Two conducting spheres of radii $r_{1}$ and $r_{2}$ are charged to the same surface charge density. The ratio of electric fields near their surface is :

{r_{1}}^{2} / {r_{2}}^{2}

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{r_{2}}^{2} / {r_{1}}^{2}

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r_{1} / r_{2}

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1 : 1

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Solution

The correct option is D $1 : 1$
As $σ_{1} = σ_{2}$
$\frac{Q_{1}}{4 π {r_{1}}^{2}} = \frac{Q_{2}}{4 π {r_{2}}^{2}} o r \frac{Q_{1}}{4 π {ε_{0} r}_{1}^{2}} = \frac{Q_{2}}{4 π {ε_{0} r}_{2}^{2}}$
$∴ E_{1} = E_{2} o r E_{1} / E_{2} \Rightarrow E : E_{2} = 1 : 1$

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