Question

Work done in carrying 2 C charge in a circular path of radius 2 m around a charge of 10 C is _________.

Answer 1

Step 1: Given parameters

Radius of circular path, $r=2\mathrm{m}$.

Charge, $q=2\mathrm{C}$

Step 2: Formula used

Calculate the work done in carrying a charge $q$in circular path by using the formula given as,

$W=qdV...\left(1\right)$

Here. $q$ is the charge, and $dV$ is the change in potential.

Step 3: Concept used

1. A force is said to be conservative, if the work done over any closed path is zero.
2. It does not depend on the path.
3. Work done over a closed-loop for conservative force is zero.

Step 3: Calculation

As we know that the potential is same at each point in a circular orbit. Thus, $dV=0$

Substitute the given values in equation (1).

$$\begin{gathered} W=qdV \\ =\left(2\right)\left(0\right) \\ =0 \end{gathered}$$

Hence, for a conservative force work done over a closed loop is zero.