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Drift velocity also referred to as axial drift velocity, is the average velocity obtained by charged particles in a material due to the effect of the electric field. Electrons, for example, move in random directions all the time. When electrons are exposed to an electric field, they travel randomly at first but eventually drift in one direction, the direction of the applied electric field.
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Keyterms: Drift Velocity, Net Velocity, Electrons, Electric Field, Ohm’s law, Current Density, Electric current, Average velocity, Collisions, Atoms, Acceleration, Conductor
Net Velocity of the Electrons
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Every conductible material above absolute zero temperature, such as metals, will contain some free electrons traveling at random speeds. When a potential is placed around a conductor, electrons will tend to flow towards the positive potential, but they will collide with atoms and bounce back or lose some of their kinetic energy in the process. However, the electrons will accelerate back due to the electric field, and these random collisions will continue to occur, but because the acceleration is always in the same direction due to the electric field, the electrons' net velocity will likewise be in the same direction.
Ohm's law can be used to derive drift velocity.
u = µE
Where,
u = Drift velocity
µ = Electron mobility
E = Electric field
These quantities are measured in m/s, m2/(V.s), and V/m, respectively.
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Drift Velocity of an Electron
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- The drift velocity is the average velocity attained by particles such as electrons under the influence of an electric field.
- The motion of the particle is believed to be in a plane, therefore the axial drift velocity can be used to characterize it.
- The random motion of free electrons traveling around the conductor can be used to understand the concept of drift velocity.
- These free electrons continue to move in the wire in an unorganized and random manner.
- When the conductor is exposed to an electric field, however, some form of electrical force is delivered to the randomly traveling electrons in the field's direction.
- While retaining the unpredictability of the motion, the field drives the electrons to switch to a high potential.
- Furthermore, it has been discovered that each electron has its velocity as it moves towards the conductor's higher potential point.
- The drift velocity of electrons is the name given to this net velocity.
- The current created by the drift movement of electrons in an electrically charged conductor is known as the drift current because the electron's travel is known as the drift velocity.
- Drift current is the name for the current that flows through a conductor.
- When charged particles move about in a conductor, they do not move in a straight line because they hit with other particles.
- As a result, the average speed of the particles in the conductor is measured. This is called drift velocity.
- The average velocity is achieved by free electrons under the influence of the electric field, due to which the electrons drift.
Drift Velocity Formula
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Drift velocity can be calculated by the following formula:
I = nAv Q
Where,
- I = current flowing through the conductor which is measured in amperes
- n = number of electrons
- A = area of the cross-section of the conductor which is measured in m2
- v = drift velocity of the electrons
- Q = charge of an electron which is measured in Coulombs
Derivation of Drift Velocity
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Following is the derivation of drift velocity:
F = - μE a = F/m = - μE/ m u = v + at
Where,
v = 0
t = T (relaxation time, the time that is required by an electron to return to its initial equilibrium value)
u = aT (substituting for v and u)
Therefore,
u = (- μE/ m) T (substituting for a)
This is the final equation that explains drift velocity.
However, with the increase in temperature, the drift velocity of electrons also increases in a metallic conductor.
Relation between Drift velocity and Electric current
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Drift velocity of an electron is relatively small, usually in the range of 10-3ms-1. Mobility is always a positive quantity and relies on the type of the charge carrier. As a result, electrons will take approximately 17 minutes to flow through a 1-meter conductor at this velocity. However, we can turn on electrical gadgets in our homes at lightning speeds with a flick of a switch because an electric current is established with the speed of light rather than the drift velocity.
As soon as the electric field is generated, current begins to flow within the conductor at the speed of light, not the speed at which the electrons are wandering, resulting in an insignificant little delay between the input and output when an electric bulb is turned on.
Relation between Drift velocity and Current density
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The total amount of current traveling through a unit cross-sectional conductor in unit time is known as current density. The formula for drift velocity is I = nAvQ, which we know from drift velocity.
J = I/A = nVQ
Were,
The current density is measured in Amperes per square meter and is denoted by J.
The electrons' drift velocity is v.
Thus, we can say that the electrons' current density and drift velocity are proportional to each other. Additionally, as the electric field intensity rises, the drift velocity rises, and the current flowing through the conductor rises as well.
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Things to Remember
- The drift velocity is the average velocity attained by particles such as electrons under the influence of an electric field.
- The SI unit of drift velocity is m/s. It is also measured in m2/ (V.s).
- Drift velocity can be calculated by the formula: I = nAv Q
- The derivation of drift velocity: F = - μE a = F/m = - μE/ m u = v + at
- The drift velocity of an electron is relatively small, usually in the range of 10-3ms-1.
- The current created by the drift movement of electrons in an electrically charged conductor is known as the drift current because the electron's travel is known as the drift velocity.
Previous Year Questions
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Sample Questions
Ques. What exactly do you mean when you say "saturated drift velocity" in the context of electric conductors? (2 marks)
Ans: The highest velocity attained by a charge carrier in a semiconductor, usually an electron, in the presence of extremely strong electric fields is known as saturation velocity. The semiconductor is in a condition of velocity saturation when this happens.
Ques. Is Diameter a Factor in Drift Velocity? (2 marks)
Ans: Any conductor's drift velocity is independent of its cross-sectional area or diameter. With V across the conductor, an increase in the cross-sectional area lowers the resistance for the same p.d.
