| A metal sphere having radius r, charged to a potential V is enveloped by a thin walled conducting spherical shell of radius 4r asymmetrically. |
 |
| Sphere is connected with shell by a conducting wire for a short time, then connection is removed. |
| Potential of sphere after removing connecting wire is |
A) \[V\]
B) \[\frac{V}{2}\]
C) \[4V\]
D) \[\frac{V}{4}\]
Correct Answer: D
Solution :
| Charge on inner sphere is \[q=4\pi {{\in }_{0}}\cdot V\cdot r\] |
| When sphere is connected to shell, whole of the charge is transferred to outer shell. So, potential of sphere inside shell will be potential of any inner point of shell. As, potential at any interior point of shell is equal to its surface potential, final potential of sphere is |
| \[{{V}_{2}}=\frac{q}{4\pi {{\in }_{0}}(4r)}=\frac{4\pi {{\in }_{0}}Vr}{4\pi {{\in }_{0}}4r}=\frac{V}{4}\] |
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