Electric Field Due to a Sphere and Thin Shell

Q.

State and prove Gausss theorem in electrostatics.

Q.

A charge Q is to be distributed on two conducting spheres. What should be the value of charges on the spheres so that the repulsive force between them is maximum when they are placed at a fixed distance from each other in the air.

Q.

A conducting sphere of radius 10 cm has an unknown charge. If
the electric field 20 cm from the centre of the sphere is $1.5\times {10}^{3}N/C$ and points radially inward, what is the net charge on the sphere?

Q.

State Biot Savart law.

Q. Three concentric metallic spherical shells of radii R, 2R, 3R are given charges Q1, Q2, Q3 respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells Q1 : Q2 : Q3 is

1. 1 : 2 : 3

2. 1 : 3 : 5

3. 1 : 4 : 9

4. 1 : 8 : 18

Q.

How does the electric flux due to a point charge enclosed by a spherical gaussian surface get affected when its radius is increased?

Q. A dipole having charges +q and -q is fixed on a rough surface as shown. Another charge Q of mass m is placed at dis†an ce d from this dipole. Find the minimum value of d for which charge Q will not move.(given a is much smaller than d, co efficient of static friction u=0.5

Q. A parallel plate air capacitor has a capacitance C. When it is half filled with a dielectric of dielectric constant 5, the percentage increase in the capacitance will be:

1. $200\%$
2. $400\%$
3. $66.6\%$
4. $33.3\%$

Q. A spherical conductor of radius 12 cm has a charge of 1.6 × 10–7C distributed uniformly on its surface. What is the electric field (a) inside the sphere (b) just outside the sphere (c) at a point 18 cm from the centre of the sphere?

Q. A solid sphere of radius R has a charge Q distributed in its volume with a charge density $\rho =k{r}^a$, where k and a are constants and r is the distance from its centre. If the electric field at $r=\frac{R}{2}is\frac{1}{8}$ times that at r = R, find the value of a.

Q. Find the net electric field at an equatorial point $\text{P}$ of a dipole as shown in figure.

1. $1.3\times {10}^9\text{N/C}$
2. $2.3\times {10}^9\text{N/C}$
3. $3.3\times {10}^9\text{N/C}$
4. $4.3\times {10}^9\text{N/C}$

Q.

The radius of a gold nucleus (Z=79) is about $7.0\times {10}^{-15}m$. Assume that the positive charge is distributed uniformly throughout the nuclear volume. Find the strength of the electric field at (a) the surface of the nucleus and (b) at the middle point of a radius. Remembering that gold is a conductor, is it justified to assume that the positive charge is uniformly distributed over the entire volume of the nucleus and does not come to the outer surface ?

Q. Find the net electric field at an axial point $\text{P}$ of a dipole as shown in figure.

1. $1.50\times {10}^{-3}\text{N/C}$
2. $2.25\times {10}^{-3}\text{N/C}$
3. $1.88\times {10}^{-3}\text{N/C}$
4. $2.88\times {10}^{-3}\text{N/C}$

Q. A parallel plate capacitor with circular plates of radius $R$ is being charged as shown. At the instant shown, the displacement current in the region between the plates enclosed between $\frac{R}{2}$ and $R$ is given by,

1. $\frac{3}{4}i$
2. $\frac{i}{4}$
3. $3i$
4. $\frac{4}{3}i$

Q.

Define electric feild intensity and give its unit.

Q. A solid conducting sphere of radius a has a net positive charge 2Q. A conducting spherical shell of inner radius band outer radius c is concentric with the solid sphere and has a net charge -Q. The surface charge density on the inner and outer surfaces of the spherical shell will be

1. $-\frac{2Q}{4\pi b^2},\frac{Q}{4\pi c^2}$
   
   
2. $-\frac{Q}{4\pi b^2},\frac{Q}{4\pi c^2}$
   
3. $0,\frac{Q}{4\pi c^2}$
   
4. $Noneofthese$
   

Q. A hollow metal sphere of radius $R$ is uniformly charged. The electric field due to the sphere at a distance $r$ from the centre

1. increases as $r$ increases for $r<R$ and for $r>R$
2. zero as $r$ increases for $r<R$, decreases as $r$ increases for $r>R$
3. zero as $r$ increases for $r<R$, increases as $r$ increases for $r>R$
4. decreases as $r$ increases for both$r<R$ and $r>R$

Q. A solid metallic sphere has a charge + 3Q. concentric with this sphere is a conducting spherical shell having charge –Q. The radius of the sphere is a and that of the spherical shell is b. (b > a). What is the electric field at a distance R (a < R < b) from the centre.

1. $\frac{Q}{2\pi {ϵ}_{0}R}$
2. $\frac{3Q}{2\pi {ϵ}_{0}R}$
3. $\frac{3Q}{4\pi {ϵ}_0{R}^2}$
4. $\frac{4Q}{2\pi {ϵ}_0{R}^2}$

Q.

A circular disc of radius R carries surface charge density $\sigma \left(r\right)={\sigma }_0\left(1-\frac{r}{R}\right)$, where ${\sigma }_0$ is a constant and $r$ is the distance from the center of the disc. Electric flux through a large spherical surface that encloses the charged disc completely is ${\varphi }_0$. Electric flux through another spherical surface of radius $R/4$ and concentric with the disc is $\varphi$. Then the ratio $\frac{{\varphi }_0}{\varphi }$ is _________.

Q.

12 equal charges q are situated at the corners of a regular 12 sided polygon . What is the net force on the test charge Q at the centre?

Q. Volume charge density of a non conducting solid sphere of radius $R=30cm$ is given as $\rho ={\rho }_o(1-\frac{r}{R}).$ Electric field inside sphere is minimum at

1. $r=15cm$
2. $r=30cm$
3. $r=10cm$
4. $r=20cm$

Q.

If earth suddenly contracts to half its present radius keeping the mass constant, what would be the length of the day?

Q.

In a region of space, suppose there exists a uniform electric field E= 10i (V/m) If a positive charge moves with a velocity v=-2j, its potential energy at this moment.

(1) Increases

(2) Decreases

(3) Does not change

(4) Both (1) and (2)

Q. Three concentric conducting spherical shell have radii $r,2r$ and $3r$ and charges $q_1,q_2,\text{and}{q}_3$ respectively. Innermost and outermost shells are earthed as shown n figure. Select the correct alternative(s).

1. $q_1=-\frac{q_2}{4}$
2. $\frac{q_3}{q_2}=-\frac{1}{3}$
3. $\frac{q_3}{q_1}=3$
4. $q_1+q_3=-q_2$

Q.

27 identical drops of mercury are charged to the same potential of 10 V.what will be the potential if all the charged drops are made to combine to form one large drop ? Assume the drops to be spherical

Q.

In the absence of an electric field, the mean velocity of free electrons in a conductor at absolute temperature (T) is

Q. Variation of electric field along x-axis is shown in figure. If potential at origin is 10 V, then potential at x = 2 is

1. 50 V
2. 30 V
3. -40 V
4. -10 V

Q. Two concentric conducting thin spherical shells A, and B having radii $r_A$ and $r_B(r_B>r_A)$ are charged to $Q_A$ and $-Q_B(|Q_B|>|Q_A|)$. The electrical field along a line, (passing through the centre) is

1. 
2. 
3. 
4. 

Q.

What is difference between the statement electric field due to spherical shell and electric field due to solid sphere And also find difference between spherical shell and solid sphere

Q. Displacement current is set up between the plates of a capacitor when the potential difference across the plates is

1. maximum
2. zero
3. minimum
4. varied with time