Content Strategy Manager
Faraday’s law of electromagnetic induction, also called Faraday’s law, is the fundamental law of electromagnetism. It helps to predict how a magnetic field interacts with an electric circuit to produce emf. Faraday’s Law of Electromagnetic Induction can be seen in transformers, inductors, and several other types of electrical motors, generators and solenoids. Faraday’s Laws of Electromagnetic Induction are based on two laws.
The first law explains the induction of emf in a conductor, while the second law generally quantifies the emf generated in the conductor. The law was proposed as a result of observations of three experiments conducted by Faraday.
Michael Faraday first proposed the laws of electromagnetic induction in 1831. Upon observation by Faraday and Henry, Faraday concluded that emf is induced if, across the coil, magnetic flux changes with time.
Read Also: Magnetism and Matter
| Table of Content |
Key Terms: Faraday’s law, Electromagnetism, Electric circuit, Bar Magnet, Galvanometer, Electromagnetic Induction, Magnetic Field, EMF
Faraday’s Laws of Electromagnetic Induction
[Click Here for Previous Year Questions]
Faraday’s Laws of Electromagnetic Induction mainly contain two laws. The first law explains the induction of emf in a conductor, while the second law generally quantifies the emf generated in the conductor.
Faraday’s First Law of Electromagnetic Induction
Faraday, from experiments conducted by him and Henry, concluded that emf is induced in a coil as the magnetic flux changes leading to the formation of the first law of electromagnetic induction. Faraday’s First law of Electromagnetic Induction can be expressed as:
| “Whenever a conductor is placed in a varying magnetic field, an electromotive force is induced. If the conductor circuit is closed, a current is induced which is called induced current.” |
Faraday’s Law of Electromagnetic Induction Detailed Explanation
Faraday’s Laws of Electromagnetic Induction Video Explanation
Thus, it can be said: E ∝ dΦ
This implies that current flows in a circuit as the magnetic flux changes over time which leads to some emf getting induced in the circuit.
Faraday’s First Law of Electromagnetic Induction
Changing Magnetic Field Intensity in a Closed Loop
According to faraday's law of electromagnetic induction, there are several ways via which we can change the magnetic field intensity in a closed loop:
- Rotate the coil relative to the magnet.
- Change the area of a coil set in the magnetic field.
- Move the magnet toward or away from the coil.
- Move the coil in or out of the magnetic field.
Magnetic Field Intensity in a Closed Loop
Faraday’s Second Law of Electromagnetic Induction
Faraday’s Second Law of Electromagnetic Induction can be expressed as “the induced emf in a coil is equal to the rate of change of flux linkage.”
Thus,
| \(\epsilon = -N \frac{\Delta \phi}{\Delta t}\) |
Where,
- ε is the electromotive force
- N refers to the number of turns
- Φ is the magnetic flux
Faraday’s second law of Electromagnetic Induction
The negative sign in the formula indicates that the direction of change in the direction of magnetic fields and induced EMFs have opposite signs. Hence, it can be concluded from the above formula that
- An increase in the number of turns in the coil leads to an increase in the induced emf.
- An increase in the speed of the relative motion between the coil and the magnet leads to an increased emf
- An increase in the magnetic field strength increases the induced emf.
Read More: Inductance formula
| Topic Related Links | ||
|---|---|---|
| Energy Consideration | Eddy Currents | Inductance |
| Magnetic Properties of Material | Lenz’s law | Solenoid Engine |
Faraday’s Law Derivation
[Click Here for Sample Questions]
Assuming that a magnet approaches a coil, thus considering two-time instances, T1 and T2.
- Flux linkage with coil at time T1 = NΦ1.
