Two point charges lie along the y axis. A charge of q 1 = -10.0 µC isat y = 7.0

Question

Two point charges lie along the y axis. A charge ofq1 = -10.0 µC isat y = 7.0 m, and a charge ofq2 = -7.0 µC isat y = -1.0 m. Locate the point(other than infinity) at which the total electric field iszero.
I thought i was suppose to use the ke q1 q2 formula but imgetting the wrong answer Two point charges lie along the y axis. A charge ofq1 = -10.0 µC isat y = 7.0 m, and a charge ofq2 = -7.0 µC isat y = -1.0 m. Locate the point(other than infinity) at which the total electric field iszero.
I thought i was suppose to use the ke q1 q2 formula but imgetting the wrong answer

Explanation / Answer

Let p be a point on y axis which is at a distance d above thecharge q1 The electric field at point p due to charge q1is E1 = k * (q1/d2) k = (1/4o) = 9 * 109Nm2/C2 q1 = -10.0 C = -10.0 * 10-6C The electric field due to charge q2 is E2 = k * (q2/(d +8.0)2) q2 = -7.0 C = -7.0 * 10-6 C When the electric field at point p is zero then we have E1 + E2 = 0 or k * (q1/d2) + k * (q2/(d +8.0)2) = 0 or (q1/d2) = -(q2/(d +8.0)2) or -(d + 8.0/d)2 =(q2/q1) or -(d + 8.0/d) = (q2/q1)1/2 or -(1 + (8.0/d)) =(q2/q1)1/2 or (8.0/d)) = -((q2/q1)1/2 +1) or d = -(8.0/(q2/q1)1/2 +1)) The negative value of distance indicates that the point p isin the opposite direction. or -(1 + (8.0/d)) =(q2/q1)1/2 or (8.0/d)) = -((q2/q1)1/2 +1) or d = -(8.0/(q2/q1)1/2 +1)) The negative value of distance indicates that the point p isin the opposite direction.

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