Four identical charged particles (q = +10.2 µC) are located on the corners of a
ID: 1266285 • Letter: F
Question
Four identical charged particles (q = +10.2 µC) are located on the corners of a rectangle as shown in the figure below. The dimensions of the rectangle are L = 63.0 cm and W = 13.7 cm.
(a) Calculate the electric field at the lower left corner due only to the two charges on the far right side of the rectangle.
E with arrowtwo charges on right N/C)i hat + ( N/C)j hat
(b) Calculate the electric field at the lower left corner due to all three charges not at that location.
E with arrowat lower left = ( N/C)i hat + ( N/C)j hat
(c) Calculate the magnitude of the total electric force exerted on the charge at the lower left corner by the other three charges.
N
(d) Calculate the direction of the total electric force exerted on the charge at the lower left corner by the other three charges.
Explanation / Answer
q = +10.2 µC) L = 63.0 cm and W = 13.7 cm.
F = kQ^2/r^2
F[1] = {8.988 x 10^9 x (10.2 x 10^-6)^2}/(0.63)^2 = 2.33 N
F[2] = 3.595/(0.137)^2 = 49.33 N
Diagonal = 0.644 m
F[3] = 0.925/(0.6447)^2 = 2.23 N
Angle diagonal makes with horizontal = tan^1(0.137/0.644) = 12.009 deg
Resolve diagonal force into a horizontal and vertical component.
Vertical: 2.23sin(12.009) = 0.464 N
Horizontal: 2.23cos(12.009) = 2.18 N
Total vertical component of force = 0.464 + 49.33 = 49.794 N
Total horizontal component of force = 2.33 + 2.18 = 4.51 N
Magnitude of resultant = SQRT(49.794^2 + 4.51^2) = 49.99 N
angle: tan^-1(49.79/4.51) = 84.82 deg below horizontal.
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