Question

Two conducting sphere of radii r₁ and r₂ are equally charged then the ratio of their potential is

Answer 1

Step 1: Given

The radius of sphere 1 and sphere 2 is r₁ and r₂ respectively.

V is electric potential on sphere 1 and sphere 2 is V₁ and V₂ respectively.

Step 2: Formula used

Potential due to conducting sphere(V)=$\frac{Q}{\text{4πϵ}r}$ (where Q is charge, V is electric potential on the sphere).

Step 3: Finding the ratio of their potential

As both sphere equally charged so Q is constant and V∝$\frac{1}{r}$

Hence, V*r=constant,

V₁r₁=V₂r₂

$\frac{V_1}{V_2}=\frac{r_2}{r_1}$

Hence, the ratio of their potential is $\frac{r_2}{r_1}$.