- Flux linkage with coil at time T2 = NΦ2
Faraday's law
The change in the flux linkage can be expressed as:
⇒ N(Φ2 – Φ1)
Now assuming a change in flux linkage:
⇒ Φ = Φ2 – Φ1
Thus, the change in flux linkage can be further shown by, NΦ
The rate of change of flux linkage can be demonstrated by:
⇒ N\(\frac{ \phi}{t}\)
Now considering the derivative of the given equation, we can obtain:
⇒ N \(\frac{d \phi}{dt}\)
As per Faraday’s second law of electromagnetic induction, we are already aware that the induced emf in a coil is equivalent to the rate of change of flux linkage. Thus,
⇒ E = N\(\frac{d \phi}{dt}\)
As per Lenz law,
= E = – N\(\frac{d \phi}{dt}\)
| \(\therefore\) Now, from the given equation, the following can be concluded:
|
What is Lenz's Law?
[Click Here for Previous Year Questions]
Lenz’s Law claims that:
| “The polarity of the induced emf tends to yield current that opposes the change in magnetic flux which generated it.” |
Lenz’s Law is based on the principle of Newton’s Third law and Conservation of Energy. It is one of the simplest ways to determine the direction of induced current. Lenz’s Law is named after Emil Lenz. There are several Lenz’s Law applications as well. The principle of Lenz’s Law is used in metal detectors, eddy current balances, card reader, AC generators and more.
Lenz’s Law Formula
The formula of Lenz’s Law is:
⇒ \(\begin{array}{l}Emf=-N\left ( \frac{\Delta \phi }{\Delta t} \right )\end{array}\)
Where,
- Emf = induced voltage (or, electromotive force)
- N = Number of loops
- Δϕ = Change in magnetic flux
- Δt = Change in time
What is the difference between Lenz’s law and Faraday’s law?
Lenz’s law is based on the conservation of energy which is applied to electromagnetic induction. Faraday’s law, on the other hand, is based upon the electromagnetic force yielded.
What is the importance of Lenz’s law?
Lenz’s law can be widely used to deduce the direction of the induced current.
Read More: Magnetic Properties of Materials
Faraday’s Experiment
[Click Here for Sample Questions]
In this experiment, we have a coil attached to a bar magnet and a galvanometer.
Faraday's Experiment
- Initially, the coil does not have a source of current which implies the battery is not attached, thus no current circulates inside the coil. When the bar magnet is moved in the direction of the coil, the galvanometer starts showing a deflection even without the presence of a battery. So how was the current induced in the coil?
- Due to the motion of the bar magnet, emf was induced in the coil causing electromagnetic induction. Now, when the magnet is moved towards the coil with a velocity “v”, it is observed that the galvanometer shows a deflection only till the bar magnet remains in motion.
- The moment the motion is stopped and v becomes zero, the galvanometer does not show any deflection. Hence if v = 0 then emf = 0. It was observed that the greater the velocity is, the greater the induced emf and when the direction of v is changed, the current moves in opposite direction as the galvanometer shows a deflection on the opposite side.
Relation Between Induced EMF and Flux from Faraday’s ExperimentHe conducted a set of three experiments through which he arrived at observations that resulted in Faraday’s laws. These observations are: From his first experiment, he proved that current is induced only when the strength of the magnetic field is varied:
From his second experiment, he concluded that an electromagnetic force will be induced when there is a relative motion between the coil and the magnet:
From his third experiment, he observed that there was no deflection in the galvanometer, when the coil was moved away in a stationary magnetic field and when the magnet was moved away from the loop, the ammeter showed deflection in the opposite direction:
|
Relationship Between Position of Magnet and Deflection of Galvanometer
After summarizing the above points, the relation between the Position of the Magnet and the Deflection in the Galvanometer can be shown as:
| Position of Magnet | Deflection in Galvanometer |
|---|---|
| Magnet found at Rest | No deflection |
| Magnet pushes towards the coil | Deflection in one direction |
| Near the coil, the magnet is stationary at the same point | No deflection |
| Magnet shifts away from coil | Deflection in opposite direction |
| Magnet (away from coil) held stationary at the same point | No deflection |
Conclusion of Faraday’s Experiments
Upon conducting the experiments, Faraday concluded that:
- Relative motion can be found between a conductor and a magnetic field, the flux linkage with the coil mainly varies. The flux change generates a voltage across a coil.
