Millikan's Experiment and the Weight of Oil Drop

Millikan's oil drop experiment was conducted to determine the charge on an electron. In this experiment, oil drops were allowed to fall through a small hole in the top of a metal cylinder. The oil drops were charged by friction as they passed through the hole.

The oil drops then entered a region of uniform electric field between two parallel plates. The electric field caused the oil drops to be attracted to the bottom plate. By adjusting the voltage across the plates, the electric force on the oil drop could be balanced by the gravitational force on the drop, allowing the drop to remain stationary.

The weight of the oil drop can be calculated using the following formula:

Weight = Mass x Gravity

where Mass = Density x Volume

1. Finding the Volume of the Oil Drop

The volume of the oil drop can be determined by measuring the diameter of the drop using a microscope and calculating the volume using the formula for the volume of a sphere:

Volume = (4/3) x π x (Radius)^3

2. Finding the Mass of the Oil Drop

The mass of the oil drop can be determined using the density of the oil and the volume of the drop:

Mass = Density x Volume

3. Finding the Charge on the Oil Drop

The charge on the oil drop can be calculated by measuring the voltage required to stop the drop from falling under the influence of gravity and the electric field. The electric force on the drop is given by:

Electric Force = Charge x Electric Field

The electric field can be calculated from the voltage and the distance between the plates:

Electric Field = Voltage / Plate Separation

By equating the electric force to the gravitational force, the charge on the oil drop can be calculated:

Charge = Weight / Electric Field

4. Finding the Weight of the Oil Drop

Using the formula for the weight of the oil drop:

Weight = Mass x Gravity

Substituting the value of mass and gravity, we get:

Weight = Density x Volume x Gravity

However, the weight of the oil drop is balanced by the electric force on the drop, which is given by:

Electric Force = Charge x Electric Field

Substituting the value of electric field, we get:

Electric Force = Charge x Voltage / Plate Separation

Setting these two equations equal to each other and solving for the weight, we get:

Weight = Charge x Voltage / Plate Separation x Gravity

Simplifying this equation, we get:

Weight = Charge x Voltage / Plate Separation / g

Since Charge x Voltage / Plate Separation is equal to the electric force on the oil drop, we can write:

Weight = Electric Force / g

Substituting the value of electric force from the equation above, we get:

Weight = (Density x Volume x Electric Field) / g

Finally, substituting the values of Volume, Density, Electric Field, and g, we get:

Weight = q V / d

where q is the charge on the oil drop, V is the voltage across the plates, and d is the distance between the plates.

Thus, the correct answer is option 'A': q V / d.