| ASSERTION: The surface densities of two spherical conductors of different radii are equal. Then the electric field intensities near their surface are also equal. |
| REASON: Surface density is equal to charge per unit area. |
A) If both assertion and reason are true and reason is the correct explanation of assertion.
B) If both assertion and reason are true and reason is not the correct explanation of assertion.
C) If assertion is true but reason is false.
D) If both assertion and reason are false.
E) If assertion is false but reason is true.
Correct Answer: B
Solution :
As \[{{\sigma }_{1}}={{\sigma }_{2}}\](given) \[\therefore \,\,\,\frac{{{q}_{1}}}{4\pi r_{1}^{2}}=\frac{{{q}_{2}}}{4\pi r_{2}^{2}}\] 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 conductors, \[\frac{{{E}_{1}}}{{{E}_{2}}}=\frac{{{q}_{1}}}{4\pi {{\varepsilon }_{0}}r_{1}^{2}}\times \frac{4\pi {{\varepsilon }_{0}}r_{2}^{2}}{{{q}_{2}}}=\frac{{{q}_{1}}}{q{{ & }_{2}}}\times \frac{r_{2}^{2}}{r_{1}^{2}}=\frac{{{q}_{1}}}{{{q}_{2}}}\times \frac{{{q}_{2}}}{{{q}_{1}}}=1\] i.e. \[{{E}_{1}}={{E}_{2}}\].
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