Question

A point charge of 4 μС is located at x =-30 cm, and a second point charge of-10 pC is located at x-+4.0 cm. where should a third charge of +6.0 pC be placed so that the electric field at x = 0 is zero?

Answer 1

it is to be placed at x = 3.1 cm

Step-by-step explanation:

Electric field due to charge placed at x = -30 cm

so we have

`E_1 = (kq)/(x^2)`

`E_1 = (9 * 10^9(4* 10^(-12)))/(0.30^2)`

`E_1 = 0.4 N/C` towards left

now electric field due to another charge placed at x = 4 cm

`E_2 = (9 * 10^9(10* 10^(-12)))/(0.04^2)`

`E_2 = 56.25 N/C` towards Right

now we need electric field due to 6 pC must be equal to

`E = 56.25 - 0.4`

`E = 55.85 N/C` towards Left

so we have

`55.85 = (9 * 10^9(6 * 10^(-12)))/(r^2)`

`r = 0.031 m`

so it is to be placed at x = 3.1 cm