Four identical charges of 2.0 10⁻⁶ C each are secured at the four corners of a square with a side length of 5 cm . Determine the Coulomb force experienced by one of the charges due to the remaining three.

Step-by-step solution

Let the four charges q = 2.0 10⁻⁶ C be placed at the corners A, B, C, and D of a square of side a = 0.05 m . We calculate the net force on the charge at corner D due to the charges at A, B, and C. The force due to the charge at A is directed along AD: F_A = 1 4 ₀ q^2 a^2 = 9 10^9 (2.0 10⁻⁶)^2 (0.05)^2 = 14.4 N The force due to the charge at C is directed along CD: F_C = 1 4 ₀ q^2 a^2 = 14.4 N The force due to the charge at B is directed along the diagonal BD: F_B = 1 4 ₀ q^2 ( 2 a)^2 = F_A 2 = 7.2 N The forces F_A