Question

125 identical charged small spheres coalesce to form a big charged sphere. If the electric potential on each small sphere is 60 mV, then the electric potential on the bigger sphere formed is:

• A. \( 30 \) V
• B. \( 15 \) V
• C. \( 1.5 \) V
• D. \( 3 \) V

Hint:

When small spheres merge to form a larger sphere, the total charge increases linearly, but the radius increases proportionally to the cube root of the number of spheres.

Answer 1

The Correct Option is C

Step 1: Define the Potential Relation for a Sphere The electric potential on a sphere is given by: \[ V = \frac{Q}{R} \] When 125 spheres merge, the total charge increases by a factor of 125, while the radius increases by a factor of: \[ R_{\text{new}} = R_{\text{old}} \times 125^{1/3} = 5 R \]
Step 2: Compute the New Potential Since \( V \propto \frac{Q}{R} \), the new potential is: \[ V_{\text{new}} = \frac{60 \text{ mV} \times 125}{5} = 1.5 \text{ V} \]