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} $



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