Question

For point charge 10 µC and point charge -4 µC located at the same positions as in the previous question (5 m and 4 m, respectively), determine the magnitude of the net electric field E at the origin (in N/C).

Your answer should be a number with two decimal places, do not include the unit.

Hint: 1µC = 10^-6C

Answer 1

The first point charge $q_1=10\,\mu C=10*10^{-6}\,C$ is located at $x_1=5\,m$

Electric field at origin due to charge $q_1$ is $E_1=-\frac{q_1}{4\pi\epsilon_0x_1^2}$ , negative sign indicates that it is directed towards left. (away from charge $q_1$)

The second point charge $q_2=-4\,\mu C=-4*10^{-6}\,C$ is located at $x_2=4\,m$

Electric field at origin due to charge $q_2$  is $E_2=+\frac{q_2}{4\pi\epsilon_0x_2^2}$ , positive sign indicates that it is directed towards right. (towards the charge $q_2$)

Net electric field at origin due to the two charges is  $E=E_1+E_2=-\frac{q_1}{4\pi\epsilon_0 x_1^2}+\frac{q_2}{4\pi\epsilon_0x_2^2}$

$E=-\frac{10*10^{-6}}{4\pi(8.85*10^{-12}) (5)^2}+\frac{4*10^{-6}}{4\pi(8.85*10^{-12})(4)^2}$

$|E|=1348.77\,N/C=1.35*10^3\,N/C$

Magnitude of electric field at the origin is $|E|=1348.77\,N/C=1.35*10^3\,N/C$