Question

Two charges q and –2q are kept on a straight line. the number of points on this line where the electric potential is zero, is

Answer 1

There are two points where potential is zero.

Case 1 :- q --------------•A--------- -2q
Let A is the point where potential is zero.
Let distance between q and -2q = r
and distance between q and A = x
∴ distance between -2q and A = (r - x)

Potential at A = Kq/x + K(-2q)/(r - x)
⇒0 = k[ q/x - 2q/(r - x) ]
⇒1/x = 2/(r - x)
⇒r - x = 2x
⇒ r/3 = x

Hence, potential is zero at x = r/3

Case 2 :- q---------------------- -2q ----------• B
let B is the point where potential is zero.
Let distance between -2q and B = x
∴ distance between q and B = (r + x)

Now, potential at B = kq/(r + x) + k(-2q)/x
⇒0 = kq/(r + x) - 2kq/x
⇒1/(r + x) = 2/x
⇒ x = 2r + 2x
⇒ x = -r but x is distance so, x ≠ -r

Case 3 :- C ----------q------------------ -2q
distance between q and C = x
∴ distance between -2q and C = (r + x)
Now, potential = kq/x - 2kq/(r + x)
⇒0 = 1/x - 2/(r + x)
⇒1/x = 2/(r + x)
⇒2x = r + x
⇒x = r

Hence at x = r potential will be zero.

So, there are two points