Question

Two charges , q1=+2.0 x 10-6C, and q2= +4.0 x 10-6C, are placed in a vacuum, 20cm apart. At what point on the line joining the two charges is the electric field strength equal to zero?

Answer 1

`x=8.3 cm`
`"The Point O(8.3,0)"`

Explanation:

`"Since The Electrical fields vectors of the charges Q1 and Q2"`
`"is at opposite direction,The point that we are looking for "`
`"should be in the white area."`
`"The vectors at the green and blue areas have the same direction."` `"The sum of these vectors not be zero."`

`cancel(K)*Q_1/x^2=cancel(K)*Q_2/(0.2-x)^2`

`(cancel(2)*cancel(10^(-6)))/x^2=(cancel(4)*cancel(10^(-6)))/(0.2-x)^2`

`1/x^2=2/(0.2-x)^2`

`sqrt(1/x^2)=sqrt(2/(0.2-x)^2)`

`1/x=(1.41)/(0.2-x)`

`1.41x=0.2-x`

`2.41x=0.2`

`x=(0.2)/(2.41)`

`x=0.083 " "m`

`x=8.3 cm`