Two conducting spheres of radii R1 and R2 are at the same potential. The electric intensities on their surfaces are in the ratio of

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Two conducting spheres of radii R₁ and R₂ are at the same potential. The electric intensities on their surfaces are in the ratio of

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R₂ : R₁

R₁: R₂

$R_{1}^{2} : R_{2}^{2}$

1 : 1

answer is C.

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Detailed Solution

As the spheres are at same potential

$\frac{1}{4 {πε}_{0}} \frac{Q_{1}}{R_{1}} = \frac{1}{4 {πε}_{0}} \frac{Q_{2}}{R_{2}}$

$\Rightarrow \frac{Q_{1}}{Q_{2}} = \frac{R_{1}}{R_{2}}$

So the ratio of electric fields will be given by $\frac{E_{1}}{E_{2}} = (\frac{Q_{1}}{Q_{2}}) {(\frac{R_{2}}{R_{1}})}^{2} = \frac{R_{2}}{R_{1}}$

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