A charge Q1 = 0.1 μC is located at the origin, while Q2 = 0.2 μC is at A(0.8,−0.6, 0). Find the
locus of points in the z = 0 plane at which the x component of the force on a third positive charge is
zero.
To solve this problem, the z coordinate of the third charge is immaterial, so we can place it in the
xy plane at coordinates (x, y, 0). We take its magnitude to be Q3. The vector directed from the first
charge to the third is R13 = xax + yay ; the vector directed from the second charge to the third is
R23 = (x − 0.8)ax + (y + 0.6)ay . The force on the third charge is now