In: Physics
Two point charges q and 2q lie on the x-axis. Which region(s) on the x-axis include a point where the electric field due to the two point charges is zero?
(a) To the right of 2q
(b) Between 2q and point P
(c) Between point P and q
(d) To the left of q
(e) Both (a) and (c)
(f) Both (b) and (d)
The expression used to find the value of electric field intensity is as follows,
E = kQ/r2
Here, k is the electrostatic constant, Q is the charge and is the point where electric filled intensity is to be calculated.
In between the charges the fields are in opposite directions. So their resultant field may be zero. Either left of the q or the right of the 2q fields due to the two charges are in the same direction. So their resultant field will never be zero.
Consider that the position where the resultant electric filed intensity is zero is x from right.
Field due 2q charge,
E2q = k(2q)/x2
Field due q charge,
Eq = k(q)/(3d – x)2
Since, the field is zero,
E2q = Eq
k(2q)/x2 = k(q)/(3d – x)2
On solving the above equation,
√2(3d – x) = 2
3√2d = x + √2x
Therefore,
x = 3√2d/√2 + 1
= 1.76d
So, the electric field intensity is zero in between 2q and point P.
Therefore, option (a), (c), (d), (e) and (f) is incorrect.
The correct option is (b).