Explain Faraday's law and also explain Lent's law. In Detail
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Faraday's laws of of electromagnetic induction explains the relationship between electric circuit and magnetic field. This law is the basic working principle of the most of the electrical motors, generators, transformers, inductors etc.

Faraday's First Law:
Whenever a conductor is placed in a varying magnetic field an EMF gets induced across the conductor (called as induced emf), and if the conductor is a closed circuit then induced current flows through it.
Magnetic field can be varied by various methods -
1. By moving magnet
2. By moving the coil
3. By rotating the coil relative to magnetic field
Faraday's Second Law:
Faraday's second law of electromagnetic induction states that, the magnitude of induced emf is equal to the rate of change of flux linkages with the coil. The flux linkages is the product of number of turns and the flux associated with the coil.
Formula Of Faraday's Law:
Consider the conductor is moving in magnetic field, then
flux linkage with the coil at initial position of the conductor = NΦ1 (Wb) (N is speed of the motor and Φ is flux)
flux linkage with the coil at final position of the conductor = NΦ2 (Wb)
change in the flux linkage from initial to final = N(Φ1 - Φ2)
let Φ1 - Φ2 = Φ
therefore, change in the flux linkage = NΦ
and, rate of change in the flux linkage = NΦ/t
taking the derivative of RHS
rate of change of flux linkages = N (dΦ/dt)
According to Faraday's law of electromagnetic induction, rate of change of flux linkages is equal to the induced emf
So, E = N (dΦ/dt) (volts)
Phenomenon Of Mutual Induction
Alternating current flowing in a coil produces alternating magnetic field around it. When two or more coils are magnetically linked to each other, then an alternating current flowing through one coil causes an induced emf across the other linked coils. This phenomenon is called as mutual induction.
Lenz's Law
Lenz's law of electromagnetic induction states that, when an emf is induced according to Faraday's law, the polarity (direction) of that induced emf is such that it opposes the cause of its production.
Thus, considering Lenz's law
E = -N (dΦ/dt) (volts)
The negative sign shows that, the direction of the induced emf and the direction of change in magnetic fields have opposite signs.

Faraday's First Law:
Whenever a conductor is placed in a varying magnetic field an EMF gets induced across the conductor (called as induced emf), and if the conductor is a closed circuit then induced current flows through it.
Magnetic field can be varied by various methods -
1. By moving magnet
2. By moving the coil
3. By rotating the coil relative to magnetic field
Faraday's Second Law:
Faraday's second law of electromagnetic induction states that, the magnitude of induced emf is equal to the rate of change of flux linkages with the coil. The flux linkages is the product of number of turns and the flux associated with the coil.
Formula Of Faraday's Law:
Consider the conductor is moving in magnetic field, then
flux linkage with the coil at initial position of the conductor = NΦ1 (Wb) (N is speed of the motor and Φ is flux)
flux linkage with the coil at final position of the conductor = NΦ2 (Wb)
change in the flux linkage from initial to final = N(Φ1 - Φ2)
let Φ1 - Φ2 = Φ
therefore, change in the flux linkage = NΦ
and, rate of change in the flux linkage = NΦ/t
taking the derivative of RHS
rate of change of flux linkages = N (dΦ/dt)
According to Faraday's law of electromagnetic induction, rate of change of flux linkages is equal to the induced emf
So, E = N (dΦ/dt) (volts)
Phenomenon Of Mutual Induction
Alternating current flowing in a coil produces alternating magnetic field around it. When two or more coils are magnetically linked to each other, then an alternating current flowing through one coil causes an induced emf across the other linked coils. This phenomenon is called as mutual induction.
Lenz's Law
Lenz's law of electromagnetic induction states that, when an emf is induced according to Faraday's law, the polarity (direction) of that induced emf is such that it opposes the cause of its production.
Thus, considering Lenz's law
E = -N (dΦ/dt) (volts)
The negative sign shows that, the direction of the induced emf and the direction of change in magnetic fields have opposite signs.
manishprajapat191120:
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Lenz's law is shown by the negative sign in Faraday's law of induction:
{\displaystyle {\mathcal {E}}=-{\frac {\partial \Phi _{\mathbf {B} }}{\partial t}},}
which indicates that the induced electromotive force {\displaystyle {\mathcal {E}}} and the rate of change in magnetic flux {\displaystyle \Phi _{\mathbf {B} }} have opposite signs.[3] It is a qualitative law that specifies the direction of induced current but says nothing about its magnitude. Lenz's law explains the direction of many effects in electromagnetism, such as the direction of voltage induced in an inductoror wire loop by a changing current, or why eddy currents exert a drag force on moving objects in a magnetic field.
Lenz's law can be seen as analogous to Newton's third law in classic mechanics
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Faraday's law of induction (shortly called Faraday's law throughout this document) is a basic law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (EMF)—a phenomenon called electromagnetic induction. It is the fundamental operating principle of transformers, inductors, and many types of electrical motors, generators and solenoids.[1][2]
The Maxwell–Faraday equation (listed as one of Maxwell's equations) describes the fact that a spatially-varying (and also possibly time-varying depends on how a magnetic field varies in time) electric field always accompanies a time-varying magnetic field, while Faraday's law states that there is EMF (Electromotive Force, defined as electromagnetic work done on a unit charge when it has traveled one round of a conductive loop) on the conductive loop when the magnetic flux through the surface enclosed by the loop varies in time.
{\displaystyle {\mathcal {E}}=-{\frac {\partial \Phi _{\mathbf {B} }}{\partial t}},}
which indicates that the induced electromotive force {\displaystyle {\mathcal {E}}} and the rate of change in magnetic flux {\displaystyle \Phi _{\mathbf {B} }} have opposite signs.[3] It is a qualitative law that specifies the direction of induced current but says nothing about its magnitude. Lenz's law explains the direction of many effects in electromagnetism, such as the direction of voltage induced in an inductoror wire loop by a changing current, or why eddy currents exert a drag force on moving objects in a magnetic field.
Lenz's law can be seen as analogous to Newton's third law in classic mechanics
----/------/------/-----
Faraday's law of induction (shortly called Faraday's law throughout this document) is a basic law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (EMF)—a phenomenon called electromagnetic induction. It is the fundamental operating principle of transformers, inductors, and many types of electrical motors, generators and solenoids.[1][2]
The Maxwell–Faraday equation (listed as one of Maxwell's equations) describes the fact that a spatially-varying (and also possibly time-varying depends on how a magnetic field varies in time) electric field always accompanies a time-varying magnetic field, while Faraday's law states that there is EMF (Electromotive Force, defined as electromagnetic work done on a unit charge when it has traveled one round of a conductive loop) on the conductive loop when the magnetic flux through the surface enclosed by the loop varies in time.
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