Answer to Question #179517 in Physics for Louis

Question

Two identical metallic spheres are suspended as bobs of a simple pendulum as shown in the figure. The spheres come to equilibrium when a charge of +7.5×10^–9 C, with each string making an angle 5° with the vertical. The string is 0.5 m long. Find the electric force between the spheres.

Answer 1

The key thing here is to find distance between the spheres:

$$D=2d=2L\sin\theta.$$

Now find the electric force according to Coulomb's law:

$$F=k\frac{q·q}{D^2}=k\frac{q^2}{4L^2 \sin^2\theta}=66.6·10^{-6}\text{ N}.$$