Question

Two charges q1=5*10-6 C and q2=10*10-6 C are located on the x axis on a coordinate system. They are both positive, but the second charge has twice the magnitude of the first. q1 is at -0.5 m while q2 is at +0.5 m. determine the overall direction and magnitude of the E-field at the origin.

Answer 1

$$E_1=k\frac{q_1}{r_1^2}=9\cdot10^{9}\frac{5\cdot10^{-6}}{0.5^2}=1.8\cdot10^{5}\frac{V}{m}$$

$$E_2=k\frac{q_2}{r_2^2}=9\cdot10^{9}\frac{10\cdot10^{-6}}{0.5^2}=3.6\cdot10^{5}\frac{V}{m}$$

The magnitude of the E-field at the origin

$$E=E_2-E_1=3.6\cdot10^{5}-1.8\cdot10^{5}=1.8\cdot10^{5}\frac{V}{m}$$

Direction: negative x-direction.