Question

Four identical charged particles (q = +10.9 µC) are located on the corners of a rectangle as shown in the figure below. The dimensions of the rectangle are L = 57.0 cm and W = 13.5 cm.(a) Calculate the magnitude of the total electric force exerted on the charge at the lower left corner by the other three charges.(b) Calculate the direction of the total electric force exerted on the charge at the lower left corner by the other three charges. ° (counterclockwise from the +x-axis)

Four identical charged particles (q +10.9 μC) are located on the corners of a rectangle as shown in the figure below. The dimensions of the rectangle are L = 57.0 cm and W 13.5 cm. (a) Calculate the magnitude of the total electric force exerted on the charge at the lower left corner by the other three charges (b) Calculate the direction of the total electric force exerted on the charge at the lower left corner by the other three charges. (counterclockwise from the +x-axis)

Answer 1

F = kQ^2 /r^2

F1 = 9*10^9*(10.9*10^-6)^2 /((0.57)^2 = 3.3 N

F2 = 9*10^9*(10.9*10^-6)^2 /(0.135)^2 = 58.67 N

Diagonal = 0.58 m

F3 = 9*10^9*(10.9*10^-6)^2 /(0.58)^2 = 3.18 N

Angle diagonal makes with horizontal = arctan(0.135/0.57) = 13.32 degree

F3 (vertical) = 3.18*sin 13.32 degree = 0.73 N

F3 (horizontal) = 3.18*cos 13.32 degree = 3.09 N

F(vertical) = 0.73 + 58.67 = 59.4 N

F(horizontal) = 3.09 + 3.3 = 6.39 N

Magnitude = sqrt(59.4^2 + 6.39^2) = 59.74 N

Direction = arctan (59.4/6.39) = 83.86 degree below horizontal