

d)

$-\frac{KQ}{R}$

2.

Initially switch S was open and capacitors C, 2C were having charges Q and 2Q respectively as shown in figure.

Find charge flown in the direction 1 shown in figure after switch S is closed.

a)

$\frac{2Q}{5}$

b)

$-\frac{4Q}{5}$

c)

$\frac{4Q}{5}$

d)

$-\frac{2Q}{5}$

3.

Four non-conducting plates each of area A having charges Q, 2Q, –Q and 4Q distributed uniformly are placed

parallel to each other as shown in figure. Find potential difference across P and R.

a)

$\frac{3Qd}{2A\epsilon_0}$

b)

$\frac{Qd}{2A\epsilon_0}$

c)

$\frac{3Qd}{A\epsilon_0}$

d)

$\frac{Qd}{A\epsilon_0}$

4.

Two metallic plates are arranged as shown in figure forming a non-parallel capacitor. Then

a)

Surface charge density on plates is uniform

b)

Electric field between the plates is uniform

c)

Surface charge density at point 1 is greater than that at point 2

d)

Surface charge density at point 2 is greater than that at point 1

5.

In the given circuit, the switch S was initially open. If the switch is closed now, then amount of charge flown

through the switch S is

a)

$15\ \mu C$

b)

$30\ \mu C$

c)

$40\ \mu C$

d)

$90\ \mu C$

6.

Three identical conducting plates are arranged as shown in figure and they are given charges as indicated.

When switch S is closed, the amount of charge flown through the switch is

a)

$20\ \mu C$

b)

$60\ \mu C$

c)

$120\ \mu C$

d)

Zero

7.

CVA charged particle having charge q and mass m accelerated by a potential difference V₀ enters inside a parallel

plate capacitor (parallel to length l of plates) at midpoint of its separation between plates at t = 0. Potential

difference across capacitor varies with time t as, V = a d t, where a is constant and d is separation between

plates. Angle of deviation as it comes out of plates, is $\frac{\pi}{4}$ , Value of $\frac{ma^2l^4}{2qV_0^3}$ will be

a)

16

b)

32

c)

8

d)

4

8.

Six capacitors each of capacitance ‘C’ is connected as shown in the figure and initially all the capacitors are

uncharged. Now a battery of emf = ε is connected. How much charge will flow through the battery if the switch is

closed?

a)

$\frac{9C\epsilon}{5}$

b)

$\frac{11C\epsilon}{5}$

c)

$\frac{13C\epsilon}{5}$

d)

$\frac{7C\epsilon}{5}$

9.

There are two conducting spheres of radius a and b (b > a ) carrying equal and opposite charges. They are placed

at a separation d (>>> a and b). The capacitance of system is

a)

$\frac{4\pi\epsilon_0}{a-b-d}$

b)

$\frac{4\pi\epsilon_0}{\frac{1}{a}-\frac{1}{b}-\frac{1}{d}}$

c)

$\frac{4\pi\epsilon_0}{\frac{1}{a}+\frac{1}{b}-\frac{1}{d}}$

d)

$\frac{4\pi\epsilon_0}{\frac{1}{a}+\frac{1}{b}-\frac{2}{d}}$

10.

Figure shows a system of three concentric metal shells A, B and C with radii a, 2a and 3a respectively. Shell

B is earthed and shell C is given a charge Q. Now if shell C is connected to shell A, then the final charge on

the shell B is equal to

a)

$-\frac{4Q}{13}$

b)

$-\frac{8Q}{11}$

c)

$-\frac{5Q}{3}\$

d)

$-\frac{3Q}{7}$

electrostatics and capacitors

Total questions: 10

Worksheet time: 50mins

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