Two point charges of - `16muC` and + `9muC` are placed 8 cm apart in air. Determine the point at which resultant electric field is zero.

Explanation

Let two charges `- 16 muc, 9 muc` lie at A and B respectively.
`AB = r = 8 cm `
Consider a point C at distance x from B, where resultant electric field is zero.
Let `E_1` = Electric field at C due to `- 16 muC` lying at A.
So `E_1 = 1/(4 pi epsilon_0) (q_1)/(AC^2)` along CB
But `AC = r + x = 8 + x`
and `E_2` = Electric field at C due to `9 mu` lying at B.
`E_1 = 1/(4pi in_0) (q_1)/(BC^2)` along CX
According to question
`E_1 = E_2`
`implies 1/(4pi in_0) (q_1)/(AC^2) = 1/(4 pi in_0) (q_2)/(BC^2)`
`implies (16 xx 10^(-6))/((8 + x)^2) = (9 xx 10^(-6))/(x^2)`
Taking square root on both sides
`4/(8 + x) - 3/x`
`implies 4x = 24 + 3x implies x = 24 cm`