A solid spherical conducting shell has an inn | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the total excess charge on the conducting shell be $q$. Due to the point charge $+Q$ at the center,an induced charge of $-Q$ appears on the in

Vedclass · Accepted Answer

$-5Q$

Vedclass · Answer

(A) Let the total excess charge on the conducting shell be $q$. Due to the point charge $+Q$ at the center,an induced charge of $-Q$ appears on the inner surface of the shell. The charge density on the inner surface is $\sigma_{in} = \frac{-Q}{4 \pi a^2}$. Since the total charge on the shell is $q$,the charge on the outer surface is $q_{out} = q - (-Q) = q + Q$. The charge density on the outer surface is $\sigma_{out} = \frac{q + Q}{4 \pi (2a)^2} = \frac{q + Q}{16 \pi a^2}$. For the charge densities to be equal,we set $\sigma_{in} = \sigma_{out}$: $\frac{-Q}{4 \pi a^2} = \frac{q + Q}{16 \pi a^2}$ $-Q = \frac{q + Q}{4}$ $-4Q = q + Q$ $q = -5Q$.

$A$ solid spherical conducting shell has an inner radius $a$ and an outer radius $2a$. At the center of the shell is located a point charge $+Q$. What must the excess charge of the shell be in order for the charge density on the inner and outer surfaces of the shell to be exactly equal?

Similar Questions

The figure shows three concentric metallic spherical shells. The outermost shell has charge $q_2$,the innermost shell has charge $q_1$,and the middle shell is uncharged. The charge appearing on the inner surface of the outermost shell is

Consider two concentric spherical metal shells of radii $r_{1}$ and $r_{2}$ $(r_{2} > r_{1})$. If the outer shell has a charge $q$ and the inner one is grounded,the charge on the inner shell is

For a spherical shell,which of the following statements is correct?

Two charged conducting spheres of radii $a$ and $b$ are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:

$A$ conducting sphere of radius $10 \ cm$ is charged with $10 \ \mu C$. Another uncharged sphere of radius $20 \ cm$ is brought into contact with it and then separated. The ratio of the surface charge densities on the spheres will be ....... (in $: 1$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module