Question

Charge q1 = 7.00 μC is at the origin, and charge q2 = -5.00 μC is on the x-axis, 0.300 m from

the origin as shown below. (a) Find the magnitude and direction of the electric field at point P,

which has coordinates (0, 0.400) m. (b) Find the force on a charge of 2.00 × 10-8 C placed at �

Answer 1

(a) The field is

$$E_1=\dfrac{kq_1}{r_1^2},\space E_2=\dfrac{kq_2}{r_2^2},\\\space\\ E_y=E_1-E_2\cos(\arctan\dfrac{0.3}{0.4}),\\\space\\ E_x=E_2\sin(\arctan\dfrac{0.3}{0.4}),\\\space\\ E=\sqrt{E_x^2+E^2_y}=292000\text{ V/m},\\\space\\ \theta=\arctan\dfrac{E_x}{E_y}=31.19°$$

above the x-axis.