- Faraday's law claims that, “The electromagnetic force is generated when the magnetic flux or the magnetic field changes with time.”. Hence, Michael Faraday developed two laws based on the above experiments.
Faraday's Law Applications
[Click Here for Previous Year Questions]
There are several applications of faraday’s Laws, some include:
- Equipment, such as, transformers is based on Faraday’s law.
- Induction cooker is based on mutual induction, which is a principle of Faraday’s law.
- Velocity of fluids is recorded by inducing electromotive force into an electromagnetic flowmeter.
- Electric guitar and electric violin are applications of Faraday’s law.
- Maxwell’s equation is on the basis of the converse of Faraday’s laws, stating that a change in the magnetic field obtains a change in the electric field.
Read Also:
Previous Year Questions
- 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?
- X -rays are….
- 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]
- Coefficient inductance is a vector quantity... [KEAM 2016]
Things to Remember
- Faraday’s law of electromagnetic induction which is also regarded as Faraday’s law is a basic law of electromagnetism which helps to predict how a magnetic field will interact with an electric circuit to produce emf.
- The law was given by the renowned experimental physicist known as Michael Faraday, in the year 1831.
- The law was proposed as a result of observations of three experiments conducted by Faraday.
- There are 2 laws of electromagnetic induction where the first one deals with the induction of emf in a conductor while the second one is concerned with quantifying the emf in the conductor.
- Some applications of Faraday’s laws of electromagnetic induction is the working of transformers and induction cookers.
Read More:
Sample Questions
Ques. State Faraday’s law of electromagnetic induction. (Foreign 2009,’12) (3 marks)
Ans. Based on his experiments, Faraday gave the following two laws of induction:
First law- An emf is induced in it which lasts whenever magnetic flux linked with a circuit changes, so long as change in flux continues.
Second law- The emf that is induced in the loop or closed circuit is directly proportional to the rate of change of magnetic flux linked with the loop.
Where N is the number of turns in the coil and the negative sign indicates Lenz's law.
Ques. What are the factors the magnitude of the emf induced in the circuit due to magnetic flux depend on? (Foreign 2013) (2 marks)
Ans. The magnitude of the emf induced in the circuit due to magnetic flux depends on the time rate of change of the magnetic flux through the circuit or the rate of cutting of the magnetic field lines.
Ques. (i) When primary coil P is moved towards the secondary coil S as shown in the figure below, the galvanometer shows momentary deflection. What is to be done to have a larger deflection in the galvanometer with the same battery?
(ii) State the related law. (Delhi 2010) (3 marks)
Ans. (i) The coil P should be moved towards or away from coil S. The laws related here are Faraday’s law of electromagnetic induction.
(ii) Based on his experiments, Faraday gave the following two laws of induction:
First law- An emf is induced in it which lasts whenever magnetic flux linked with a circuit changes, so long as change in flux continues.
Second law- The emf that is induced in the loop or closed circuit is directly proportional to the rate of change of magnetic flux linked with the loop.
Where N is the number of turns in the coil and the negative sign indicates Lenz's law.
Ques. (i) State Faraday’s law of electromagnetic induction.
(ii) A jet plane is travelling towards the west at a speed of 1800 km/h. Find out the voltage difference developed between the wings having a span of 25m if the earth’s magnetic field at the location has magnitude of 5 x 10-4T and the dip angle is 30°. (All India 2009) (5 marks)
Ans. (i) Based on his experiments, Faraday gave the following two laws of induction:
First law- An emf is induced in it which lasts whenever magnetic flux linked with a circuit changes, so long as the change in flux continues.
Second law- The emf that is induced in the loop or closed circuit is directly proportional to the rate of change of magnetic flux linked with the loop.
Where, N is the number of turns in the coil and the negative sign indicates Lenz's law.
(ii) Voltage difference between the ends of the wings of a plane is generated because the plane is intersecting the vertical component of Earth’s magnetic field for which change in magnetic flux takes place.
