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# Electromagnetic Induction

The phenomenon in which electric current is generated by varying magnetic field is called electromagnetic induction

What is cause of generation of electric current between magnet and coil?

Ans - The relative motion ie change in magnetic flux is cause of generation of electric current between magnet and coil This current is also known as induced current

Magnetic Flux --

Magnetic flux through a surface of area A placed in a uniform magnetic field is

Flux = BA cos ¢

Where theta angle is angle between magnetic field and Area vector
Its SI unit is weber or Tesla meter² It is a scalar quantity

Faraday concluded that an emf is induced in a coil when magnetic flux through the coil changes with time
The magnitude of induced emf in a circuit is equal to the time rate of change of magnetic flux through the circuit

induced emf = change in flux / time

€ = d¢/dt

If N is number of turns then

€= - N d¢/dt

Note --

# Induced emf is increased by increasing number of turns

Lenz's Law

In 1834 Lenz gives a law known as Lenz Law

Statement --

The polarity of induced emf is such that it tends to produce a current which opposes change in magnetic flux that produced it

When magnetic flux increases direction of induced current is anti clock wise

When magnetic flux decreases direction of induced current is clock wise

Motional Emf

When a metal rod of length l is placed normal to magnetic field B moved perpendicular with a velocity v induced emf across its ends is known as rotional emf

If a length of conductor 'l' is placed in a magnetic field of area If it is moved through a distance of dx then

Flux = BA cos o
= Blx

emf = change in flux / time

= Bldx/dt

= Blv

Alternating current

The current whose magnitude keeps on changing continously with time between 0 and a maximum value and the direction also reverses periodically is called alternating current

i= i0sinwt =i0sin2πnt = i0sin 2πt/T

i - instantaneous value of current

i0 - peak value of current

n= frequency in Hz

T= time period

Root mean square value (rms)

Root mean square of current in an AC circuit for one complete cycle is called RMS value
i(rms)=i0/√2

RMS value of alternating current is also called virtual value or effective value

Mean or average value (i(av))

The average of instantaneous values of current in one cycle is called its mean value the average value of alternating quantity for one complete cycle is zero

The average value of alternating current over half cycle is

iav= 2i0/π

Impedence

Z= √{(Xl~Xc)^2+ R^2}

Resonant frequency

w0= 1/√LC

v0 = 1/2π√LC

Resonant frequency does not depend upon the resistance of the circuit
Resonant frequency admittance is minimum and impedance is maximum

Quality Factor

Quality factor of the circuit determines the sharpness of resonance

Formula

Q= wL/R = 1/wRC

AC Generator
An electrical machine used to convert mechanical energy into electrical energy is known as a c generator it works on the principle of electromagnetic induction that is when a coil is rotated in a uniform magnetic field and induced EMF is produced in it

induced emf = -Nd¢/dt = NBAwsinwt

Current in coil =
i= e/ R
Electromagnetic Wave
The waves in which electric and magnetic fields vary sinusoidally in space and with time the electric and magnetic fields are mutually perpendicular to each other and also to the direction of propagation of the wave

Displacement Current

The plates of a charged capacitor a joint through a conductor then the charge arises due to flow of electrons and conduction current flows in the conductor Maxwell proposed that as the charge on the plates of capacitor decreases the electric field between the plates also decreases with time and time varying electric field produces magnetic field which signifies there must be some current flowing between the plates this current is known as displacement current
Ampere maxwell law
Maxwell in 1862 case the basic laws of electricity and magnetism in the form of four fundamental equations which are known as Maxwell equations

1 Gauss law of electrostatics

Just now give the total electric flux in the terms of the charge enclosed by the closed surface

This law states that the electric lines of force start from positive charge and end at negative charge that is electric lines of force do not form a continuous closed path

InE.ds= q/€o

2 Gauss law for magnetism
This law shows that number of magnetic lines of force entering a closed surface is equal to the number of magnetic lines of force leaving that closed surface

Bds=0

3 Faraday law of electromagnetic induction

It gives relationship between electric field and changing magnetic flux It tells that changing magnetic field is the source of the electric field

E.dl= d¢/dt

¢= flux

4 Ampere Maxwell law

Law states that a magnetic field can be produced by a conduction current as well as by displacement current
At any instant in a circuit the conduction current is equal to the displacement current

Relation between Electric and Magnetic Field

E=B×C

E is electric field

B is magnetic field

C is speed of light

Energy density of electromagnetic wave

Energy density is defined as energy crossing through unit area in unit time

Watch lecture in order to understand how to solve the different questions based on electromagnetic waves

Sun Dec 25, 2022