 |
| Numerical 03 |
|
| 03. If a piece of metal has a charge +0.1mC and is placed inside a hollow metal sphere of radius 20 cm (with touching it), what is the potential of the sphere? What will the potential of the sphere become, if a) the sphere is temporarily Earthed and then left insulated? |
| |
| b) if the metal subsequently touched the inside of the sphere? |
| |
| Suggested answer: |
| |
| Induced charge of -0.1mC and 0.1mC are induced on the inner surface and outer surface respectively of the sphere. The potential of the sphere relative to Earth is determined solely by the outer surface charge q. |
| |
 |
| |
| |
| |
| where r is the radius of the sphere |
| |
| Now, |
| |
 |
| |
| (a) When the sphere is momentarily Earthed, its potential is reduced to zero. The positive charge on the outer surface disappears but the induced negative charge inside remains. So, the potential of the sphere is zero. |
| |
| Note: There is a potential difference between the sphere and the metal holding the charge inside so that the alter has a positive potential relative to the sphere. |
| |
 |
| |
| (b) When the metal touches the sphere, the induced negative charge and the metal holding the charge inside, both are at the same potential i.e., zero potential. |
| |
