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

Explanation

Data supplied, `q_(1)=20 xx 10^(-6)C," "q_(2)=80 xx 10^(-6) C, " AP=xcm "=x xx 10^(-2)m`
`BP=(18-x) cm=(180x) xx10^(-2)m`

Let .P.be the point where electric field is vero, then `E_(PA)=E_(PB)`
`(1)/(4pi epsi_(0)) q_(1)/x^(2)=(1)/(4pi epsi_(0)) q_(2)/((18-x)^(2)) ie, (20 xx 10^(-6))/((x xx 10^(-2))^(2))=(80 xx 10^(-6))/([(18-x) xx 10^(-2)])^(-2)`
`1/x^(2)=4/((180 -x)^(2))" "(18-x)^(2)=4x^(2)=18 -x=2x therefore x=6`
Hence for x=6cm, the field at P is zero.