Mobility Formula in terms of Relaxation Time

Understanding Mobility

In general, mobility means the ability to move, in electricity mobility means the ability to move of charge under an electric field.

Definition of Mobility

The magnitude of the drift velocity per unit electric field.

The SI unit of mobility is `m^2/{Vs}`

Derivation of Mobility Formula in terms of Relaxation Time

The formula of drift velocity

`\vec v_d = - \frac{e \vec E \tau}{m}`

Where,

e = Charge of electron = `1.6 \times 10^{- 19} C`

m = Mass of electron = `9.1 \times 10^{- 31}kg`

`\tau = ` Relaxation time (average collision time for electrons)

If the temperature is constant and for a specific metal

`\tau =` Constant

`\vec v_d = \frac{e \tau}{m} (- \vec E)`

`\vec v_d = \mu (- \vec E)`

`\vec v_d = - \mu \vec E`

In magnitude

` v_d = \mu E`

`\mu = \frac {v_d}{E}`

`\mu = \frac {e \tau}{m}`

This equation is known as the equation of mobility in terms of relaxation time.

Thus, It is defined as the ratio of drift velocity to electric field.

Short Answer Type Question

Define Relaxation time.

It is the average collision time for electrons in a conductor.

What is mobility in physics?

Mobility refers to the ability of charge carriers to move under an electric field.

(or)

Mobility refers to the ease with which charge carriers move through a material under the influence of an electric field.

What is the SI unit of mobility?

The SI unit of mobility is `\frac{m^2}{V s}`

Define drift velocity.

Drift velocity is the average velocity of charge carriers in an Electric field.

How is mobility related to drift velocity and electric field?

Mobility is the ratio of drift velocity `v_d` to the electric field E.

`\mu = \frac {v_d}{E}`

What is the formula for drift velocity?

The formula for drift velocity is

`\vec v_d = - \mu \vec E`

When is the relaxation time constant?

The relaxation time is constant when the temperature is constant and for a specific metal.

What is the significance of mobility in electricity?

Mobility is crucial in understanding how charge carriers move under the influence of an electric field, which is essential in various electronic applications.

What are some factors that influence mobility?

Here are some factors that influence mobility

Temperature, impurities, crystal structure, and applied electric field strength.

How does mobility affect electrical conductivity?

Material with high mobility exhibits high conductivity and low mobility has higher resistance. High conductivity means charge carriers can move more freely in the conductor.

Write a use of mobility.

1. Designing electronic devices

2. To improve the efficiency of electrical circuits.

Numerical Questions

Q.1 Calculate the drift velocity when the electric field is 10 V/m and mobility is `0.5 \frac{m^2}{V s}`.

Q.2 If the relaxation time for electrons in a specific metal is `2 \times 10^{- 14} s`, calculate the mobility given that the charge of an electron is `1.6 \times 10^{- 19} C` and the mass of an electron is `9.1 \times 10^{- 31} kg`.

Q.3 If the drift velocity of electrons in a conductor is `8 \times 10^{- 4} kg` and the electric field applied is 200 V/m, calculate the mobility.

Q.4 Given a mobility of `0.2 \frac{m^2}{V s}`, and an electric field of 15 V/m, find the drift velocity.

Q.5 Calculate the mobility if the drift velocity of electrons in a material is `6 \times 10^{- 3} m/s` under an electric field of 150 V/m.