Question

a square with sides 10cm has three charges on it edges, two are+5mC and one is -3mC. draw a well labelled diagram to illustrate the question and compute the total field at the vacant edge due to the other charges

Answer 1

$E_1=k\frac{q_1}{r_1^2}=9\cdot10^9\cdot \frac{3\cdot10^{-3}}{0.1^2}=2.7\cdot10^9V/m$

$E_2=k\frac{q_2}{r_2^2}=9\cdot10^9\cdot \frac{5\cdot10^{-3}}{0.1^2}=4.5\cdot10^9V/m$

$E_3=k\frac{q_3}{r_3^2}=9\cdot10^9\cdot \frac{5\cdot10^{-3}}{(0.1\sqrt{2})^2}=2.25\cdot10^9V/m$

$E_x=E_3\cos45°+E_2=(2.25\cos45°+4.5)\cdot10^9=6.1\cdot10^9V/m$

$E_y=-E_3\sin45°+E_1=(-2.25\sin45°+2.7)\cdot10^9=1.1\cdot10^9V/m$

$E=\sqrt{E_x^2+E_y^2}=10^9\cdot\sqrt{6.1^2+1.1^2}=6.2\cdot10^9V/m$