Question

How do we measure electron’s charge?

Answer 1

Solution

Fir the first time electronic charge was measured by R. A. Millikan by his oil drop experiment. The experjment even used today in college laboratories to measure electronic charge.

The basic idea is to suspend charged oil droplets in air and measure the charge on many of them by some method and then take the lowest common Multiplier of these charges to get the electronic charge. As we know electric charge is always quantised, i.e,

Q= ne

Where Q is any charge(like charge on any of those oil droplets.) n is a natural number and e is the electronic(elementary unit) charge. Thus there will be always some constant multiple of electronic charge on any measured. Which means the L.C.M. of the measured charges will be electronic charge.

The oil drop experiment

A sprayer is used to spray some oil droplets into the space between two metallic plates kept horizontal to the ground. As the oil droplets move downward under acceleration due to gravity, an opposing viscous force due to air will 'slow down' the droplets. Now due to cancellation of these equal and opposite forces, the droplets move with some terminal velocity. The terminal velocity is measured by measuring the time taken to travel fixed distances marked on the microscope. Using this terminal velocity, the radius of the droplet can be estimated. After then an electric field is applied between the plates by applying a potential difference between them. This causes the oil drop to accelerate and it achieves a new terminal velocity to this new forces. This terminal velocity is a measure of its charge(since new electric force is qE which is proportional to the charge on the droplet). Thus measuring the two terminal velocities, charge on a single oil drop can be estimated and repeating this procedure with large number of droplets and taking the LCM of obtained charges will give us the electronic charge.

Formula used to work out charge on a droplet,

Eta is the coefficient of viscosity of air

E is the applied electric field

Rho and sigma are the densities of oil and air

g is the acceleration due to gravity

Finally vg and ve are the measured terminal velocities of oil drop without and with applied field.