Question

A hollow sphere of radius 2r is charged to v volts and another smaller sphere of radius r is charged to v/2 volts. Then the smaller sphere is placed inside the bigger sphere without changing the net charge on each sphere. The potential difference between the two spheres would be :

Answer 1

Answer:

The potential difference between two spheres is equal to V/4.

Explanation:

Given that the radius of smaller sphere is r and the radius of bigger sphere is 2R. Smaller sphere  got charged to v volts and bigger one  charged to v/2 volts.

Charge on the smaller sphere: $q=C(\frac{V}{2})$

                  $q=\frac{4\pi \epsilon_{o}RV}{2}$

                 $\frac{q}{4\pi \epsilon_{o}}= \frac{RV}{2}$

So the potential difference b/w the two spheres:

              $=\frac{q}{4\pi \epsilon}_{o}(\frac{1}{R} -\frac{1}{2R} )$

               $=\frac{VR}{2}(\frac{1}{2R})\\ \\ =\frac{V}{4}$

Therefore the potential difference would be V/4.