Magnetic Induction Formula

Magnetic induction was discovered by Michael Faraday in 1831. Later Maxwell described it mathematically and it came to be known as Faraday’s law of induction. Faraday had performed three experiments to understand electromagnetic induction. Then Faraday’s law became crucial to understand induction which now has several practical applications like in generators, transformers, etc. In this session, let us know more about electromagnetic induction class 12 formulas.

Table of Contents:

Law of Magnetic Induction

Magnetic induction, also called electromagnetic induction refers to the production of voltage (or EMF) across an electrical conductor placed inside a varying magnetic field. According to Faraday’s law, for a closed circuit, the induced electromotive force is equal to the rate of change of the magnetic flux enclosed by the circuit. To know more about magnetic induction, visit electromagnetic induction. Now, let us know more about electromagnetic induction class 12 formulas.

Formula For Magnetic Induction

From Faraday’s law, the EMF induced in a closed circuit is given by –

\epsilon = \frac{d\Phi_{b} }{dt}

Here, \Phi _{b} is the magnetic flux, t is the time and \epsilon is the EMF induced.

Note:

\Phi _{b} = \oint\vec{B}\cdot d\vec{s}

Where, B = magnetic field and “ds” is a very small area.

In a coil of wire with N turns, the EMF will be-

\epsilon = N\frac{d\Phi_{b} }{dt}

Later, according to Lenz law, Faraday’s equation was modified accordingly which is now given by-

\epsilon = N\frac{d\Phi_{b} }{dt}

Now, this equation determines the direction of induced current and follows the law of conservation of energy.

For a moving conductor, the EMF is given by:

\epsilon = Blv\, sin\Theta

Where, l = length of the conductor, v = velocity of the conductor and θ is the angle between the magnetic field and the direction of motion.

An example related to the magnetic induction is given below for better understanding.

Solved Examples

Example 1:

Calculate the induced EMF if the magnetic flux linked with a coil changes from 12 x 10-3 Wb to 6 x 10-3 Wb in 0.01 second.

Solution:

\(\begin{array}{l}\textup{Induced emf,} \,\, \varepsilon = -\frac{d\phi_B}{dt} = – \frac{(6 \times 10^{-3} – 12\times 10^{-3})}{0.01} = \frac{6\times 10^{-3}}{10^{-2}} = 0.6\,V\end{array} \)

Example 2:

A long solenoid having 15 turns per cm and a small loop area of 2 cm2 is placed in a solenoid to its axis. Find the induced emf in the loop while the current carried by the solenoid is changing steadily from 2.0 A to 4.0 A in 0.1 s.

Solution:

Number of turns on the solenoid – 15 turn/cm = 1500 turn/m
Number of turns per unit length, n = 1500 turns
The solenoid has a small loop of area, A = 2.0 cm2 = 2 x 10-4 m2
Current carried by the solenoid changes from 2 A to 4 A.
Therefore, change in current in the solenoid, di = 4 – 2 = 2 A
Change in time, dt = 0.1 s

According to Faraday’s law, induced emf in the solenoid is given by:

\(\begin{array}{l}e = \frac{d\phi }{dt} \,\, —\,\,(1)\end{array} \)
Where,
Φ = Induced flux through the small loop
= BA — (2)

B = Magnetic field
= μ0ni

μ0 = Permeability of free space
= 4n x 10-7 H/m

Hence, equation (1) can be reduced to:

\(\begin{array}{l}e = \frac{d}{dt}(BA)e = A \mu_0 n \times \left ( \frac{di}{dt}\right )\end{array} \)
 

\(\begin{array}{l}= 2 \times 10^{-4} \times 4\pi \times 10^{-7} \times 1500 \times \frac{2}{0.1}\end{array} \)
 

\(\begin{array}{l}= 7.54 \times 10^{-6} \, V\end{array} \)
 

Hence, the induced voltage in the loop is 7.54 x 10-6 V

See the video below, to know more about electromagnetic induction.


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Frequently Asked Questions – FAQs

Q1

Who discovered magnetic induction?

Magnetic induction was discovered by Michael Faraday in 1831.

Q2

What is magnetic induction?

Magnetic induction, also known as electromagnetic induction, refers to the production of voltage (or EMF) across an electrical conductor placed inside a varying magnetic field.

Q3

Give the formula for the EMF for a moving conductor?

\(\begin{array}{l}\epsilon = Blv sin\theta\end{array} \)
Q4

State Faraday’s first law of electromagnetic induction?

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.
Q5

State true or false: The concept of Faraday’s law is applied to generators and transformers.

True.
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