Question

Two charges `q_(1) and q_(2)` are placed at (0,0,d) and (0,0,-d) respectively. Find locus of points where the potential is zero.

Answer 1

Let any arbitrary point on the requ ired plane is (x,y,z). The two charges lies on z-axis at a separation of 2d. ltBrgt The potential at the point P due to two charges is given by
`(q_(1))/(sqrt(x^(2)+y^(2)+(z-d)^(2)))+(q_2)/(sqrt(x^(2)+y^(2)+(z+d)^(2)))=0`
`therefore(q_(1))/(sqrt(x^(2)+y^(2)+(z-d)^(2)))=(-q_(2))/(sqrt(x^(2)+y^(2)+(z+d)^(2)))`
On squaring and simplifying we get
`x^(2)+y^(2)+z^(2)+[((q_(1)//q_(2))^(2)+1)/((q_(1)//q_(2))^(2)-1)](2zd)+d^(2)-0`
This is the equation of a sphere with centre at
`(0,0,-2d[(q_(1)^(2)+q_(2)^(2))/(q_(1)^(2)-q_(2)^(2))])`