Two particles A and B having charges of `+2.00 xx 10^(-6) C` and of `- 4.00xx 10^(-6)` respectively are held fixed at a separation of 20.0 cm . Locate the point(s) on the line AB where (a) the electric field is zero (b) the electric potential is zero.

Explanation

` q_1=2.0xx10^-6C, `
` q_2=-4.0xx10^-6 `
(a) Let at the distance x from A, electric field is zero
` 1/(4piepsilon_0)q_1/x^2+q_2/(4piepsilon_0(0.2+x))=0 `
` or, 2/x^2+(-4)/(0.2+x)^2=0 `
` or, x=48.3cm from A along BA `
(b) Let the potential is zero at distance x from A
` 1/(4piepsilon_0)q_1/x+1/(4piepsilon_0)q_2/((0.2-x))=0 `
` or 2/x(-4)/((0.2-x))=0 `
` or 2(0.2-x)-4x=0 `
` x=20/3cm from A along AB `
` and x=20cm from A along BA`.