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Drift velocity refers to the average velocity gained by the electrons in the presence of an electric field. It is the drift velocity that adds to the electric current. Drift refers to the act of slowly shifting towards something. Drift velocity is directly proportional to current and also to the magnitude of an external magnetic field in the case of resistive material. Drift Velocity can be expressed in terms of Ohm’s law as μE where µ represents the electron mobility and E is the electric field.
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Key Terms: Drift velocity, net velocity, electron drift velocity, motion, electronic field, magnetic field, electron, electric force, conductor
What is Drift Velocity?
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Electrons move randomly in an electrical field. However, when electrons are moving subject to the electric field with its direction, then the net speed of movements of electrons is called a Drift velocity. The average velocity of a charged particle in a material due to the influence of an electric field is known as Drift velocity.
- When an electric field is applied to the movement of an electron, some kind of electric force is produced and due to this, the electrons will drift towards the high potentials.
- Under the electric field average velocity gained by free electrons is called drift velocity.
- The drift velocity depends on a few conditions – the basic temperature of the conductor, the material of the conductor, and the potential differences applied towards the ends of the conductor.
- The SI unit of drift velocity is m/s. It can also be measured in m2/(V.s).
Drift Velocity
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| Important Topics | ||
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| Meter Bridge | Potentiometer | Cells In Series and Parallel |
| Electromotive Force | Carbon Resistor | Types of Current |
| Electrical Current | Circuit Diagram | Electrical Charges |
Net Velocity
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At a zero degree temperature metals have some electrons which have free electrons moving randomly. So, when an electric charge is applied to the electrons they will move towards the positive potential.
- In the movement when they collide with other atoms then they bounce back and lose some kinetic energy.
- Due to the electric field, electrons will accelerate again and again and collide and this situation happens many times.
Read More: Drift Velocity Important Questions
Drift Velocity Formula
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We can calculate the drift velocity of an electron through the below-mentioned formula.
Where,
- I is the current flowing through the conductor.
- n is the number of electrons.
- A is the area of an electric field of the conductor.
- v is the drift velocity of the electrons.
- Q is the charges on electrons.
Solved ExamplesQues: Let’s assume a current of 3A that is flowing in a copper conductor with a cross-section of 1mm2 (1×10-6m2) Solution: We know that for copper, n = 8.5 x 1028 per m3 So according to the formula we have, 3 = 8.5 x 1028 x 1 x 10-6 x v x 1.6 x 10-19 Where, Q = 1.6 x 10-19 C Therefore, v = 2.205882 x 10-4 ms-1 The electrons are accelerated more rapidly towards the positive direction if the intensity of the electric field is increased, opposite to the direction of the electric field applied. |
Read More: Derivation of Drift Velocity
Mobility of an Electron
Mobility of the electron is the drift velocity of an electron for a unit electric field. In solid-state physics, electron mobility defines how quickly an electron can move through a metal or semiconductor when pulled by an electric field.
The mobility of an electron can be calculated by μ = E∣vd∣
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Relation between Drift Velocity and Electric Current
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Drift velocity is directly in proportion with the current. And also we can say that drift velocity is directly proportional to the magnitude of an electronic field.
So,
Where,
- u represents drift velocity
- mu represents electron mobility
- E represents the electric field
Basically, the SI unit of the drift velocity is m/s or m2/(VS).
Read More: NCERT Solutions Class 12 Physics
Relation between Drift Velocity and Current Density
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Current density means the total number of current passed through a conductor in the unit time.
As we, know that
I = nAvQ
But , current density = Current / Area
J = I/A
So, we can say that,
J = nvQ
Where J denotes the current density.
So, from the above-mentioned formula, we can say that current density is directly proportional to the drift velocity of an electron.
Read More: Drift Velocity MCQ
Things to Remember
- Drift Velocity can be explained as the net velocity at which the electrons move.
- Drift Velocity Formula: vd = I/neA
- Draft Velocity depends mostly on the condition, temperature, and material of the conductor.
- The mobility of electrons can be represented by μ=VdE.
- Drift velocity can be termed as a vector quantity as both magnitude and direction are required to explain it.
Previous Year Questions
- In the circuit shown, current (in A) through the 50 V and 30 V batteries are, respectively…..[JEE Main 2014]
- In the electric network shown, when no current flows through the 4Ω resistor…
- In the above circuit the current in each resistance is….
