Question

4 4 4 4

Four charges are placed on the corners of a rectangle. What is the resultant force on the positive charge (a = 1 m, b = 0.8 m, q = 2.3 × 10^-9C)?

|F| =   N

Answer 1

force due to lower adjacent charge

F1 = k q^2 /r^2

F1 = 9*10^9* (2.3*10^-9)^2 / 1^2

F1 = 4.76 *10^-8 N

force due to upper adjacent charge

F2 = 9*10^9* (2.3*10^9)^2/ 0.8^2

F2 = 7.44*10^-8 N

force due to corner charge

F3 = 9*10^9* (2.3*10^-9)^2 / ( 1^2 + 0.8^2)

F3 = 2.9*10^-8 N

angle, theta = arctan ( b/a)

theta = 38.66

now net horizontal force

Fx = F1 + F3 cos theta

Fx = (4.76 + 2.9 cos 38.66) *10^-8

Fx = 7.02 *10^-8 N

net vertical force

Fy = F2 + F3 sin theta

Fy = (7.44 + 2.9 sin 38.66)*10^-8

Fy = 9.25*10^-8 N

net force

F^2 = Fx^2 + Fy^2

F = 11.61*10^-8 N

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