Two point charges 8q and 2q are located at x=0 and x=L respectively. The location of a point on the X-axis from origin, at which the net electric field is zero, is x . Value of x is equal to

Step-by-step solution

Let the point where the net electric field is zero be at a distance x from the origin. Since both charges are positive, the null point must lie between them. The distance of this point from the charge 8q is x and from the charge 2q is L - x . Equating the magnitudes of the electric fields produced by both charges at this point: k(8q) x^2 = k(2q) (L - x)^2 4 x^2 = 1 (L - x)^2 Taking the square root on both sides: 2 x = 1 L - x 2(L - x) = x 2L - 2x = x 3x = 2L x = 2L 3 Answer: 2L 3