A) \[\frac{qQ}{4\pi {{\varepsilon }_{0}}}\left( \frac{a-b}{ab} \right)\]
B) \[\frac{qQ}{4\pi {{\varepsilon }_{0}}}\left( \frac{b-a}{ab} \right)\]
C) \[\frac{qQ}{4\pi {{\varepsilon }_{0}}}\left( \frac{b}{{{a}^{2}}}-\frac{1}{b} \right)\]
D) \[\frac{qQ}{4\pi {{\varepsilon }_{0}}}\left( \frac{a}{{{b}^{2}}}-\frac{1}{b} \right)\]
Correct Answer: A
Solution :
(a) \[\frac{qQ}{4\pi {{\varepsilon }_{0}}}\left( \frac{a-b}{ab} \right)\] Potential at point A is \[{{V}_{A}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{q}{a}\] Potential at point B is \[{{V}_{B}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\left[ \frac{1}{b}-\frac{1}{a} \right]\] Work done in taking a charge Q from A to B is \[W=Q\left( {{V}_{B}}-{{V}_{A}} \right)=\frac{Qq}{4\pi {{\varepsilon }_{0}}}\left[ \frac{1}{b}-\frac{1}{a} \right]\] \[=\frac{Qq}{4\pi {{\varepsilon }_{0}}}\left[ \frac{a-b}{ab} \right]\]
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