Electrostatics Question 767

Question: Two concepts spheres of radii R and r have similar charges with equal surface charge densities $ ( \sigma ). $ what is the electric potential at their common center?

Options:

A) $ \sigma /{\varepsilon _{0}} $

B) $ \frac{\sigma }{{\varepsilon _{0}}}( R-r ) $

C) $ \frac{\sigma }{{\varepsilon _{0}}}( R+r ) $

D) None of these

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Answer:

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}}}[ \frac{4\pi R^{2}\sigma }{R}+\frac{4\pi r^{2}\sigma }{r} ] $

$ =\frac{4\pi \sigma }{4\pi {\in _{0}}}( R+r )=\frac{\sigma }{{\in _{0}}}( R+r ) $



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