Question

Two charges 4C and -2C are placed at a distance of 200 cm apart. Which of these points have zero electric potential?

• A. On the line joining the two charges, at 200/3 cm from 4C charge
• B. On the line joining the two charges, at 200 cm from -2C charge
• C. On the line joining the two charges, at 200/3 cm from -2C charge
• D. No such point exists

Answer 1

Answer: (B), (C)

On the line joining the two charges, at 200/3 cm from -2C charge

Let’s think about this. There is a positive charge and a negative charge; they will “produce” positive and negative potential respectively so there is a possibility for the net potential to be zero. As $V=\frac{kQ}{r}$ and Q i.e. charge is fixed here, only r can change; it becomes clear that the point of zero potential will be the one closer to the smaller charge (the denominator must be smaller as the numerator is already smaller). So let’s take a point P at a distance x as shown

The potential at $P=k.\frac{4}{2-x}+k.\frac{-2}{x}$
{notice how I use the distance in S.I units. Remember that in electromagnetism it is recommended to work in S.I units all the time}
Now we want the potential at P to be zero i.e.
$k.\frac{4}{2-x}+k.\frac{-2}{x}=0$
$x=\frac{2}{3}m=\frac{200}{3}cm.$ But as this question is a multiple answer question there can be more correct answers. Let us check if we have exhausted all the possibilities. Can there be a point like P on the other side of charge -2C charge? Let’s check out

Now, in this case. The potential at P
$k.\frac{4}{2+x}+k.\frac{-2}{x}$
and this has to be equated to zero
$k.\frac{4}{2+x}+k.\frac{-2}{x}=0$
$\Rightarrow$ x = 2m or 200/3 cm.