Two point particles, each having a charge equal to q, sit on the base of an equi

Question

Two point particles, each having a charge equal to q, sit on the base of an equilateral triangle that has sides of length L as shown in the figure below. A third point particle that has a charge equal to Q = 17q sits at the apex of the triangle. A fourth point particle that has charge q' is placed at the midpoint of the baseline making the electric field at the center of the triangle equal to zero. What is the value of q' ? (The center is in the plane of the triangle and equidistant from all three vertices.)

Explanation / Answer

Here,

let the length of side is a

distance of corner from centre , d = sqrt(3)/2 * a * 2/3

d = a/sqrt(3) = 0.577 * a

Now , for the electric field at the centre

k * q/d^2 * 2 * cos(60) - k * Q/d^2 + k * q'(d/2)^2 = 0

k * q/d^2 * 2 * cos(60) - k * 17 *q/d^2 + k * q'(d/2)^2 = 0

q/d^2 * 2 * cos(60) - 17 *q/d^2 + q'/(d/2)^2 = 0

q * 2 * cos(60) - 17 *q + 4*q' = 0

q - 17 * q + 4q' = 0

q' = 4 q

the charge that must be placed is 4 q

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