Question

Which of the following quantities would be 0.5 times as greater at a distance of $2R$ from a point charge than it would be at a distance of $R$ from the charge?
I. Electric force on another point charge
II. Electric field due to the point charge
III. Electric potential due to the point charge

• A. I only
• B. II only
• C. III only
• D. I and II only
• E. I, II and III

Answer 1

The correct option is C III only

Given : $r=R$ $r^{\prime }=2R$

Initial electric force $F=\frac{K}{R^2}$ where $K=constant$

New electric force $F^{\prime }=\frac{K}{(2R{)}^2}=\frac{F}{4}$

Initial electric field $E=\frac{K^{\prime }}{R^2}$ where $K^{\prime }=constant$

New electric field $E^{\prime }=\frac{K^{\prime }}{(2R{)}^2}=\frac{E}{4}$

Initial electric potential $V=\frac{K^{\prime }}{R}$ where $K^{\prime }=constant$

New electric potential $V^{\prime }=\frac{K^{\prime }}{2R}=\frac{V}{2}$

$⟹$ Option C is correct.