Electrostatics Question 252
Question: A metallic shell has a point charge -q? kept inside its cavity. Which one of the following diagrams correctly represents the electric lines of forces [IIT-JEE (Screening) 2003]
Options:
A) x
B) $ x^{2} $
C) $ x^{3} $
D) $ 1/x $
Show Answer
Answer:
Correct Answer: B
Solution:
Initially (i) potential energy of Q is $ U _{i}=\frac{2kqQ}{a} $ ……(i) (ii)
when charge Q is displaced by small distance x then it’s potential energy now $ U _{f}=kqQ[ \frac{1}{(a+x)}+\frac{1}{(a-x)} ] $
$ =\frac{2kqQa}{(a^{2}-x^{2})} $ …….(ii)
Hence change in potential energy $ \Delta U=U _{f}-U _{i}=2kqQ[ \frac{a}{a^{2}-x^{2}}-\frac{1}{a} ] $
$ =\frac{2kqQx^{2}}{(a^{2}-x^{2})} $
Since x « a so $ \Delta U=\frac{2kqQx^{2}}{a^{2}}\Rightarrow \Delta U\propto x^{2} $