R= (rho)(length)/ (cross-sectional area)
As a result, raising the current
I=V/R
Ques. What effect will drift velocity have on random thermal velocity? Is drift velocity simply the steady-state value of velocity in the field direction, with thermal velocities in other directions? (3 marks)
Ans: The thermal velocity of charges is caused by the energy gained from the heat received from its surroundings, and such energy, of course, contains no other information than allowing those charges to travel freely in the lattice. When an electric field is applied, these charges find a purpose and receive the necessary information to travel. Drift velocity is the rate at which charges travel in the direction of the electric field when they are free to move.
The strength of the applied electric field determines whether thermal velocity or drift velocity predominate. The rate of charges in thermally induced motion along random directions will be low if the field is strong enough to influence the charges in random motion.
Ques. What happens if the electron drift velocity in an electric bulb is high? What will happen if it is extremely low? What is the significance of drift velocity, and why is it so critical? (3 marks)
Ans: The velocity of Drift is a statistical measure of the rate at which electrons move down a conductor, and thus the rate at which charge flows, or current. As a result, drift velocity is proportional to ohmic resistance. When choosing the physical qualities of an electric bulb's filament, the primary consideration is the required ohmic resistance. This parameter determines the drift velocity.
Little drift velocity simply signifies low current. It is up to the designer to figure out how much current he needs based on the given resistance in order to achieve the desired brightness.
Ques. Which has a higher velocity of drift, iron or copper? (3 marks)
Ans: Since iron and copper are both metals, the free-electron theory can be used to explain some of the differences. Copper has one free electron in the outer shell to contribute to the electron gas, but iron has two electrons in the outer shell, according to the atomic structure. As a result, the density of free electron gas in iron will be larger per unit volume than in copper. Copper has a longer mean free path than iron, according to simple kinetic theory. As a result, electrons in copper are more mobile than in iron at the same temperature. This is also true of copper's higher conductivity than iron. Copper's drift velocity should be somewhat higher than iron's.
Ques. Is drift velocity a positive or negative quantity? (2 marks)
Ans: Velocity is nothing more than a vector. A and B are sprinting away from each other, while B and C are running in the opposite direction. B is now jogging at the same speed as A and C, yet he appears to be different. As a result, depending on the frame of reference, the velocity of can be positive or negative. It isn't a predetermined value.
Ques. How can electricity be so rapid while an electron's drift velocity is so low? (3 marks)
Ans: Due to the conductor's electric field's high speed.
Explanation: Inside the conductor, the field propagates at the speed of light and acts practically instantaneously on all of the charges. When we turn on an electrical instrument, electrons do not start flowing from the switch and then reach the instrument, where they begin to operate. Free electrons exist all along the wire, and when we turn it on, the field moves those electrons inside the device as well. Consider the case of a light bulb. When we turn on the bulb, electrons inside the filament begin to move, and the bulb illuminates. That is why electricity travels so quickly.
Ques. What factors influence electron drift velocity in a conductor? (3 marks)
Ans: The emf of the source affects the electron drift velocity in a circuit element.
Drift velocity is proportional to emf assuming the circuit's load impedance remains constant i.e., as emf rises, drift velocity rises, and vice versa. If the emf remains constant and the load in the outer circuit is increased, the drift velocity in the inner circuit grows, resulting in a greater internal voltage drop, while the drift velocity in the elements of the outer circuit falls, resulting in a lower outer circuit voltage.
Ques. What happens to the drift velocity if the potential gradient is doubled? (2 marks)
Ans: The electric field's potential gradient is negative (E). As a result, when the potential gradient is twice, the field is likewise doubled. When E is doubled, according to the relationship vd= eEt/m. (t= relaxation time), vd is also doubled.
Ques. Is there a distinction between escape velocity and terminal velocity? (3 marks)
Ans: If you throw something from the surface of the earth, it will fall back. If all other forces (such as air friction) are ignored, escape velocity is the least velocity required to throw an object (in any direction) without it stopping. As it gains altitude, it will go slower and slower asymptotically, but it will never stop.
The term "terminal velocity" refers to a completely distinct idea. When a force is applied to an item in a viscous fluid, the limiting velocity is called terminal velocity. A pebble falling through water, for example, accelerates at first due to gravity, but as it gains speed, the viscous force of water seeks to slow it down. As the speed increases, the viscous drag increases as well, until the force of friction reaches a point where it perfectly balances the force of gravity. The stone cannot accelerate any farther at that point since all forces acting on it are balanced. The terminal velocity is the velocity at which it reaches equilibrium (when the pull of gravity is balanced by the force of friction).
Ques. Why is it that we can't quantify drift velocity for a short time? (4 marks)
Ans: In the case of the free electron model for metal conductivity, we define drift velocity. The effective displacement of the conduction electron after a large number of random collisions with ions at the lattice sites is used to calculate drift velocity. OR
The average velocity will be T if the average time gap between two successive ion collisions is T.
v(drift)=(Ee/m) T.
T stands for "relaxation time."
We take an average of a huge number of collisions in this case.
E is the electric field created inside the metal as a result of the applied voltage. The charge and mass of an electron are denoted by e and m.
Alternatively, we have the following relationship: v(drift)=I/(neA)
n denotes the number density of unbound electrons.
I stand for "current."
A refers to the wire's cross-section.
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