Millikan’s Oil Drops Experiment

Principle

This experiment involves application of Stoke’s law on viscosity and it is based on the study of motion of oil drops under the action of gravity alone, gravity and electric field.

Experimental arrangement

The experimental setup is as shown in the figure. It consists of a double walled chamber having three window one is for light, one is for x-rays and one is for microscope. There are two horizontal parallel plates, the upper plate having small hole on it. The clock oil is sprayed with the help of atomizer between the plates and motion of drops is observed with the help of microscope.

Case-I under the action of gravity alone

When the drop falls its velocity increases first. After some time the forces acting on it balances each other and the drop falls with terminal velocity (v₁).

At equilibrium:

Case-II under the combined action of gravity and electric field

Now the uniform electric field is applied along with gravity such that the drop moves upward with velocity (v₂).

At equilibrium:

Note: If the drop falls downward after applying electric field then,

Importance of Millikan’s Oil Drop Experiments

1. Millikan’s oil drop experiment is a direct and precise method for determination of electronic charge and gives good result.
2. This experiment shows that the smallest possible charge is the charge of an electron which is e = −1.6 × 10⁻¹⁹ C.
3. This experiment proves the quantization of charges, i.e. q = ne, where n = 1, 2, 3 … an integer and e = −1.6 × 10⁻¹⁹ C, charge of an electron.
4. Millikan’s oil drop experiment along with Thomson’s e/m experiment can be used to calculate the mass of an electron.

Motion of Charged Particle in Magnetic Field (B)

Consider a beam of electron moving with velocity v enters normally into a uniform magnetic field B such that B ⟂ v as shown in fig. The magnetic force acting on electron is given by F_m = Bev. This force provides necessary centripetal force and deflect the electron in a circular path. So,

This expression gives radius of circular path.

Since,

This gives frequency of electron.

Also, time period:

Motion of Electron Beam in Electric Field

Consider a beam of electron moving horizontally with velocity v enters normally into a uniform electric field E as shown in figure. Let the length of each plate is D and V be the potential difference between the plates separated by distance d.

The electric force acting on electron is:

Let after time t, the electron is at point P(x,y).

Along x-axis

Along y-axis

This equation is similar to y = kx² which is parabola.

Vertical component of velocity while coming out from electric field

Resultant velocity with which electron comes out

Angle made by resultant velocity with horizontal

Specific Charge

It is the ratio of charge to mass of a particle.

Principle: Cross-Field

It is the field in which both uniform electric field and uniform magnetic field are present kept perpendicular to each other such that the effect of one field is canceled by the other.

J.J. Thomson’s Experiment to Determine Specific Charge of an Electron

Principle

It is based on the principle of cross-field i.e. when an electron is passed through a cross-field the net force acting it is zero and it goes undeviated.

Construction

It consist of an evacuated glass tube having a fluorescent screen. A cathode connected to a battery an anode having small hole on it.

Working

The cathode gets heated due to a battery electron are emitted. Those electrons are accelerated by the battery connected between cathode and anode.

• In the absence of field the electron goes straight and strikes the screen at central pole.
• In the presence of magnetic field electron bends downward and strikes the screen at S₂.
• In the presence of electric field electron bends upward and strikes the screen at S₁.
• In the presence of cross field electron goes straight and strikes the screen at O. At this condition F_m = F_e.

In cross field electric force is equal to magnetic field:

Here, work done by potential = K.E. of electrons.

Using E = V/d:

This expression gives value of e/m which was found to be:

Millikan’s Experiment Formulae

Motion in Electric Field

Motion in B

J.J. Thomson’s

If drop remains stationary / balanced equilibrium / rest:

Exercise – 20

Conceptual Problem

1) Compare the specific charge of an electron with that of a proton.

Specific charge = e/m.

Proton:

Comparison

• The magnitude of the specific charge of an electron is about 1836 times greater than that of a proton.
• Electron’s specific charge is negative, while proton’s is positive.
• The electron has a much higher specific charge than the proton due to its extremely small mass even though both have the same specific charge.

2) Write down expressions for acceleration of a moving charge θ in parallel and perpendicular magnetic field.

3)

No answer is written for question 3 on this page.

What will be the expression for the charge of an oil drop if the electric field force is greater than its weight?

If the electric force acting on the oil drop is greater than its weight, then the drop will move upward.

4) Beams of electrons and protons having the same initial K.E. enter normally into an electric field, which beam will be more curved? Justify.

When beams of electron and proton with the same initial kinetic energy enter normally (perpendicular) into electric field, the electron beam will curve more than the proton beam.

Here force due to electric field:

Acceleration:

Now,

Electron beam curved more than proton beam in an electric field because:

• much smaller mass
• greater acceleration for the same force