Electrostatics Question 787

Question: Two concentric conducting spherical shells of radii $ a _{1} $ and $ a _{2} $

$ (a _{2}>a _{1}) $ are charged to potentials $ {\phi _{1}} $ and $ {\phi _{2}} $ , respectively. Find the charge on the inner shell.

Options:

A) $ q _{1}=4\pi {\varepsilon _{0}}( \frac{{\phi _{1}}-{\phi _{2}}}{a _{2}-a _{1}} )a _{1}a _{2} $

B) $ q _{1}=4\pi {\varepsilon _{0}}( \frac{{\phi _{1}}+{\phi _{2}}}{a _{2}+a _{1}} )a _{1}a _{2} $

C) $ q _{1}=4\pi {\varepsilon _{0}}( \frac{{\phi _{1}}-{\phi _{2}}}{a _{2}+a _{1}} )a _{1}a _{2} $

D) $ q _{1}=4\pi {\varepsilon _{0}}( \frac{{\phi _{1}}+{\phi _{2}}}{a _{2}-a _{1}} )a _{1}a _{2} $

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Answer:

Correct Answer: A

Solution:

[a] $ {\phi _{1}}=\frac{kq _{1}}{a _{1}}+\frac{kq _{2}}{a _{2}} $

$ {\phi _{2}}=\frac{kq _{1}}{a _{2}}+\frac{kq _{2}}{a _{2}} $ Solve to get $ q _{1}=4\pi {\varepsilon _{0}}[ \frac{{\phi _{1}}-{\phi _{2}}}{a _{2}-a _{1}} ]a _{1}a _{2} $



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