A) \[\sigma /{{\varepsilon }_{0}}\]
B) \[\frac{\sigma }{{{\varepsilon }_{0}}}\left( R-r \right)\]
C) \[\frac{\sigma }{{{\varepsilon }_{0}}}\left( R+r \right)\]
D) None of these
Correct Answer: C
Solution :
[c] Charge on the outer sphere \[={{q}_{1}}=4\pi {{R}^{2}}\sigma \] Charge on the inner sphere \[={{q}_{2}}=4\pi {{r}^{2}}\sigma \] \[v=\frac{1}{4\pi {{\in }_{0}}}\frac{{{q}_{1}}}{R}+\frac{1}{4\pi {{\in }_{0}}}\frac{{{q}_{2}}}{r}\] \[=\frac{1}{4\pi {{\in }_{0}}}\left[ \frac{4\pi {{R}^{2}}\sigma }{R}+\frac{4\pi {{r}^{2}}\sigma }{r} \right]\] \[=\frac{4\pi \sigma }{4\pi {{\in }_{0}}}\left( R+r \right)=\frac{\sigma }{{{\in }_{0}}}\left( R+r \right)\]You need to login to perform this action.
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