The figure shows two charged particles on an x axis q 800 x

The figure shows two charged particles on an x axis: -q = -8.00 x 10^-19 C at x = -1.50 m and q = 10^-19 C at x = 1.50 m. What are the (a) x-and (b) y- components of the net electric field produced at point P at y = 8.00 m?

Solution

The electric field can be calculated using E = k*q/r^2

The magnitude of the field at point P is the same for each charge due to symmetry

So E = 9.0x10^9N-m^2/C^2*(8x10^-19C)/(1.5^2 + 8^2) = 1.08 x10^-11N/C

Now the field of the left hand charge points down and to the left.

The field of the right hand charge points up and to the left.

Due to symmetry the x component will be two times the x component of either charge..

The angle that either makes with the horizontal = arctan(8/1.5) = 79.37o

So the x component of the field = 2*F*cos(74.05) = 2*1.08x10^-11)*cos(79.37) = 3.98x10^-11N/C

Due to symmetry the y component is zero.