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The motional emf is the emf generated when a conductor moves through a magnetic field. According to Faraday’s law of electromagnetic induction, when a conductor is introduced into a magnetic field, an emf is induced in the conductor known as induced emf due to its dynamic interaction with the magnetic field.
- The magnitude of induced emf is directly proportional to the rate of flow of magnetic flux linked with the conductor.
- According to Lenz’s law, the polarity of induced emf is such that it opposes the cause which produces it.
In this article, we will learn about motional emf, this emf is induced in an electric conductor which is in motion with the presence of a magnetic field. Along with that, formulas, calculations, and solved questions of motional emf will also be shared.
Read more: NCERT Solutions for Class 12 Physics Chapter 3
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Key terms: Motional emf, Conductor, circuit, motional electromotive force, magnetic field, Lenz’s Formula, Faraday’s law, induced emf, induced current.
What is Motional emf?
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Motional emf is the induced emf generated when a conductor is moved through a uniform magnetic field B. Emf is nothing but the electromotive force itself. Electromotive force or emf is needed for an electronic circuit to be able to drive currents through the circuit.
- According to Faraday’s law, whenever magnetic flux linked with a conductor or a coil changes, an emf is induced in it.
- This induced emf lasts as long as the change in magnetic flux continues in the coil.
- The emf so induced is directly proportional to the rate of change of magnetic flux.
- This induced emf can be produced by changing the magnetic field linked with the conductor or by changing the area of the conductor linked with the magnetic field.
- When a conductor or coil moves in a magnetic field its area linked with the magnetic field changes and hence the emf so induced in the conductor is known as motional emf.
Read More: Electromagnetic Induction MCQ
How is the Motional emf Induced?
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Let's say you have a metal conducting rod, and you have decided to connect that to a galvanometer.
- Now, if the metal rod is stationary in a magnetic field, then nothing would happen.
- But, if you move the metal rod through the magnetic field, then an emf is induced between the ends of the rod which causes the current to flow.
- This phenomenon takes place because when the metal rod is moved through the magnetic field, all the electrons in the rod also get into motion.
- These moving charges are deflected by the magnetic field towards one end of the metal rod, consequently, creating a potential difference.
- This is how motional emf is induced.
Read More: Electromagnetic Induction Important Questions
The Formula of Motional emf
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Consider a rectangular loop placed in a uniform magnetic field (B) in which one arm PQ of the loop having length L is moveable that moves with uniform velocity v. Change in magnetic flux (ΔΦ) in time Δt when the arm PR covers a small distance Δx in the uniform magnetic field, is given by
ΔΦ = -B x change in area = -B x LΔx
A negative sign shows that the area of the closed circuit inside the magnetic field decreases.
According to Faraday’s law, induced emf is given by
\(\epsilon= -{\Delta\phi \over \Delta t}\)
Substituting the value of ΔΦ in the above equation, we get
\(\epsilon= -{\Delta\phi \over \Delta t}={BL\Delta x \over \Delta t}\)
\(\Rightarrow\epsilon=BLv\)
Hence, for a conductor of length L, moving with velocity v in a uniform magnetic field B, the motional emf induced is given by
\(\epsilon=BLv\)
Where,
- B is the magnetic field
- L is the length
- v is the velocity of the conductor
Motional emf and Lorentz force
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We can also understand the motional emf by using the Lorentz force that acts on the free charge carriers of the conductor.
- Consider any arbitrary charge, let's assume it as q, in the conductor. Now, when the metal rod moves with a velocity of v, the charge will also be moving with the velocity of v in the magnetic field B.
- Therefore, qvB in magnitude Lorentz force on this charge and its direction is towards Q.
- Remember, regardless of their position in the metal conducting rod, all charges experience the same force in magnitude and direction. The work done in moving the charge from P to Q would be:
W = qvBl
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Lenz's Law
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According to Lenz’s law, the polarity of the induced emf is such that it tends to oppose the cause which produces it. The equation for induced emf according to Lenz’s law is given by
\(\epsilon= -{\Delta\phi \over \Delta t}\)
The negative sign shows that induced emf opposes the change in magnetic flux.
This formula provides a comprehensive way to understand the direction of induced currents.
- If magnetic flux linked with a closed loop increases, the induced current in the loop is anticlockwise.
- If magnetic flux linked with a closed loop decreases, the induced current in the loop is clockwise.
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S.I. Unit of Motional emf
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Regardless of its name, electromotive force or motional emf is not a force in real terms.
- It is usually measured in units of volts, which is equivalent to one joule per coulomb of the electric charge in the meter–kilogram–second system.
- However, the unit of emf or electromotive force is the statvolt, or one erg per electrostatic unit of charge in the electrostatic units of the centimeter–gram–second system.
Read More: emf formula
Applications of Motional emf
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Motional emf is a highly used phenomenon with a wide variety of applications. It is used in power generation as well as power transmission and in many other places. Let us discuss the scenarios where motional emf is applied.
