A small sphere of radius r1 and charge q1 is enclosed by a spherical shell of radius r2 and charge q2. Show that if q1 is positive, the charge will necessarily flow from the sphere to the shell (when the two are connected by a wire) no matter what the charge q2 on the shell is
Potential of inner sphere due to charge q1=V1=4π∈01r1q1 Potential of inner sphere due to the enclosed ophere, V2=4π∈01r2q2 Thus, Total potential of inner sphere, V=V1+V2 =4π∈01(r1q1)+4π∈01(r2q1) =4π∈01(r1q1+r2q1) and, potential of shell =V′=4π∈01r2q2 Potential difference between inner sphere and shell =V−V′ =4π∈01(r1q1+r2q2)−4π∈01(r2q2) =4π∈01[r1q1+r2q2−r2q2] =4π∈01r1q1 We can see, from above eqn q1 is positive i.e (q1>q2) Since, from the above equation, potential difference does not depend on q2. So, when inner sphere A is connected to outer shell B, the charge will flow from inner sphere A to outer shell B.
