Question

A conducting sphere of radius R, carrying charge Q, lies inside an uncharged conducting shell of radius $2$R. If they are joined by a metal wire.

• A. $Q/3$ amount of charge will flow from the sphere to the shell
• B. $2Q/3$ amount of charge will flow from the sphere to the shell
• C. $Q$ amount of charge will flow from the sphere to the shell
• D. $k\frac{Q^2}{4R}$ amount of heat will be produced

Answer 1

Answer: (C), (D)

The correct options are
C $Q$ amount of charge will flow from the sphere to the shell
D $k\frac{Q^2}{4R}$ amount of heat will be produced

When conducting sphere of charge Q is placed inside conducting spherical shell the will appear on the surface of the shell. So Q amount of charge will flow from the sphere to the shell through the wire.

By conservation of energy the electrostatic energy of shell will transfer into heat.

The potential at the surface of shell is $V=k\frac{Q}{2R}$

The electrostatic energy is $W=\frac{1}{2}\int V\sigma ds=k\frac{Q}{4R}\int \sigma ds=k\frac{Q}{4R}.Q=k\frac{Q^2}{4R}$