Question

A positive point charge $q$ is carried from a point $B$ to a point $A$ in the electric field of a point charge $+Q$ at $O$. If the permitivity of free space is $\varepsilon_0$, the work done in the process is given by

• A. $\frac{ qQ }{4 \pi \varepsilon_{ o }}\left(\frac{1}{ a }+\frac{1}{ b }\right)$
• B. $\frac{ qQ }{4 \pi \varepsilon_{ o }}\left(\frac{1}{ a }-\frac{1}{ b }\right)$
• C. $\frac{ qQ }{4 \pi \varepsilon_0}\left(\frac{1}{ a ^2}-\frac{1}{ b ^2}\right)$
• D. $\frac{ qQ }{4 \pi \varepsilon_{ o }}\left(\frac{1}{ a ^2}+\frac{1}{ b ^2}\right)$

Answer 1

Answer: (B)

$W _{ BA }= q \left( V _{ A }- V _{ B }\right)$
$= q \left[\frac{ Q }{4 \pi \varepsilon_0 a }-\frac{ Q }{4 \pi \varepsilon_0 b }\right]=\frac{ qQ }{4 \pi \varepsilon_0}\left[\frac{1}{ a }-\frac{1}{ b }\right]$