Electric Field Due to a Sphere and Thin Shell

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.

The ratio of electric field at a point A and at point B due to the uniformly charged spherical conductor as shown, is

1. 2:5

2. 1:3

3. 1:1

4. 0

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.

A uniformly charged spherical conductor has a radius of 1m and surface charge density $0.8\frac{C}{m^2}$. The electric field magnitude because of this at a point 1m radially away, from the surface of the sphere is

1. 7.2 x 10⁹ N/C

2. 2.25 x 10¹⁰ N/C

3. 9 x 10⁹ N/C

4. 4.5 x 10⁹ N/C

Q.

1. 
   

2. Zero

3. 
   

4. 
   

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.

An insulated solid sphere has a volume charge density ρ. ‘r’ is the distance of a point P from the Centre. Which graph represents the correct variation of electric field with respect to r?

1. 

2. 

3. 

4. 

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. The electric filed due to a uniformly charged spherical shell of charge 'Q' and radius 'R' at a distance 'r' is for $r<R$, and for $r>R$.

1. $\frac{kQ}{r^2}$
2. $\frac{k{Q}^2}{r^2}$
3. $zero$
4. $\frac{kQ}{r}$

Q. Some positive charge is spread uniformly over the surface of a thin spherical shell. Radius of sphere is $100cm$ and electric field on the surface is $90\times {10}^{3}N/C$. A point $A$ is at $50cm$ from the centre & point $B$ is at $150cm$ from the centre. Field at $A$ & $B$ are $E_A$ & $E_B$ respectively, then

1. $E_A=E_B=45\times {10}^{3}N/C$
2. $E_A=0,E_B=45\times {10}^{3}N/C$
3. $E_A=0,E_B=40\times {10}^{3}N/C$
4. $E_A=E_B=40\times {10}^{3}N/C$