Two Unequal Charges Two charged objects Q1 3Q and Q2 Q ar

Two Unequal Charges Two charged objects Q_1 = +3Q and Q_2 = - Q are separated by a distance D (Figure 23) Find a point near the objects where E = 0.

Solution

since the electric field is zero,

      E1 = E2

    k(3Q)/(D+x)^2 = kQ/(x - D)^2

3/(D+x)^2 = 1/(x - D)^2

Then,

(x - D)^2 = (1/3)(D+x)^2

        (x - D) = (1/sqrt(3))(D+x)

        sqrt(3)(x - D) = D+x

        sqrt(3)*x - sqrt(3)D = D+x

        [sqrt(3)-1]x = D + sqrt(3)D

                       x = {[sqrt(3) + 1] /[sqrt(3) - 1]}*D