- Find the internal resistance of the cell....[JEE Mains 2018]
- In vertical circular motion, the ratio of kinetic energy of a particle…. (MHT CET 2016)
- The motion of a particle in straight line is…. (JKCET 2013)
- A charged particle enters a uniform magnetic field with a certain speed …. (JKCET 2006)
- From the top of a tower a body AA is projected vertically up…. (JKCET 2007)
- Assuming earth to be an inertial frame…. (JKCET 2009)
- A body is sliding on a smooth inclined plane requires…. (JIPMER 1999)
- A body of mass 5kg is suspended by a spring balance on… (BITSAT 2006)
- A body of mass M hits normally a rigid wall with velocity V … (BITSAT 2018)
- A man of weight 80kg is standing in an elevator which is… (DUET 2003)
- A light inextensible string that goes over a smooth fixed pulley … (BITSAT 2013)
Sample Questions
Ques. A copper wire has a cross-sectional area of 7.85 x 10-7 m2. The number density of copper is 8.5 x 1028 m-3. Calculate the mean drift velocity of the electrons through the wire when the current is 1.4 A. (3 marks)
Ans. As we know that,
I = nAve
So, drift velocity = v = I/(nAe)
A=7.85 x 10-7 m2
n=8.5 x 1028 m-3
and I = 1.4 A
We know, e=1.6 x 10-19
So, v = 1.4 / (8.5 x 1028 * 7.85 x 10-7 * 1.6 x 10-19)
v= 1.31 x 10-4 m/s
Ques. A wire of diameter 0.02 meter contains 1028 free electrons per cubic meter. For an electric current of 100 amperes, the drift velocity for free electrons in the wire is most nearly. (2 marks)
Ans. As we know that v = I/neA
e = charge of an electron = 1.6 × 10−19 C
n = 1028 electrons/m3
A = πr2 = 0.5π × 10−4
I =100 Ampere
v = 102 / (1028× 1.6 × 10−19× 0.5π × 10−4)
= 102−28+19+4 / (1.6 × 0.5π)
≈ 10−4
Ques. The current which is assumed to be flowing in a circuit from a positive terminal to negative called, (1 mark)
(A) Direct current
(B) Pulsating current
(C) Conventional current
(D) Alternating current
Ans. C) Conventional current
Ques. When no current is passed through a conductor, (1 mark)
(A) the free electrons do not move
(B) the average speed of a free electron over a large period of time is not zero
(C) the average velocity of a free electron over a large period of time is zero
(D) the average of the velocities of all the free electrons at an instant is non zero
Ans. D) the average of the velocities of all the free electrons at an instant is non zero
Ques. What is the current involved when a truck battery sets in motion 720 C of charge in 4.00 s while starting an engine? (b) How long does it take 1.00 C of charge to flow through a handheld calculator if a 0.300-mA current is flowing? (2 marks)
Ans. As we know,
I = delta(Q)/delta(T)
= 720 c / 4 sec
= 180 A
This huge value for current shows that a large charge is shifted in very little time. The currents present in these “starter motors” are fairly large because large forces of friction are required to be overcome while setting something in motion.
Ques. Define the term electrical conductivity of a metallic wire. Write its S.I. unit. (2014)
Ans. The electrical conductivity of a metallic wire can be defined as the ratio of the density of current to the electric field created by it.
It is the reciprocal of resistivity (ρ)
Electrical conductivity, (ρ) = 1/ρ = j/E
S.I.unit = mho m-1 or (ohm m)-1 or S m-1
Ques. Define the term drift velocity of charge carriers in a conductor and write its relationship with the current flowing through it. (2014)
Ans. When there is an application of electric field across a conductor then the charge carrier present within the conductor starts to move with an average velocity that doesn’t depend on time. This is called the drift velocity.
Relation between the current I and drift velocity vd
I = neAvd
Where ne = total charge present within the conductor
A = cross-sectional area of the conductor.
Ques. Write the expression for the drift velocity of charge carriers in a conductor of length ‘l’ across which a potential difference ‘V’ is applied. (AI 2014)
Ans. I = neAvd
Where ne = total charge present within the conductor
A = cross-sectional area of the conductor.
vd = V/neρl {using A = ρl/R}
Ques. When electrons drift in metal from lower to higher potential, does it mean that all the free electrons of the metal are moving in the same direction? ( 2012)
Ans. Due to the presence of exterior electric fields, all the electrons shift in a similar direction during the drift.
Ques. Two conducting wires X and Y of the same diameter but different materials are joined in series across a battery. If the number density of the electrons in X is twice that in Y, find the ratio of the drift velocity of electrons in the two wires. (2010)
Ans. Since the wires are connected in series, current I through both is similar. Therefore ratio of drift velocity: vX/vY = (I/nXeAX)/(I/nYeAY)
Where nX, nY = respective electron densities
AX, AY = Cross section areas
vX/vY = nY/nX =½ (Given A = A, n = 2n)
vX:vY = 1:2
Ques. What do you mean by drift velocity? (2 marks)
Ans. Drift velocity is the average velocity acquired by a charged particle, like an electron or proton, in the body due to an electric field. Generally, an electron inside a conductor moves arbitrarily at the Fermi velocity, generating a zero average velocity.
Ques. What is the formula for drift velocity? (3 marks)
Ans. The formula is,
I = nAvQ
Here,
I – the current flowing through the conductor
n – the number of electrons
A – the area of the cross-section of the conductor
v – the drift velocity of the electrons
Q – the charge of an electron
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