Electromagnetic induction is the phenomenon where a changing magnetic field induces an electromotive force (EMF) or voltage in a conductor. When the magnetic field through a coil or conductor changes, it creates a self-induced EMF, also known as a self-induced voltage.
The magnitude of the self-induced EMF can be calculated using Faraday's law of electromagnetic induction, which states that the EMF induced in a circuit is directly proportional to the rate of change of magnetic flux through the circuit. Mathematically, it can be expressed as:
=
−
Φ
E=−N
dt
dΦ
Where:
E is the magnitude of the self-induced EMF in volts (V).
N is the number of turns of the coil or the conductor.
Φ
dt
dΦ
is the rate of change of magnetic flux through the coil or conductor with respect to time. Magnetic flux (
Φ
Φ) is the product of the magnetic field (
B) through the coil and the area (
A) perpendicular to the field:
Φ
=
⋅
Φ=B⋅A.
The negative sign in the equation represents Lenz's law, which states that the direction of the induced current (and EMF) opposes the change in magnetic flux that produced it. This law ensures that the induced current creates a magnetic field that counteracts the change in the original magnetic field.
To summarize, the magnitude of the self-induced EMF depends on factors such as the number of turns in the coil, the rate of change of magnetic flux, and the characteristics of the circuit. It's important to note that the self-induced EMF doesn't depend on the resistance of the circuit; it's solely determined by the rate of change of magnetic flux through the circuit.