For Class 12 students, here is a thorough introduction of electromagnetic induction:
Electrical Induction:
A fluctuating magnetic field can induce an electric field and an electric current in a conductor, a phenomenon known as electromagnetic induction. Michael Faraday first identified this occurrence in 1831.
The electromagnetic induction law of Faraday
According to Faraday's law of electromagnetic induction, the amount of electromotive force (EMF) induced in a circuit is inversely related to how quickly the magnetic field changes inside the circuit.
The induced EMF can be calculated mathematically by:
EMF = -dt
where t is the passage of time, is the magnetic flux through the circuit, and EMF is the electromotive force.
Lenz's Rule
According to Lenz's law, the induced current's direction is such that it
EMF = -dΦ/dt
where EMF is the electromotive force, Φ is the magnetic flux through the circuit, and t is time.
Lenz's Law:
Lenz's law states that the direction of the induced current is such that it opposes the change that produced it. In other words, the direction of the induced current is such that it creates a magnetic field that opposes the change in the magnetic field that produced it.
This law is based on the principle of conservation of energy, which states that energy cannot be created or destroyed, but only transformed from one form to another. Therefore, any change in the magnetic field must be accompanied by a corresponding change in the electric field, and vice versa.
Applications of Electromagnetic Induction:
Electromagnetic induction has many practical applications, some of which are:
Transformers: Transformers are devices that use electromagnetic induction to change the voltage of an alternating current (AC) without changing its frequency.
Generators: Generators use electromagnetic induction to convert mechanical energy into electrical energy.
Induction cooktops: Induction cooktops use electromagnetic induction to heat food by creating a magnetic field that induces an electric current in the metal of the cookware.
Magnetic levitation trains: Magnetic levitation (maglev) trains use electromagnetic induction to levitate and propel the train by creating a magnetic field that repels the train from the track.
Conclusion:
Electromagnetic induction is a fundamental principle of physics that has many practical applications. It is the basis for the functioning of many electrical devices and is essential for the generation, transmission, and distribution of electrical power.
SOME FORMULA
Faraday's Law:
ε = -dφ/dt
Where ε is the induced electromotive force, φ is the magnetic flux, and t is the time.
Lenz's Law:
The direction of the induced electromotive force is such that it opposes the change in magnetic flux that produced it.
Magnetic Flux:
φ = BAcos(θ)
Where B is the magnetic field, A is the area of the surface, and θ is the angle between the magnetic field and the normal to the surface.
Magnetic Field due to a Long Straight Conductor:
B = μ0I/(2πr)
Where B is the magnetic field, μ0 is the magnetic constant, I is the current, and r is the distance from the conductor.
Magnetic Field due to a Current Loop:
B = μ0I/(2R)
Where B is the magnetic field, μ0 is the magnetic constant, I is the current, and R is the distance from the center of the loop.
Magnetic Flux Density:
B = μ0*H
Where B is the magnetic flux density and H is the magnetic field intensity.
Induced Electromotive Force in a Moving Conductor:
ε = Blv*sin(θ)
Where ε is the induced electromotive force, B is the magnetic flux density, l is the length of the conductor, v is the velocity of the conductor, and θ is the angle between the velocity vector and the magnetic field vector.
Inductance of a Coil:
L = N*Φ/I
Where L is the inductance, N is the number of turns in the coil, Φ is the magnetic flux, and I is the current.
Self-Inductance of a Coil:
ε = -L*(dI/dt)
Where ε is the induced electromotive force, L is the self-inductance of the coil, and dI/dt is the rate of change of the current in the coil.
Mutual Inductance of Two Coils:
ε2 = -M*(dI1/dt)
Where ε2 is the induced electromotive force in the second coil, M is the mutual inductance between the two coils, and dI1/dt is the rate of change of the current in the first coil.
