Question

g Two tiny identical spheres of mass m = 66.7 g carry identical positive charge q. The charges hang from identical massless threads of length L = 84.8 cm attached to a ceiling at the same point. The spheres repel, and the angle between the threads is θ = 33o. Find q, the charge on each sphere, in μC.

Answer 1

Step-by-step explanation:

a

The angle each thread is making with the vertex = 16.5 degree

weight acting downwards = 66.7 x 10⁻³ x 9.8 N .

distance between two charges = 2 x 84.8 x 10⁻² sin 33/2

= .48 m

repulsive force between the two charges

= 9 x 10⁹ x q² / .48²

F = 39 x 10⁹ q²

Now, the tension in the thread be T

T cos 16.5 = mg

T sin 16.5 = F

dividing

tan 16.5 = F / mg = 39 x 10⁹ x q² / 66.7 x 10⁻³ x 9.8

.296 x 66.7 x 10⁻³ x 9.8 = 39 x 10⁹ x q²

q² = 4.96 x 10⁻¹²

q = 2.23 x 10⁻⁶ C

= 2.23 μC