Question

Two identical small metal coated spheres R and S are given identical charges of 40nC each. They are suspended at the same point from a ceiling by means of identical light inextesible insulating threads of equal length.the threads are of negligible mass. When the system is in equilibrium the angle between the threads is 60° while the distance between R and S is 5 cm. Calculate the mass of sphere R

Answer 1

Find the electrostatic force F:

$$F=k\frac{q^2}{r^2}.$$

The spheres are in equilibrium, so, the sum of forces along horizontal and vertical are zero. Begin with horizontal:

$$F-T\text{ sin}30°=0,\\ T=\frac{F}{\text{sin}30°}.$$

Vertical:

$$T\text{ cos}30°-mg=0, \\ m=\frac{T\text{ cos}30°}{g}=\frac{F}{g}\text{ cot}30°=\frac{kq^2}{gr^2}\text{ cot}30°=113\text{ mg}.$$