- Airplanes: Motional emf can be measured on airplanes. As the airplane flies through the Earth's magnetic field, an induced emf is generated between the wingtips of the plane.
- Spinning motor: When an electronic motor is spinning, it also generates a Motional emf.
Read More: Electromagnetic Induction Ncert Solutions
Previous Year Questions
- Two identical circular coils A and B are kept on a horizontal tube side by side… [KCET 2013]
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- If a transformer of an audio amplifier has output impedance 8000 0 and the speaker has input impedance…...[JCECE 2005]
- A conducting loop in the shape of a right angled isosceles triangle of height 10cm10cm is kept such that the 90∘ vertex is…..[JEE Advance 2016]
- A 10m long horizontal wire extends from North East to South West. It is falling with a speed of 5.0ms−1……. [ JEE Main 2019]
- If a current of 2.0A2.0A flows through the smaller loop, then the flux linked with bigger loop is…… [JEE Main 2013]
- A coil of cross-sectional area A having n turns is placed in a uniform magnetic field B….. [JEE Main 21018]
- A copper rod of mass m slides under gravity on two smooth parallel rails, with separation ll and set at an angle of θ with the horizontal….. [JEE Main 2018]
- A copper wire is wound on a wooden frame, whose shape is that of an equilateral…. [JEE Main 2019]
- A metallic rod of length ll is tied to a string of length 2l and made to rotate with angular speed…. [JEE Main 2013]
- A square frame of side 10 cm and a long straight wire carrying current 1 A are in the plane of the paper…. [JEE Main 2014]
- If the rod makes n rotations per second, then the time averaged magnetic moment of the rod is… [JEE Main 2019]
- Figure shows a circular area of radius R where a uniform magnetic field….
- In a coil of resistance 100Ω , a current is induced by changing the magnetic flux through it….. [JEE Main 2017]
- When current in a coil changes from 5A to 2A…. [JEE Main 2015]
- Which radiation in sunlight, causes heating effect?
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- Arrange the following in decreasing order of wavelength
- Which is having minimum wavelength...[NEET 2002]
- The speed of radio-waves is equal to….. [JIPMER 1998]
- Gamma rays and visible light waves rays are a,ba,b and cc respectively, then….[UPSEE 2016]
- the circular loop of wire is moved with velocity towards the infinite current carrying wire…… [VITEEE 2016]
- A conducting wire frame is placed in a magnetic field which is directed into the paper…...[VITEEE 2019]
Things to Remember
- Motional emf is induced emf in a moving conductor at a magnetic field B.
- Motion is the cause of the induction of emf.
- Motional emf is stationary and related to the earth.
- The formula of emf is Emf = Blv, where B is the magnetic field, l is length and v is the velocity of the conductor.
- For emotional emf to be applicable, length, velocity, and magnetic field should be at a right angle or perpendicular to each other.
Read More: Electromagnetic Damping
Sample Questions
Ques: A conductor of length 100cm, moves at a right angle to a uniform field flux density of 1.5Wb/m2 with a velocity of 50m/s. The emf induced in the conductor will be: (3 marks)
(a) 150V
(b) 75V
(c) 35V
(d) 50V
Ans: Option b) 75V is the correct answer.
Explanation: The conductor moves at a right angle to a uniform magnetic field.
Already given; Length of the conductor: 100cm or 1m, the density of field: 1.5Wb/m2, velocity: 50m/s
Now, we have to find out, the emf induced in the conductor.
The formula of emf:
emf = Blv
emf = 1.5 x 1 x 50
emf = 75V.
Hence, 75V (option b) would be the answer.
Ques: Static electromagnetic induction is used in: (2 marks)
(a) Generator
(b) Alternator
(c) Transformer
(d) All of the above
Ans: Option c) transformer is the correct answer.
Explanation: generator and alternator come together as DC and AC when the conductor is rotating i.e. when the electromagnetic induction is static. Meanwhile, the transformer is there when the conductor is stationary. So, all of the above options won't fit with the condition. Hence, the transformer is the odd one out there.
Ques: The amount of emf induced in coil cutting the magnetic lines of force is determined by the following given factors. Choose the odd one out: (2 marks)
(a) Length: the length of the coil or conductor passing through the magnetic field.
(b) Strength: the strength of the magnetic field.
(c) Temperature: the temperature of the magnetic field.
(d) Speed: the speed at which the coil rotates inside the magnetic field.
Ans: Option c) Temperature: the temperature of the magnetic field.
Explanation: emf induced in the coil depends on the strength, length, and speed but not temperature. Hence, the temperature is the odd one out there.
Ques: Commercial electric motors do not use: (2 marks)
(a) An electromagnet to rotate the armature.
(b) An effectively large number of turns of conducting wire in the current-carrying coil.
(c) A permanent magnet to rotate the armature.
(d) A soft iron core on which the coil is bound.
Ans: Option c) a permanent magnet to rotate the armature is the correct answer.
