A metallic spherical shell has an inner radius R1 and outer radius R2. A charge is placed at the centre of the spherical cavity, the surface charge density on the outer surface is

Question

A metallic spherical shell has an inner radius R1 and outer radius R2. A charge is placed at the centre of the spherical cavity, the surface charge density on the outer surface is (A) (-q/4π R21) (B) (q/4π R22) (C) (q2/4π R21) (D) (2q/4π R22)

Tardigrade Admin · Accepted Answer

Surface charge density on the outer surface

= \frac{+ q}{4 π R _{2}^{2}}

When a charge

+ q

is placed at the centre of spherical cavity as shown in figure.

Charge induced on the inner surface of shell

= - q ... (i)

Charge induced on the outer surface of shell

= + q ... (ii)

∴

Surface charge density on the inner surface

= \frac{- q}{4 π R _{1}^{2}}

Q. A metallic spherical shell has an inner radius $R_{1}$ and outer radius $R_{2}$ . A charge is placed at the centre of the spherical cavity, the surface charge density on the outer surface is

$\frac{- q}{4 π R _{1}^{2}}$

$\frac{q}{4 π R _{2}^{2}}$

$\frac{q ^{2}}{4 π R _{1}^{2}}$

$\frac{2 q}{4 π R _{2}^{2}}$

Q. A metallic spherical shell has an inner radius R1​ and outer radius R2​. A charge is placed at the centre of the spherical cavity, the surface charge density on the outer surface is

4πR12​−q​

4πR22​q​

4πR12​q2​

4πR22​2q​

Q. A metallic spherical shell has an inner radius $R_{1}$ and outer radius $R_{2}$ . A charge is placed at the centre of the spherical cavity, the surface charge density on the outer surface is

$\frac{- q}{4 π R _{1}^{2}}$

$\frac{q}{4 π R _{2}^{2}}$

$\frac{q ^{2}}{4 π R _{1}^{2}}$

$\frac{2 q}{4 π R _{2}^{2}}$