Question

Charge $+q$ and $-q$ are placed at points $A$ and $B$ respectively which are at distance $2L$ apart, $C$ is the midpoint between $A$ and $B$. The work done in moving a charge $+Q$ along the semicircle $CRD$ is:

• A. $\frac{1}{2}(\frac{q}{{\epsilon }_0}-\varphi )$
• B. $\frac{q}{2{\epsilon }_0}$
• C. $\frac{q}{{\epsilon }_0}$
• D. $\frac{q}{{\epsilon }_0}-\varphi$

Answer 1

The correct option is A $\frac{1}{2}(\frac{q}{{\epsilon }_0}-\varphi )$

Let electric flux linked with surfaces A, B,and C are ${\varphi }_A,{\varphi }_B,{\varphi }_C$ respectiely

thus total ${\varphi }_{total}={\varphi }_A+{\varphi }_B+{\varphi }_C$

we know ${\varphi }_A={\varphi }_C$ and ${\varphi }_{total}=\frac{q}{{ϵ}_o}$

${\varphi }_{total}=2{\varphi }_A+{\varphi }_B$ but ${\varphi }_B=\varphi$

Hence $\frac{q}{{ϵ}_o}=2{\varphi }_A+\varphi$

or. $2{\varphi }_A=\frac{q}{{ϵ}_o}-\varphi$

${\varphi }_A=\frac{1}{2}(\frac{q}{{ϵ}_o}-\varphi )$