Question

One unknown charge is located at the origin and another charge of -6 micro-coulombs is located at x = + 0.3 m, y = 0 m. If at the point x = 0, y = +0.4m, the total electric potential is +7.8 x 10⁴ V, what is the unknown charge at the origin in micro-coulombs? If negative, include a negative sign.

Answer 1

Electric potential is a scalar quantity which is given by:

V = k*Q/R

Net electric potential at the point P will be:

V_net = V1 + V2 = k*q1/r1 + k*q2/r2

Given that: q1 = q at (0, 0) m

q2 = -6*10^-6 C at (0.3, 0) m

P (0, 0.4) m

V_net = 7.8*10^4 V

r1 = distance between q1 and P = 0.4 m

r2 = distance between q2 and P = sqrt (0.3^2 + 0.4^2) = 0.5 m

So,

7.8*10^4 = 9*10^9*q/0.4 - 9*10^9*6*10^-6/0.5

q = (0.4*10^-9/9)*(7.8*10^4 + 10.8*10^4)

q = 8.27*10^-6 C = +8.27 micro-coulombs = +8.27 C = Unknown charge

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