Chapter 6 Electromagnetic Induction | class 12th | quick revision notes physics

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Chapter 6 Electromagnetic Induction Class 12 Physics Hand Written Notes By Ashish Anand Sir

Magnetic Flux: Magnetic flux through a plane of area dA placed in a uniform magnetic field B $Electromagnetic Induction Class 12 Notes PhysicsElectromagnetic Induction Class 12 Notes Physics$ where $\theta$ is the angle between magnetic field lines and area vector of the surface.
Dimensions of magnetic flux: $Electromagnetic Induction Class 12 Notes Physics$
SI unit:- Weber (Wb)
Faraday’s Law:
a) First Law: whenever there is a change in the magnetic flux linked with a circuit with time, an induced emf is produced in the circuit which lasts as long as the change in magnetic flux continues.
b) Second Law: The magnitude of the induced emf is directly proportional to the rate of change of magnetic flux linked with the closed circuit. $Electromagnetic Induction Class 12 Notes Physics$
Lenz’s Law: The direction of the induced emf or current in the circuit is such that it opposes the cause due to which it is produced i.e. it opposes the change in magnetic flux, so that-
$Electromagnetic Induction Class 12 Notes Physics$ Where N is the number of turns in the coil
Lenz’s law is based on energy conservation.
Induced EMF and Induced Current: $Electromagnetic Induction Class 12 Notes Physics$ $Electromagnetic Induction Class 12 Notes Physics$
Charge depends only on net change in flux does not depends on time.

Induced EMF,
Induced current, $\begin{align} & I=\frac{E}{R}=-\frac{N}{R}\left( \frac{d\phi }{dt} \right) \\ & =-\frac{N}{R}\frac{\left( {{\phi }_{2}}-{{\phi }_{1}} \right)}{t} \\ \end{align}$

Induced Emf due to Linear Motion of a Conducting Rod in a Uniform Magnetic Field
The induced emf, $Electromagnetic Induction Class 12 Notes Physics$
If $\overrightarrow{l},\overrightarrow{v}\text{ }and\overrightarrow{B}$ are perpendicular to each other, then $E=Bvl$
Fleming’s Right Hand Rule is used to find the direction of induced current set up in the conductor.
Induced EMF due to Rotation of a Conducting Rod in a Uniform Magnetic Field:The induced emf, $Electromagnetic Induction Class 12 Notes Physics$ Where n is the frequency of rotation of the conducting rod.
Induced EMF due to Rotation of a Metallic Disc in a Uniform Magnetic Field: ${{E}_{OA}}=\frac{1}{2}B\omega {{R}^{2}}=B\pi {{R}^{2}}n=BAn$
Induced EMF, Current and Energy Conservation in a Rectangular Loop Moving in a Non – Uniform Magnetic Field with a Constant Velocity:
Energy supplied in this process appears in the form of heat energy in the circuit.

The net increase in flux crossing through the coil in time Δt is, $Electromagnetic Induction Class 12 Notes Physics$
Induced emf in the coil is, $Electromagnetic Induction Class 12 Notes Physics$
If the resistance of the coil is R, then the induced current in the coil is, $Electromagnetic Induction Class 12 Notes Physics$
Resultant force acting on the coil is $Electromagnetic Induction Class 12 Notes Physics$
The work done against the resultant force $Electromagnetic Induction Class 12 Notes Physics$
Energy supplied due to flow of current I in time Δt is, $Electromagnetic Induction Class 12 Notes Physics$
$Electromagnetic Induction Class 12 Notes Physics$
Or H = W

Magnetic flux linked with coil $Electromagnetic Induction Class 12 Notes Physics$
Induced emf in the coil $Electromagnetic Induction Class 12 Notes Physics$
Induced current in the coil. $Electromagnetic Induction Class 12 Notes Physics$
Both Emf and current induced in the coil are alternating.

