question_answer

As per this diagram a point charge + q is placed at the origin O. Work done in taking another point  charge -Q from the point A [co-ordinates (0, a)] to another point B [co-ordinates (a, 0)] along the straight path AB is

A)  Zero                

B) \[\left( \frac{-qQ}{4\pi {{\varepsilon }_{0}}}\frac{1}{{{a}^{2}}} \right)\sqrt{2}\,a\]

C)  \[\left( \frac{qQ}{4\pi {{\varepsilon }_{0}}}\frac{1}{{{a}^{2}}} \right)\frac{a}{\sqrt{2}}\]          

D) \[\left( \frac{qQ}{4\pi {{\varepsilon }_{0}}}\frac{1}{{{a}^{2}}} \right)\sqrt{2}\]

Correct Answer: A

Solution :

Potential at A \[{{V}_{A}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{q}{a}\] Potential at B \[{{V}_{B}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{q}{a}\] Thus, work done in carrying a test charge - Q from  A to B \[W=({{V}_{A}}-{{V}_{B}})(-Q)=0\]