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} $
Show Answer
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} $
