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Solution :

If point P is at a distance `r_(1)` from point charge +q and `r_(2)` from charge `-2 q( Fig . 3.8)`, then <br> `V_P = V_1 + V_2 = (1)/(4 pi epsilon _0)[(+q )/r_(1)+(-2 q)/r_(2)]` <br> According to the problem, `V_P = 0, i.e.,` <br> `q/r_(1) - (2 q)/r_(2) = 0` <br> or `r_2 = 2r_1` (i) <br> But if the charge q is assumed to be situated at the origin, then <br> `r_1^2 = x^2 + y^2 and r_2 ^2 = (6 -x)^2 + y^2` <br> So substituting these values of `r_(1)` and `r_(2)` in Eq. (i), we get <br> `(x + 2)^2 + y^2 = 16` <br> So the locus of the point P is a circle with radius 4 m and center `(- 2, 0)`.