Two points charges of `+20 muC and + 80 muC` are plaed 18 cm apart. Find the position of the point where electric field is zero.

Explanation

Let the two charges `q_1 = - 80 muC and q_2 = + 20 muC` lie at A and B.
`AB = r = 18` cm
Let C is the point at distance x from B and so `BC = x `and `AC = r + x = 18 + x `
`E_1 = 1/(4 pi in_0)(q_1)/(AC^2)` along CX
and `E_2` = Electric field at C due to `q_2` at B.
`E_2 = 1/(4pi in_0) (q_2)/(BC^2)` along CB.
According to question
`E_1 = E_2`
`1/(4 pi in_0) (q_1)/(AC^2) = 1/(4pi in_0) (q_2)/(BC^2)`
`implies (80 xx 10^(-6))/((18 + x)^2) = (20 xx 10^(-6))/(x^2)`
`implies 4/((18 + x)^2) = 1/(x^2)`
Taking square root on both sides
`2/(18 + x) = 1/x`
`implies 2x = 18 + x`
`x = 18 `cm form charge `20 mu C` lying at B.