Electromagnetic induction is the phenomenon in which an electromotive force (EMF) is induced in a conductor when the conductor passes through a magnetic field or when there is a change in the magnetic flux linked with it. This can occur either when a conductor moves in a magnetic field or when the magnetic field around a stationary conductor changes.
This phenomenon was discovered by Michael Faraday through experiments in which a coil of wire connected to a galvanometer showed a voltage when a bar magnet was moved through it. The experiment demonstrated that electrical energy can be produced using magnetic fields instead of batteries.
Faraday law
Faraday gave two laws of electromagnetic induction that are called the Faraday law of Electromagnetic Induction that are,
- Faraday's First Law of Electromagnetic Induction
- Faraday's Second Law of Electromagnetic Induction
Faraday's First Law
Faraday’s First Law states that whenever a conductor is placed in a changing magnetic field, an electromotive force (EMF) is induced in the conductor. If the conductor forms a closed circuit, an induced current will also flow through it.
Faraday's Second Law
Faraday’s Second Law states that the magnitude of the induced electromotive force (EMF) in a conductor is equal to the rate of change of magnetic flux linked with the conductor. It means that the induced EMF depends on it.
- Number of Turns in the Coils: The induced voltage is proportional to the number of turns/coils. The more turns there are, the more voltage is created.
- Changing Magnetic Field: The induced voltage is affected by changes in the magnetic field. This can be accomplished by rotating the magnetic field around the conductor or by rotating the conductor inside the magnetic field.
Mathematically, it is expressed as:
where
- E = induced EMF
- N = number of turns in the coil
- Φ = magnetic flux
Eddy Currents
Eddy currents are loops of electric current induced in a conductor when it is placed in a changing magnetic field. These currents create a magnetic field that opposes the change in the original magnetic field, in accordance with Lenz’s Law. They are also called Foucault currents.
Applications
- Electromagnetic induction in AC generator
- Electrical Transformers
- Magnetic Flow Meter
Electromagnetic induction in AC generator
An AC generator works on the principle of electromagnetic induction to produce alternating current (AC).
When a coil rotates in a magnetic field, the magnetic flux linked with the coil changes continuously, inducing an electromotive force (EMF) in the coil.
If the area of the coil is A and the magnetic field is B, the effective flux through the coil at any instant is Φ = BA cosθ, where θ is the angle between the coil’s area vector and the magnetic field. As the coil rotates, θ changes, causing a continuous change in flux and thus inducing an alternating EMF in the coil.
Electrical Transformers
An electrical transformer is a device that works on the principle of electromagnetic induction to change the voltage of alternating current (AC) electricity from one level to another. It consists of a primary and a secondary coil linked by a magnetic field. In a step-down transformer, the voltage in the primary coil is higher than in the secondary coil, which is used to reduce voltage for safe household use. In a step-up transformer, the secondary voltage is higher than the primary, which helps increase voltage for long-distance power transmission and reduces energy loss in the lines.
Magnetic Flow Meter
A Magnetic Flow Meter (or Electromagnetic Flow Meter) is a device used to measure the velocity or volumetric flow of fluids. It works on the principle of electromagnetic induction. This device, commonly called a Magmeter, can measure only the flow of electrically conductive fluids.
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Solved Problems
Question 1: When a bar magnet is placed near the circular coil having 50 turns, the magnetic field density changes at a rate of 0.10 T ⁄ s. Find the emf induced in the coil.
Solution: Number of turns, N = 50 turns
Rate of change of magnetic flux, dϕ ⁄ dt = 0.10 T ⁄ s
E = - N (dϕ ⁄ dt)
⇒ E = - 50 × 0.10 V
⇒ E = - 5 V
Hence, the emf induced in the coil is 5 V.
Question 2: A loop of wire is placed in a magnetic field, and the magnetic flux through the loop is increasing at a rate of 0.02 T·m²/s. if the resistance of the loop of wire is 5 ohms, then what is the induced current in the loop?
Solution: For a loop of wire, N=1, and the rate of flux increase is 0.02 Tm2/s i.e., dϕ ⁄ dt = 0.02 Tm2/s
resistance of loop of wire is 5 ohm,
According to Lenz's Law, E = -N(dϕ ⁄ dt)
E = -1×(0.02) = -0.02 Volts (we can neglect the sign as it tells the direction only)
We know Ohm's Law states, V = IR
⇒ I = V/R = 0.02/5 = 0.004 Ampere = 4 Milli-Ampere
Thus, the Induced current in the wire loop is 4 milliampere(mA).
Question 3: A coil of 100 turns is placed in a magnetic field. The magnetic flux through each turn decreases uniformly from 0.5 Wb to 0 Wb in 0.2 s. Find the induced EMF in the coil.
Solution: Given
Number of turns, N = 100 N
Initial flux, Φi = 0.5 Wb
Final flux, Φf = 0 Wb
Time, t = 0.2 s
Rate of change of flux
\frac{d\Phi}{dt} = \frac{\Phi_f - \Phi_i}{t}
= \frac{0 - 0.5}{0.2} = -2.5 \, \text{Wb/s} \\[2mm] Induced EMF
E = -N \frac{d\Phi}{dt}
= -100 \times (-2.5) = 250 \, \text{V} \\[1mm] The induced EMF is 250 V.
Question 4: A rectangular coil of 20 turns, each of area 0.1 m², is placed in a magnetic field of 0.5 T. The coil is rotated such that the plane of the coil becomes perpendicular to the field in 0.05 s. Find the average EMF induced in the coil.
Solution: Given
N = 20
Area of each turn, A=0.1 m²
Magnetic field, B = 0.5 T
Change in angle, from 0o to 90o → flux changes from BA = 0.5 × 0.1 = 0.05 Wb to 0
Time, t = 0.05 s
Rate of change of flux
\frac{d\Phi}{dt} = \frac{\Phi_f - \Phi_i}{t}
= \frac{0 - 0.05}{0.05} = -1 \, \text{Wb/s} \\[2mm] Induced EMF
E = -N \frac{d\Phi}{dt}
= -20 \times (-1) = 20 \, \text{V} \\[1mm] The average induced EMF is 20 V.
Unsolved Problems
Question 1: A coil of 80 turns is placed in a magnetic field. The magnetic flux through each turn decreases uniformly from 0.6 Wb to 0 Wb in 0.3 s. Find the induced EMF in the coil.
Question 2: A single-turn circular loop of radius 0.1 m is placed perpendicular to a magnetic field of 0.8 T. The magnetic field is reduced to zero in 0.2 s. Find the induced EMF in the loop.
Question 3: A rectangular coil of 30 turns, each of area 0.05 m², is placed in a magnetic field of 0.4 T. The coil is rotated from a position parallel to the field to perpendicular to the field in 0.1 s. Find the average induced EMF.
Question 4: A coil of 50 turns is placed in a magnetic field that changes at a rate of 0.15 T/s. If the resistance of the coil is 10 Ω, calculate the induced current.
Question 5: A bar magnet is moved towards a coil of 40 turns such that the magnetic flux linked with the coil increases from 0 Wb to 0.2 Wb in 0.05 s. If the resistance of the coil is 8 Ω, calculate the induced EMF and the induced current in the coil.