Four identical charged particles ( q = +10.6 µC) are located on the corners of a
ID: 1999855 • Letter: F
Question
Four identical charged particles (q = +10.6 µC) are located on the corners of a rectangle as shown in the figure below. The dimensions of the rectangle are L = 54.6 cm and W= 15.4 cm.
(a) Calculate the magnitude of the total electric force exerted on the charge at the lower left corner by the other three charges. (Answer in N)
(b) Calculate the direction of the total electric force exerted on the charge at the lower left corner by the other three charges. (Answer in °) (counterclockwise from the +x-axis)
Explanation / Answer
F = kQ^2/r^2
F[1] = {8.988 x 10^9 x (10.6 x 10^-6)^2}/(0.546)^2 1.009/0.2981 = 3.3847 N
F[2] = 1.009/(0.154)^2 = 42.5738N
Diagonal = 0.567 m
F[3] = 1.009/(0.567)^2 = 3.1393 N
Angle diagonal makes with horizontal = tan^1(0.154/0.546) = 15.7484 deg
Resolve diagonal force into a horizontal and vertical component.
Vertical: 3.1393sin(15.7484) = 0.8520 N
Horizontal: 3.1393cos(15.7484) = 3.0314 N
Total vertical component of force = 0.8520 + 42.5738 = 43.42 N
Total horizontal component of force = 3.0314 + 3.3847 = 6.4161 N
Magnitude of resultant = SQRT(43.42^2 + 6.4161^2) = 43.89N
angle: tan^-1(43.42/6.4161) = 81.60 deg below horizontal.
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