Question

Two charged spheres of radius $R_{1}$ and $R_{2}$ respectively are charged and joined by a wire. The ratio of electric field of the spheres is

• A. $\frac{R_{1}}{R_{2}}$
• B. $\frac{R_{2}}{R_{1}}$
• C. $\frac{R_{1}^{2}}{R_{2}^{2}}$
• D. $\frac{R_{2}^{2}}{R_{1}^{2}}$

Answer 1

Answer: (B)

$\frac{R_{2}}{R_{1}}$

Answer 2

After connection their potential becomes equal i.e.,

$k.\frac{Q_{1}}{R_{1}} = \frac{k.Q_{2}}{R_{2}}$; ⇒ $\frac{Q_{1}}{Q_{2}} = \frac{R_{1}}{R_{2}}$

Ratio of electric field $\frac{E_{1}}{E_{2}} = \frac{Q_{1}}{Q_{2}} \times \left( \frac{R_{2}}{R_{1}} \right)^{2} = \frac{R_{2}}{R_{1}}.$