The phenomenon in which an induced emf is produced by changing the current in a coil is called self induction.
$\begin{align}& \phi \propto I\text{ or }\phi =LI \\ & or\text{ L=}\frac{\phi }{I} \\ \end{align}$
$\begin{align} & E=-L\frac{dI}{dt} \\ & L=\frac{E}{-(dI/dt)} \\ \end{align}$
where L is a constant, called self inductance or coefficient of self – induction.
S.I. Unit- Henry (H)
Dimension- [ML²T^-2A^-2]
Self inductance of a circular coil $Electromagnetic Induction Class 12 Notes Physics$
Self inductance of a solenoid $L=\frac{{{\mu }_{0}}{{N}^{2}}A}{l}$
Two coils of self – inductances L₁ and L₂, placed far away (i.e., without coupling) from each other.
For series combination: $L={{L}_{1}}+{{L}_{2}}.......{{L}_{n}}$
For parallel combination:

On changing the current in one coil, if the magnetic flux linked with a second coil changes and induced emf is produced in that coil, then this phenomenon is called mutual induction. $Electromagnetic Induction Class 12 Notes Physics$ Or $M=\frac{{{\phi }_{2}}}{{{I}_{1}}}$ $Electromagnetic Induction Class 12 Notes Physics$ $Electromagnetic Induction Class 12 Notes Physics$ Thefore, M₁₂ = M₂₁ = M
Mutual inductance two coaxial solenoids $Electromagnetic Induction Class 12 Notes Physics$
If two coils of self- inductance L₁ and L₂ are wound over each other, the mutual inductance is, $M=K\sqrt{{{L}_{1}}{{L}_{2}}}$ Where K is called coupling constant.
Mutual inductance for two coils wound in same direction and connected in series $L={{L}_{1}}+{{L}_{2}}+2M$
Mutual inductance for two coils wound in opposite direction and connected in series $L={{L}_{1}}+{{L}_{2}}-2M$
Mutual inductance for two coils in parallel $L=\frac{{{L}_{1}}{{L}_{2}}-{{M}^{2}}}{{{L}_{1}}+{{L}_{2}}\pm M}$

Energy Stored in an Inductor: ${{U}_{B}}=\frac{1}{2}L{{I}^{2}}_{\max }$
Magnetic Energy Density: ${{U}_{B}}=\frac{{{B}^{2}}}{2{{\mu }_{0}}}$
Eddy Current: When a conductor is moved in a magnetic field, induced currents are generated in the whole volume of the conductor. These currents are called eddy currents.
Transformer:

It is a device which changes the magnitude of alternating voltage or current. $\frac{{{E}_{s}}}{{{E}_{p}}}=\frac{{{n}_{s}}}{{{n}_{p}}}=K$
For ideal transformer: $\frac{{{I}_{p}}}{{{I}_{s}}}=\frac{{{n}_{s}}}{{{n}_{p}}}$
In an ideal transformer: ${{E}_{p}}{{I}_{p}}={{E}_{s}}{{I}_{s}}$
In step – up transformer: ${n_s} > {n_p}{\text{ or K > 1}}$ ${{\text{E}}_s} > {E_p}{\text{ and }}{{\text{I}}_s} < {I_p}$
In step – down transformer: ${n_s} < {n_p}{\text{ or K < 1}}$ ${{\text{E}}_s} < {E_p}{\text{ and }}{{\text{I}}_s} > {I_p}$
Efficiency $\eta =\frac{{{E}_{s}}{{I}_{s}}}{{{E}_{p}}{{I}_{p}}}\times100\%$

Generator or Dynamo: It is a device by which mechanical energy is converted into electrical energy. It is based on the principle of electromagnetic induction.
Different Types of Generator:

Motor: It is a device which converts electrical energy into mechanical energy.
Back emf $e\propto \omega$
Current flowing in the coil, $\begin{align} & {{i}_{a}}=\frac{E-{{e}_{b}}}{R} \\ & E={{e}_{b}}+{{i}_{a}}R \\ \end{align}$
Where R is the resistance of the coil.
Out put Power = ${{i}_{a}}{{e}_{b}}$
Efficiency, $\eta =\frac{{{e}_{b}}}{E}\times 100%$

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