Question

In the electric field of charge $Q$, another charge is carried from $\text{A}$ to $\text{B}$, $\text{A}$ to $\text{C}$, $\text{A}$ to $\text{D}$ and $\text{A}$ to $\text{E}$, then work done will be:

• A. minimum along the path $\text{AB}$
• B. minimum along the path $\text{AD}$
• C. minimum along the path $\text{AE}$
• D. zero along each path

Answer 1

The correct option is D zero along each path

As we know that work done by external agent in potential difference $\Delta V$ is given by

$W=q_0\Delta V$

Here, $q_0$ is the test charge

In the given question, source charge is at the centre, so potential $V$ will be the same for all the points because of circumferential points.

$\therefore V_{circm}=\left(\frac{kQ}{R}\right)=V_A=V_B=V_C=V_D=V_E$

So, $\Delta V(=V_{cirm}-V_A)$ for each path given $\text{AB or AD or AE}=0$

Since $\left(\Delta V\right)$ for all given path is zero.

So work done, $W=q_0\Delta V=0$, for all path.

Why this question: To relate workdone with change in potential energy.