As given, v = 1800 km/h
v = 1800 x 5/18 = 500 m/s (towards west)
d = 25m
Be = 5 x 10-4T
Angle of dip, δ = 30° = Π/6 rad
The plane intersects the vertical component of the magnetic field when flying the plane toward west which is given by,
V = Be sin \(\delta\) = 5 x 10-4 sin 30°
= 2.5 x 10-4 T
Here, V is the vertical component of magnetic field,
PD = v (V) l
= 500 x (2.5 x 10-4) x 25
= 3.125 V
Ques. A coil of number of turns N and area A is rotated at a constant angular speed ω in a uniform magnetic field B and connected to a resistor R. Deduce expressions for
(i) maximum emf induced in the coil.
(ii) power dissipation in the coil. (Delhi) (5 marks)
Ans. (i) Initially, area vector A of the coil makes an angle θ with the direction of the magnetic field.
Let us assume that the coil rotates by an angle θ with the magnetic field in time t.
…(i)
Therefore, magnetic flux linked with each turn of rectangular coil,
From equations (i) and (ii), we get
(ii)
Ques. (i) Describe a simple experiment to show that the polarity of emf induced in a coil is always such that it tends to produce current which opposes a change in magnetic flux that produces it.
(ii) The current flowing through an inductor of self-inductance L is increasing constantly. Plot a graph showing the variation of
Magnetic flux versus the current
Induced emf versus dl/dt
Magnetic potential energy stored versus the current. (Delhi 2014) (3 marks)
Ans. (i) The coil P should be moved towards or away from coil S. The laws related here are Faraday’s law of electromagnetic induction.
Based on his experiments, Faraday gave the following two laws of induction:
First law- An emf is induced in it which lasts whenever magnetic flux linked with a circuit changes, so long as the change in flux continues.
Second law- The emf that is induced in loop or closed circuit is directly proportional to the rate of change of magnetic flux linked with the loop.
Where N is the number of turns in the coil and the negative sign indicates Lenz's law.
(ii) (a) magnetic flux versus current
(b) Induced emf versus dl/dt
dI/dt is positive and e is constant and negative.
(c) Magnetic potential energy stored versus current
Ques. State Faraday’s law of electromagnetic induction.
A rectangular conductor PQRS as shown in the figure below, within which the conductor PQ is free to move in a uniform magnetic field B is perpendicular to the plane of the paper.
The field extends from x = 0 to x = b and zero for x > b.
Consider that only the ram PQ possesses resistance r. When the arm PQ is pulled outward from x = 0 to x = 2b and is then moved backward to x = 0 with a constant speed v, brain the expressions for the flux and the induced emf.
Sketch the variation of these quantities with distance 0 ≤ x ≤ 2b. (All India 2010) (5 marks)
Ans. Based on his experiments, Faraday gave the following two laws of induction:
First law- An emf is induced in it which lasts whenever magnetic flux linked with a circuit changes, so long as change in flux continues.
Second law- The emf that is induced in loop or closed circuit is directly proportional to the rate of change of magnetic flux linked with the loop.
Where, N is the number of turns in the coil and negative sign indicates Lenz's law.
Case I: when PQ moves forward,
(i) For 0 ≤ x < b
Magnetic field exists in the region.
Thus, the area of loop PQRS = lx
Thus, the magnetic flux linked with the loop PQRS,
… (i) (b > x ≥ 0)
(ii) For 2b ≥ x ≥ b
B = 0
Therefore, flux linked with the loop PQRS is uniform and is given by,
… (ii)
Forward journey,
Thus for b > x ≥ 0
Return journey,
For b ≤ x ≤ 2b
(decreasing)
Graphical representation
Case II: for b > x ≥ 0, B = 0
Forward journey
For b > x ≥ 0
Backward journey
For b > x ≥ 0
Variation of induced emf
For Latest Updates on Upcoming Board Exams, Click Here:https://t.me/class_10_12_board_updates
Also Read:
Comments