A point charge q_1 = -2.1 mu C is located at the origin of a co-ordinate system.

Question

A point charge q_1 = -2.1 mu C is located at the origin of a co-ordinate system. Another point charge q_2 = 6.7 mu C is located along the x-axis at a distance x_2 = 6.8 cm from q_1. What is F_12, x, the value of the x-component of the force that q_1 exerts on q_2? Charge q_2 is now displaced a distance y_2 = 2.9 cm in the positive y-direction. What is the new value for the x-component of the force that q_1 exerts on q_2? A third point charge q_3 is now positioned halfway between q_1 and q_2. The net force on q_2 now has a magnitude of F_2, net = 7.724 N and points away from q_1 and q_3. What is the value (sign and magnitude) of the charge q_3?

Explanation / Answer

1) f12 = kq1q2/x2^2 = 9*10^9*-2.1*10^-6*6.7*10^-6/0.068^2

f12 = -27.385 N

2) r = sqrt(6.8^2+2.9^2) = 7.39 cm

f = 9*10^9*-2.1*10^-6*6.7*10^-6/0.0739^2 = -23.19 N

theta = tan^-1(2.9/6.8) = 23.1 degrees

fx = fcostheta = -21.33 N

3) 7.724 = fq1+fq3

The force due to q3 on q2 = kq2q3/d^2 = 9*10^9*6.7*10^-6*q3/0.03695^2 = 4.42*10^7*q3

-23.19+4.42*10^7*q3 = 7.724

q3 = 0.699*10^-6 C

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