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.
Faraday’s Law of 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.
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.
Electromagnetic Induction Formula for Moving Conductor
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)
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.
Conclusion
The production of voltage (or EMF) over an electrical conductor placed inside a varying magnetic field is referred to as electromagnetic induction. The induced electromotive force in a closed circuit is equal to the rate of change of the magnetic flux enclosed by the circuit, according to Faraday’s law.