Question

An electric point charge q= +4μC is located at the origin of coordinate axes. Another point charge q0 = -1 μC is carried from point A(0,2) cm to point C(3,0) cm via point B(4,3) cm. Find the net amount of work done.

Answer 1

Given :

Magnitude of the point charge q located at the origin of coordinate axes = 4$\muC$$\mu C$

Magnitude of the other charge $q_0$ = -1$\mu C$

$q_0$  is carried from point A(0,2) cm to point C(3,0) cm via point B(4,3) cm.The

To Find :

What is the net amount of work done in this process = ?

Solution :

We know that the total amount of work done in moving a charge from one point to another is equal to the change in potential energy taking place .

Now potential at point C (3,0) =$\frac{K \times 4 \times (-1)}{3}$

                                                 =$\frac{-4}{3} K$

And potential at point A (0,2) =$\frac{K \times 4 \times (-1)}{2} = -2K$

Here ,  $K = \frac{1}{4 \pi \epsilon_0}$

So, the change in potential energy  = Potential at (0,2) - potential at (3,0)

=$-2K - \frac{-4}{3}K = -2K + \frac{4}{3}K = \frac{-2}{3} K$

=$\frac{-2}{3} \times J9 \times 10^9 J = -6 \times 10^9 J$

Hence, the total work done is $-6 \times 10^9 J$ .