Physics ELECTROMAGNETIC INDUCTION

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ELECTROMAGNETIC INDUCTION

SELF-INDUCTION :

When a current is established through a closed conducting loop or coil, it produces a magnetic field which in turn creates a flux through the area bounded within the loop or coil. Therefore if the current through it is made to change with respect to time, the flux through the loop or coil changes accordingly and by application of Faraday's law of electromagnetic induction an emf is induced in the loop or coil. This process is called self induction and since the emf induced opposes the change in flux (Lenz's law), it is also known as back emf.

The magnetic field at any point due to a current is proportional to the current. The magnetic flux through the area bounded by a current-carrying loop or coil is therefore also proportional to the current. So if `i` is the current then the magnetic flux

`phi_B = Li................................(1)`

Where L is the constant depending on the geometrical construction of the loop alone called coefficient of self-induction or simply inductance.

So 'coefficient of self-induction' of a coil or circuit is numerically equal to the flux linked with it when unit current is passing through it.

The induced emf E, when the current in the coil changes, is given by

`E = -(d phi_B)/(dt)` Using equation ...........................(1)

`=> E = -L((di)/(dt))`........................................(2)

The Sl unit of self-inductance L is `text(weber)//text(ampere)` from (1) or `text(volt-second)//text(ampere)` from (2) and is called `text(Henry)` (`H`).

When a current is established through a closed conducting loop or coil, it produces a magnetic field which in turn creates a flux through the area bounded within the loop or coil. Therefore if the current through it is made to change with respect to time, the flux through the loop or coil changes accordingly and by application of Faraday's law of electromagnetic induction an emf is induced in the loop or coil. This process is called self induction and since the emf induced opposes the change in flux (Lenz's law), it is also known as back emf.

The magnetic field at any point due to a current is proportional to the current. The magnetic flux through the area bounded by a current-carrying loop or coil is therefore also proportional to the current. So if `i` is the current then the magnetic flux

`phi_B = Li................................(1)`

Where L is the constant depending on the geometrical construction of the loop alone called coefficient of self-induction or simply inductance.

So 'coefficient of self-induction' of a coil or circuit is numerically equal to the flux linked with it when unit current is passing through it.

The induced emf E, when the current in the coil changes, is given by

`E = -(d phi_B)/(dt)` Using equation ...........................(1)

`=> E = -L((di)/(dt))`........................................(2)

The Sl unit of self-inductance L is `text(weber)//text(ampere)` from (1) or `text(volt-second)//text(ampere)` from (2) and is called `text(Henry)` (`H`).

MUTUAL INDUCTION :

Suppose two closed circuits (isolated electrically) are placed close to each other in such a manner that when current is passed through one circuit, it creates a magnetic flux through a coil or a loop in the second circuit, then a variation in the current through the first circuit with respect to time will create an induced emf through the loop or coil in the second circuit and will therefore create an induced current in it. This phenomena is called 'mutual induction'.

The coil or circuit through which the a time varying current is passed is called the 'primary' while the other in which the induced emf is created is called the 'secondary'. The diagram above represents the schematic picture of this situation.

The flux linked with the secondary due to the current `i`, in the primary will be proportionate to `i_p`

`phi_B = Mi_p.............................................(1)`

where `M` is a constant depending on the geometrical shapes of the two coils or circuit and their overlap called mutual inductance for the given pair of circuits. From equation (1 ), if, `i_p = 1` then `phi_B = M` .

So 'coefficient of mutual-inductance' of two coils or circuits is numerically equal to the flux linked with one circuit or coil when unit current flows through the other.

The emf induced in the secondary coil or circuit is given by

`E_s = - (dphi_B)/(dt) = -M((di_p)/(dt))................................(2)`

The Sl unit of M is same as that of L and is `text(weber)//text(ampere)` or `text(volt-second)//text(ampere)` or `text(Henry)` (`H`).

Suppose two closed circuits (isolated electrically) are placed close to each other in such a manner that when current is passed through one circuit, it creates a magnetic flux through a coil or a loop in the second circuit, then a variation in the current through the first circuit with respect to time will create an induced emf through the loop or coil in the second circuit and will therefore create an induced current in it. This phenomena is called 'mutual induction'.

The coil or circuit through which the a time varying current is passed is called the 'primary' while the other in which the induced emf is created is called the 'secondary'. The diagram above represents the schematic picture of this situation.

The flux linked with the secondary due to the current `i`, in the primary will be proportionate to `i_p`

`phi_B = Mi_p.............................................(1)`

where `M` is a constant depending on the geometrical shapes of the two coils or circuit and their overlap called mutual inductance for the given pair of circuits. From equation (1 ), if, `i_p = 1` then `phi_B = M` .

So 'coefficient of mutual-inductance' of two coils or circuits is numerically equal to the flux linked with one circuit or coil when unit current flows through the other.

The emf induced in the secondary coil or circuit is given by

`E_s = - (dphi_B)/(dt) = -M((di_p)/(dt))................................(2)`

The Sl unit of M is same as that of L and is `text(weber)//text(ampere)` or `text(volt-second)//text(ampere)` or `text(Henry)` (`H`).

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