Two charges of `1.0xx10^(-6)` coulomb are separated by a distance 10 cm . Where will the electric field be zero on the line joining the two charges ?

Explanation

This is clear that such a point should be some where between the charges because in that case only , electric field will be in opposite direction . Suppose that point is at a distance x from the charge `q_(1)` , therefore this distance from the charge `q_(2)` will be `(10-x)`.
`thereforeE_(1)=(1)/(4piepsilon_(0))(q_(1))/(x^(2))`
and `E_(2)=(1)/(4piepsilon_(0))(q_(2))/((r-x)^(2))`
But according to the problem `E_(1)=E_(2)`
`therefore(1)/(4piepsilon_(0))(q_(1))/(x^(2))=(1)/(4piepsilon_(0))(q_(2))/((r-x)^(2))`
or , `(1.0xx10^(-6))/(x^(2))=(2.0xx10^(-6))/((10-x)^(2))`
or , `(1)/(x)=(sqrt(2))/((10-x))` (Taking positive sign)