Question

Two point charges, Q1 = 3.6 μC and Q2 = -1.8 μC , are placed on the x axis. Suppose that Q2 is placed at the origin, and Q1 is placed at the coordinate x1 = − 6.0 cm At what point(s) along the x axis is the electric field zero? Determine the x-coordinate(s) of the point(s). At what point(s) along the x axis is the potential zero? Determine the x-coordinate(s) of the point(s).

Answer 1

Here since Q2 has smaller magnitude, the point has to be right side of Q2 (point should be nearer to Q2 than to Q1 in order to cancel the field due to other)

Electric field E = kQ1/[x-x1]^2 + kQ2/[x-0]^2 = 0

3.6/[x- -6]^2 -1.8/x^2 = 0

2/[x+6]^2 = 1/x^2

x = 14.485 cm answer

For potential to be zero, the addition will be a scalar addition, therefore two such points will be there, one between the charges, other on the side of lesser magnitude charge.

V = kQ1/[x-x1] +kQ2/x = 0

3.6/[x- -6] -1.8/x = 0 and 3.6/[x- -6] -1.8/(-x) = 0

x= 6 cm and x=-2 cm Answer