In Millikan oil drop experiment, when the switch is opened and by altering supply the charge of electron is determined.
Millikan's oil drop experiment is held to determine the terminal velocity and charge of the oil drop.
Firstly without any supply of voltage when an oil drop is sprinkled and these droplets gather electrons together and gives negative charge as they pass through air.
By applying and altering voltage applied on the plates, drop can be suspended in air. Millikan observed one drop after another, varying the voltage and noting the effect. After many repetitions he concluded that charge could assume only certain fixed values.
After conducting many times he concluded 1.602176487 ×10−19 C as the charge of an electron.
To find the value of the charge Q you take into account both gravitational force and electric force over each ball. By symmetry you can use the fact that both balls experiences the same forces. Hence you only take into account the forces for one ball for the x component and y component:
M: mass of the ball = 0.09kg
T: tension of the string
F_e: electric force between charges
angle = 45°
The electric force is given by:
Q: charge of the balls
r: distance between balls = 2m
You divide both equation in order to eliminate the tension T:
By doing Q the subject of the formula and replacing you obtain: