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
Show Answer
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 ) $
