A metal sphere having a radius r1 charged to a potential V1 is enveloped by a thin-walled conducting spherical shell of radius r2. Determine the potential V 2 acquired by the sphere after it has been connected for a short time to the shell by a conductor.

Question

A metal sphere having a radius r1 charged to a potential V1 is enveloped by a thin-walled conducting spherical shell of radius r2. Determine the potential V 2 acquired by the sphere after it has been connected for a short time to the shell by a conductor. (A) (V1 r2/r1) (B) (V1 r1/r2) (C) V 1 (D) (V1(r1+r2)/r2)

Tardigrade Admin · Accepted Answer

Charge on the metal sphere: v1=(k q/r1) ⇒ q=(v1 r1/k) . On connecting the sphere with shell, entire charge will be transferred to the shell. So, potential of sphere now is V 2=( kq / r 2)=( V r r 1/ r 2)

Q. A metal sphere having a radius $r_{1}$ charged to a potential $V_{1}$ is enveloped by a thin-walled conducting spherical shell of radius $r_{2}$ . Determine the potential $V_{2}$ acquired by the sphere after it has been connected for a short time to the shell by a conductor.

$\frac{V _{1} r _{2}}{r _{1}}$

$\frac{V _{1} r _{1}}{r _{2}}$

$V_{1}$

$\frac{V _{1} ( r _{1} + r _{2} )}{r _{2}}$

Charge on the metal sphere : $v_{1} = \frac{k q}{r _{1}}$
$\Rightarrow q = \frac{v _{1} r _{1}}{k} .$
On connecting the sphere with shell, entire charge will be transferred to the shell. So, potential of sphere now is
$V_{2} = \frac{k q}{r _{2}} = \frac{V _{r} r _{1}}{r _{2}}$

Q. A metal sphere having a radius r1​ charged to a potential V1​ is enveloped by a thin-walled conducting spherical shell of radius r2​. Determine the potential V2​ acquired by the sphere after it has been connected for a short time to the shell by a conductor.

r1​V1​r2​​

r2​V1​r1​​

V1​

r2​V1​(r1​+r2​)​