Question

Two identical 1.00 g insulating balls with equal charges hang on 21.0 cm long strings as shown in Figure 17.43. Find their charge. (C 0P10 Figure 17.43

Answer 1

We know Sigma F_y = 0 so T cos 10 degree = mg and Sigma F-x = 0 so T sin 10 degree = F_e = k q^2/r^2 Divide the bottom equation by the top one, and remember that sine/cosine = tangent: T sin 10 degree/T cos 10 degree = kq^2/r^2/mg q^2 = mgr^2 tan 10 degree/k q = r squareroot mg/k tan 10 degree But from the diagram (above right), r = 2 times 21 sin 10 degree = 7.2 cm. Then q = (0.072 m) squareroot (1 times 10^-3 kg) (9.8 m/s^2)/9.0 times 10^9 N middot m^2/C^2 tan 10 degree = 3.15 times 10^-8 C The force of + q on -aq separated at 3 cm= F = k(q1q2)/r2, where r = 5 cm, F = 9 times 109 times (5 times 5 times 7.50)/0.052 = 675 N, F2 = 9 times 109(5 times 5 times 7.50)/0.032 = 1875 N total force = F1 + F2 = 675 + 1875 = 2550 N

The force of +q on -aq separated at 3 cm= F=k(q1q2)/r2, where r= 5 cm,

F= 9*109*(5*5*7.50)/0.052=675 N,

F2= 9*109(5*5*7.50)/0.032=1875 N

total force= F1+F2= 675+1875= 2550 N