FARADAY LAW OF ELECTROMAGNETIC INDUCTION
First, we explain what is electromagnetic induction?
ELECTROMAGNETIC INDUCTION "A PHENOMENON IN WHICH ELOCTROMOTIVE FORCE IS INDUCED DUE TO RELATIVE MOTION OF COIL AND MAGNET"
EXPLANATION
when a coil or magnet moves relatively then due to a change in magnetic flux or magnetic field lines a force acts upon the charges of the coil, due to applied force charge carriers move in the closed circuit and a potential difference produces in the circuit. This potential difference is called electromotive force. This electromotive force induces an electric current called induced current.
THERE ARE TREE WAYS TO EXPLAIN ELECTROMAGNETIC INDUCTION
1. WHEN COIL IS IN REST AND MAGNET IS MOVING
when a bar magnet is moved in the coil then due to a change in magnetic flux in the coil an EMF is induced and induced current flows through the coil which is detected by galvanometer as shown in the figure
. THE SECOND METHOD IS
2. WHEN COIL IS MOVING AND MAGNET IS IN REST
When a coil is moved in the magnet then due to a change in magnetic flux in the coil an EMF is induced which induces a current in the coil as shown in the figure
. THE THIRD METHOD IS
3. BY MUTUAL INDUCTION
When a changing current passes through a coil, a changing magnetic field is produced in the coil which when passes through a nearby coil an EMF is induced in this secondary coil as shown in the figure.
The question arises here that induced EMF depends upon which factors? For the answer, we derive a relation for induced EMF
When a metal rod of length l is placed on two metal rails connected with an ammeter it makes a closed circuit. A uniform perpendicular magnetic field is applied to the circuit. When the rod is moved rightward with uniform velocity v then a magnetic force is applied on the electron (in the rod ) moving with the same velocity v (the force is downward in the figure according to the right-hand rule ). Due to this force electron moves downward and an electric field produces across the ends of the conductor. This potential difference is called induced EMF. Due to produced electric field electric force applies on an electron in the opposite direction of magnetic force. When these forces become equal then by equating these forces we derive a relation for induced EM.
DERIVATION
Fe = qEo ...........(1)
Fm = qvB …….(2)
AS
Fe = Fe
So
qEo = qvB
Eo =vB ……(3)
We know that
Eo = −∆V∕ l …..(4)
By equation 3 and 4
∆V = −VBL
The induced potential difference is called induced EMF in this case
SO
ԑ = −VBL
ԑ = −VBLsinѲ …..(5)
The above equation shows that emf depends on rod length, the velocity of the rod, external magnetic field strength, and angle between magnetic field and length of the rod.
HOW FARADAY LAW RELATES INDUCED EMF TO RATE OF CHANGE OF MAGNETIC FLUX
Let us derive an expression for FARADAY LAW
From the figure when we move the rod with uniform velocity to the right side, the rod moves through distance ∆x in time ∆t then
v = ∆x ∕ ∆t put above equation in equation 5
ԑ = -∆x BLsinѲ ∕ ∆t
ԑ = - (∆XL ) BsinѲ ∕ ∆t
ԑ = -∆ A BsinѲ ∕ ∆t
For the maximum value of emf sine function equal to 1
ԑ = - A B ∕ ∆t
ԑ = -∆φ ∕ ∆t
If we replace the conductor with a coil of N turns then
ԑ = -N∆φ ∕∆t
The above equation can be defined as
“THE EMF INDUCED IN A COIL OF N TURNS IS DIRECTLY PROPORTIONAL TO THE RATE OF CHANGE OF MAGNETIC FLUX ONLY “
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