Four point charges are located at the corners of a square, $1.00 \mathrm{~m}$ by $1.00 \mathrm{~m}$. On each of two diagonally opposite corners are $1.00 \mu \mathrm{C}$ charges. On each of the other two corners are $-1.00 \mu \mathrm{C}$ charges. What is the magnitude of the force on one of the positive charges?

Question

Quizplus · Accepted Answer

The force on one of the positive charges can be calculated using Coulomb's law. The net force is the vector sum of the forces due to the other three charges. The forces due to the charges on the adjacent corners are equal in magnitude, directed along the sides of the square, and at 45 degrees to the force due to the charge on the opposite corner. The magnitude of the force between two charges is given by $F = k \frac{|q_1 q_2|}{r^2}$, where $k = 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2$, $q_1 = q_2 = 1.00 \mu \text{C} = 1.00 \times 10^{-6} \, \text{C}$, and $r = 1.00 \, \text{m}$ for adjacent charges and $r = \sqrt{2} \, \text{m}$ for the diagonal charge. Calculating the forces and summing them vectorially gives a result of $8.2 \times 10^{-3} \, \text{N}$.

Four Point Charges Are Located at the Corners of a Square