Two small plastic balls hang from threads of negligible mass. Each ball has a ma

Question

Two small plastic balls hang from threads of negligible mass. Each ball has a mass of 0.170 g and a charge of magnitude q. The balls are attracted to each other, and the threads attached to the balls make an angle of 20.0 degrees with the vertical. The distance between the balls is 2.05 cm.

a) Find the magnitude of electric force acting on each ball.
F= N

b) Find the tension in each of the threads.
T= N

c) Find the magnitude of the charge on the balls.
q= nC

Explanation / Answer

The idea is to equate the horizontal forces due to gravity (Fg) and to electrostatic attraction (Fe). A. Fe = Fg = mgtanT = 0.00017*9.81*tan(20 d) = 6.4269864E-04 N C. From the link, r = 0.0205 m Fe = kq^2/r^2 mgtanT = kq^2/r^2 ==> q = sqrt(mgtanT*r^2/k) = sqrt(6.4269864E-04*0.0205^2/8.98755E9) = 5.4819723E-09 C B. TcosT = mg ==> T = mg/cosT = 0.00017*9.81/cos(20 deg) = 1.8791251E-03 N

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