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Magnetic induction is the phenomenon of the generation of electromotive force or e.m.f. in a conductor pertaining to the change in magnetic flux linked with it. It was discovered by the scientist Michael Faraday in 1831. Faraday’s law of induction was later mathematically represented by Maxwell. Magnetic induction is a very important scientific phenomenon and a crucial topic in physics. To understand what the magnetic induction formula signifies let us understand Faraday’s Law of Induction. Here we will also study the emf induced formula, faraday's law formula, and a few other important features of magnetic induction.

The magnetic field induction formula of Faraday states by a change in the magnetic flux linked to a conductor, an electromotive force (emf) is induced. The rate of change of the magnetic flux enclosed by a closed circuit is equal to that of emf.

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According to Faraday’s experiments

ε is directly proportional to the change in flux

ε is inversely proportional to Δt

ε produced in a coil having N turns is N times that of a single current-conduction coil (ε ∝ N)

The magnetic flux passing through a surface of vector area A:

ΦB =B⋅A = BAcosθ

For a varying magnetic field the magnetic flux is dΦB through an infinitesimal area dA:

dΦB = B⋅dA

The surface integral gives the total magnetic flux through the surface.

ΦB = ∫∫A B⋅dA

According to Faraday’s law formula, in a coil of wire with N turns, the emf induced formula in a closed circuit is given by

EMF (ε) = - N\[\frac{\Delta \phi }{\Delta t}\]

When flux changes by Δ in a time Δt.

The minus sign shows that a current I and magnetic field B opposite to the direction of change in flux is produced. This is known as Lenz’s law.

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For a moving rod, N=1 and the flux Φ=BAcosθ, θ=0º and cosθ=1, a B is perpendicular to A.

The area swept out by the rod is ΔA= lΔx

∴ ε = \[\frac{B \Delta A }{\Delta t}\] = \[\frac{Bl \Delta x}{\Delta t}\] = Blv

where v (velocity) is perpendicular to the B (magnetic field)

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In the above scenario of a generator, the velocity is at an angle θ with B, so that its component perpendicular to B is vsinθ.

ε = Blv sinθ

Where, l = length of the conductor,

v = velocity of the conductor

θ = the angle between the magnetic field and the direction of motion.

Thus, the induced current formula signifies the close relationship between electric field and magnetic field which is dependent on a specific time variation.

FAQ (Frequently Asked Questions)

1. Determine the Magnetic Flux Formula in Terms of Current.

Ans: As the flux is produced in response to the current, the flux induced by a current is proportional to the current

Thus, change in flux induces a current and a voltage which is proportional to the rate of change of flux. This is similar to Ohm's Law (V = IR).

Thus we can say ΦB ∝ I

As we know Φ_{B}=B⋅A

Where B = µ_{0}NI

[µ_{0} (permeability constant) = 4π10^{-7} T ]

Therefore, Φ_{B} = µ_{0}NIA

2. How to Establish an Inductor Energy Formula?

Ans: Energy is stored within a magnetic field of an inductor.

Due to energy conservation, the energy needed to drive the original current should have an escape route. In the case of an inductor, the magnetic field is the escape route of that current. The energy stored in an inductor is equal to the work needed to generate a current through the inductor. The formula for this energy is given as:

E = ½ LI²

where L is the inductance (unit - Henry) and I (Ampere).