A) \[\frac{\sigma }{2{{\in }_{0}}}\left[ {{\left( {{r}^{2}}+{{R}^{2}} \right)}^{1/2}}-r \right]\]
B) \[\frac{\sigma }{2{{\in }_{0}}}\left[ R-r \right]\]
C) \[\frac{\sigma }{8{{\in }_{0}}}\left[ {{\left( {{r}^{2}}+{{R}^{2}} \right)}^{1/2}}-r \right]\]
D) none of these
Correct Answer: C
Solution :
[c] The potential at P due to whole disc is \[V=\frac{\sigma }{2{{\in }_{0}}}\left[ \sqrt{{{R}^{2}}+{{r}^{2}}-r} \right].\] Now potential due to quarter disc, \[V=\frac{V}{4}=\frac{\sigma }{8{{\in }_{0}}}\left[ \sqrt{{{R}^{2}}+{{r}^{2}}-r} \right].\]
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