Question

wo equal positive charges are kept at points A and B. Then electric potential at the points between Aand
B (excluding these points) is studied while moving from A to B. The potential
(1) continuously increases
(2) continuously decreases
(3) increases then decreases
(4) decreases then increases
​

Answer 1

Given that,

Two equal positive charges are kept at points A and B.

Let the distance between  A and B be d.

The potential at any distance x from point A is

$V=\dfrac{kq}{x}+\dfrac{kq}{d-x}$

$V=kq(\dfrac{1}{x}+\dfrac{1}{(d-x)})$

On differentiating

$\dfrac{dV}{dx}=\dfrac{kqd(2x-d)}{(x(x-d))^2}$

If $x<\dfrac{d}{2}$ then $\dfrac{dV}{dx}<0$

Therefore, potential decrease.

If $x>\dfrac{d}{2}$ then $\dfrac{dV}{dx}>0$

Therefore, potential increases.

Hence, The potential is decreases and increases.

(4) is correct option.