Question

Two small balls, each of mass 5.0 g, are attached to silk threads 50 cm long, which are in turn tied to the same point on the ceiling, as shown below. when the balls are given the same charge q, the threads hang at 5.0° to the vertical, as shown below. what is the magnitude of q? what are the signs of the two charges?

Answer 1

In triangle ABC

Sin5 = BC/AC

BC = (AC) Sin5

BC = (50) Sin5 = 4.36 cm

r = distance between the two balls = 2 BC = 2 x 4.36 = 8.72 cm = 0.0872 m

q = charge on each ball

m = mass of each ball = 5 g = 0.005 kg

electric force between the two balls is given as

F = $\frac{kq^{2}}{r^{2}}$

using equilibrium of force in vertical direction

T Cos5 = mg eq-2

Using equilibrium of force in horizontal direction

T Sin5 = F eq-3

dividing eq-3 by eq-2

T Sin5 /(T Cos5) = F/mg

F = mg tan5

using eq-1

$\frac{kq^{2}}{r^{2}}$ = mg tan5

inserting the values

$\frac{(9 \times 10^{9})q^{2}}{(0.0872)^{2}}$ = 0.005 x 9.8

q = 2.03 x 10⁻⁷ C

sign of charge is same on both the balls. either it is negative or positive