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 inner surface is:

\frac{q}{4 π R_{1}^{2}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{- q}{4 π R_{1}^{2}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{q^{2}}{4 π R_{2}^{2}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{q}{4 π R_{2}^{2}}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $\frac{q}{4 π R_{2}^{2}}$
When a charge $+ q$ is placed at the centre of spherical cavity as shown in figure.
Charge included o the inner surface of shell $= - q . . . . . (i)$
Charge induced on the outer surface of shell $= + q . . . . . (i i)$
$∴$ Surface charge density on the inner surface $= \frac{+ q}{4 π R_{2}^{2}}$

Suggest Corrections

Similar questions

Q. A metallic spherical shell of inner radius

R_{1}

and outer radius

R_{2}

is shown in figure below. A charge is placed at the centre of the spherical cavity. The surface charge density on the inner surface is:

Q. A metallic spherical shell has an inner radius

R_{1}

and outer radius

R_{2}

. A charge

Q

is placed at the centre of the spherical cavity. What will be surface charge density on (i) the inner surface, and (ii) the outer surface?

A spherical conducting shell of inner radius $r_{1}$ and outer radius $r_{2}$ has a charge Q. (a) A charge q is placed at the centre of the shell. What is the surface charge density on the inner and outer surfaces of the shell? (b) Is the electric field inside a cavity (with no charge) zero, even if the shell is not spherical, but has any irregular shape? Explain.

Q. A spherical conducting shell of inner radius r1 and outer radius r2 has a charge Q. A charge q is placed at the centre of the cell.
(a) What is the surface charge density on the (i) inner surface (ii) outer surface of the shell.
(b) Write the expression for electric field at a point x r2 from the centre of the shell.

Q. A hollow spherical conducting shell of inner radius

r_{1}

and other radius

r_{2}

has a charge Q. A charge -q is placed at the centre of the sphere. The surface charge densities on the inner and outer surfaces of the sphere will be respectively:-

Join BYJU'S Learning Program

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 inner surface is:

The correct option is D q4πR22When a charge +q is placed at the centre of spherical cavity as shown in figure.Charge included o the inner surface of shell =−q.....(i)Charge induced on the outer surface of shell =+q.....(ii)∴ Surface charge density on the inner surface =+q4πR22

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 inner surface is: