Question

Professor Rikman, friend and assistant of M. V. Lomonosov, built one of the word's first electrometers. The instrument consisted of a vertical metal rod to the top of which was fastened flaxen string. The string was deflected away from the rod by the action of the electric charge (Fig.). The readings of the instrument were made on a quadrant in marked degrees. The string length was l and its mass was m.

Find the magnitude of the charge on the string which would cause the electrometer to deflect by an angle a. Make the calculations on the assumptions that: (a) the charge of the electrometer is equally divided between the rod and the string; (b) the charges are concentrated at point A on the string and at point B on the rod.

Answer 1

Explanation:

Acting on the deflected string are the weight F₁ = mg, applied to the centre of gravity of the string, and the force due to the charges F₂ = e²/a² (Fig.), applied to the end of the

string. The string is in equilibrium when the sum of the moments of these forces is zero. From simple geometrical considerations it follows that the moment of force F₁ is (1/2)mgl sinα; the moment