Explanation: A permanent magnet is a comparatively weak magnet when it comes to commercial units. A permanent magnet won't be able to provide the magnetic field required by the commercial electric motor. Hence, a permanent magnet would be the answer there.
Ques: A coil having n turns and Area A is initially placed with its plane normal to the magnetic field B. It is then rotated 180 degrees in just 0.2 sec. The emf induced at the ends of the coil is: (2 marks)
(a) 0.1nAB
(b) nAB
(c) 5 nAB
(d) 10 nAB
Ans: Option d) 10 nAB is the correct answer.
Explanation: We would divide the total change in flux by the total change in time.
Already given; the total change in flux is 2nAB, and the total change in time is 0.2s.
Emf induced: 2nAB/0.2s = 10nAB.
Hence, 10nAB (option d) is the correct answer.
Ques: A straight line conductor of 0.4 m is moved with a speed of 7ms-1 perpendicular to a magnetic field of the intensity of 0.9 wbm-2. The emf induced across the conductor is: (2 marks)
(a) 25.2 V
(b) 2.52 V
(c) 5.24 V
(d) 1.26 V
Ans: Option b) 2.52 V is the correct answer.
Explanation: Already given; Length of the conductor: 0.4m, density of field: 0.9Wb/m-2, velocity: 7m/s-1
Now, we have to find out the emf induced in the conductor.
The formula of emf is emf = Blv
Putting the values into the formula, we will get…
emf = 0.98 x 0.4 x 7
emf = 2.52 V
Ques: Two conducting rings of radius r and 2r move in opposite directions with velocity is 2V and V respectively on a conducting surface S. There is a uniform magnetic field of magnitude V perpendicular to the plane of the rings. the potential difference between the highest points of the two rings is: (2 marks)
(a) Zero
(b) 2rvB
(c) 4rvB
(d) 8rvB
Ans: Option d) 8rvB is the correct answer.
Explanation: Here, we have to find out the potential difference between the highest points of the two rings.
So, we would change the emf in the rings by the cells.
E1= B2r(2V) = 4Brv
E2 = B(4r)v = 4Brv
When V2 – V1 = 8Brv
Hence, 8Brv is the potential difference between the highest points of the two rings.
Ques: A wire loop is rotated in a magnetic field. The frequency of change of direction of the induced e.m.f. Is: (2 marks)
(a) Once per revolution
(b) Twice per revolution
(c) Eight times per revolution
(d) Six times per revolution
Ans: Option b) twice per revolution is the correct answer.
Explanation: The induced emf cannot change the directions more than twice per revolution and it will change the directions more than once per revolution. Hence, option b is the correct answer there.
Ques: Two similar circular coaxial loops carry equal currents in the same direction. If these two loops are brought nearer, the current in them will: (2 marks)
(a) Change direction
(b) Decrease
(c) Increase
(d) Remain same
Ans: Option b) decrease is the correct answer.
Explanation: when the two loops are brought together the flux linking the two loops increases. According to Lenz's law, a current would be induced so that it opposes the change of flux. Hence, to oppose the change of flux, the current in these two loops would decrease.
Ques: If we keep two similar loops made up of copper and constantan in a magnetic field for the same amount of time, in which loop the induced e.m.f will be greater. (2 marks)
(a) Constantan loop
(b) None of these
(c) Copper loop
(d) Both of them
Ans: Option c) copper loop is the correct answer.
Explanation: Because copper has high electrical conductivity. Hence, higher e.m.f would be induced in the copper loop.
Ques: The motional emf produced across a wire moving through a magnetic field does not depend on its: (2 marks)
(a) Velocity
(b) Length
(c) Diameter
(d) Orientation
Ans: Option c) diameter is the correct answer.
Explanation: Motional emf (electromotive force) depends on length, velocity, and orientation. But it doesn't depend on the diameter. It's independent of diameter
Ques: A rod of length L is moved horizontally with a uniform velocity v in a direction perpendicular to its length through a region in which a uniform magnetic field is acting vertically downward.
(i) Derive the expression for the emf induced across the ends of the rod.
(ii) How does one understand this motional emf by invoking the Lorentz force acting on the free charge carriers of the conductor? Explain. (3 marks)
Ans: (i) Consider a conductor moving with velocity v and U shaped conductor placed in perpendicular with magnetic field. There, the emf induced across the ends of the rod would be:
emf = Blv, where B is the magnetic field, l is the length and v is the velocity.
(ii) One can also understand the motional emf by invoking the Lorentz force acting on the free charge carriers of the conductor, this way:
Consider any arbitrary charge q in the conductor. Now, when the metal rod moves with the velocity of v, the charge will also be moving with the velocity of v in the magnetic field B.
Therefore, qvB in magnitude Lorentz force on this charge and its direction is towards Q. Remember, regardless of their position in the metal conducting rod, all charges experience the same force in the magnitude and direction. The work done in moving the charge from P to Q would be:
W = qvBl
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