Read the assertion and reason carefully to mark the correct option out of the options given below:
Assertion : The surface charge densities of two spherical conductors of different radii are equal. Then the electric field intensities near their surface are also equal.
Reason : Surface charge density is equal to charge per unit area.

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If both assertion and reason are true and the reason is the correct explanation of the assertion.

If the assertion and reason both are false.

If assertion is true but reason is false.

If both assertion and reason are true but reason is not the correct explanation of the assertion.

answer is B.

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Detailed Solution

As $σ_{1} = σ_{2}$ (Given) $∴ \frac{q_{1}}{4 π r_{1}^{2}} = \frac{q_{2}}{4 π r_{2}^{2}}$ , or $\frac{q_{1}}{q_{2}} = \frac{r_{1}^{2}}{r_{2}^{2}}$ [Let $r_{1}$ and $r_{2}$ be two different radii]
Then the ratio of electric field intensities near the surface of spherical conductor,
$\frac{E_{1}}{E_{2}} = \frac{q_{1}}{4 π ε_{0} r_{1}^{2}} \times \frac{4 π ε_{0} r_{2}^{2}}{q_{2}} = \frac{q_{1}}{q_{2}} \times \frac{r_{2}^{2}}{r_{1}^{2}} = 1 or E_{1} = E_{2}$