Electromagnetic Induction Concept Page - 5

Definition

Differences between self and mutual inductance

	Self-induction	Mutual induction
1.	When the current flows in coil changes, an induced current is produced in the same coil. This is called Self induction	When 2 coils are placed near each other and current is changing in one coil, an induced current is produced in another coil. This is called Mutual induction
2.	Here one coil is used	Here 2 coils are used
3.	Induced current affects the main current	The induced current is produced in the second coil, therefore main current is not affected.

Definition

Mutual inductance between 2 plane circular coils

Consider 2 plane circular coils close to each other having same axis. The radius of first coil is r1$r_1$ and turns n1$n_1$ and secondary coil be r2$r_2$ and turns be n2$n_2$.
When current I flows through primary coil then magnetic field at centre be 
B=μon1I2r1$B={\displaystyle \frac{{\mu }_o{n}_{1}I}{2r_1}}$
Due to magnetic field the flux linked with secondary coil be 
ϕ=n2BA$\varphi =n_{2}BA$
ϕ=n2μon1I2r1πr22$\varphi =n_2{\displaystyle \frac{{\mu }_o{n}_{1}I}{2r_1}}\pi r{}_2^2$
but ϕ=MI$\varphi =MI$
M=μon1n2πr222r1$M={\displaystyle \frac{{\mu }_o{n}_1{n}_2\pi r{}_2^2}{2r_1}}$

Example

Mutual inductance of two long co-axial solenoids

A straight solenoid of length 1$1$ m has 5000$5000$ turns in the primary and 200$200$ turns in the secondary. If the area of cross section is 4cm2$4c{m}^2$, the mutual inductance will be:M=μN1N2Al=4×π×10−7T×5000×200×4×10−41=502.4×10−6H$M={\displaystyle \frac{\mu N_1{N}_{2}A}{l}}={\displaystyle \frac{4\times \pi \times {10}^{-7}T\times 5000\times 200\times 4\times {10}^{-4}}{1}}=502.4\times {10}^{-6}H$

Definition

Self inductance

Self inductance is defined as the induction of a voltage in a current-carrying wire when the current in the wire itself is changing. In the case of self-inductance, the magnetic field created by a changing current in the circuit itself induces a voltage in the same circuit. Therefore, the voltage is self-induced.The self-inductance of the coil depends on its geometry and on the permeability of the medium.

Definition

Experimental demonstration of Self Inductance

The circuit of experiment is shown in fig.,
L is insulated copper coil wound on soft iron core. Cell E, rheostat Rh and key K is connected in series to coil. A bulb is connected in parallel

When Key K is closed, the bulb glows and then becomes bright and when key K is open the bulb flashes brightly and then goes out. This is because of self induction
Reason:When key is opened the flux linked with coil decreases to zero. Thus, induced current flows in the direction of main current causes increase in the intensity of current momentarily and hence the bulb flashes brightly, and then it goes out.

It is for this reason that of switch is suddenly made off, then bulb gets fused.

Definition

Back emf

The back electromotive force, is the voltage, or electromotive force, that pushes against the current which induces it. Back emf is the voltage drop in an alternating current (AC) circuit caused by magnetic induction.For example, the voltage drop across an inductor is due to the induced magnetic field inside the coil.The voltage's polarity is at every moment the reverse of the input voltage.

Definition

Voltage drop in internal resistance of a cell

Voltage drop in internal resistance of a cell is given by:
Vb=Ir$V_b=Ir$
where
I:$I:$ Current drawn from the cell
r:$r:$ Internal resistance of the cell

In the attached figure, its value is Vb=rR+rE$V_b={\displaystyle \frac{r}{R+r}}E$

Definition

Back emf playing the role of inertia

The self-induced emf is also called the back emf as it opposes any change in the current in a circuit. Physically, the self-inductance plays the role of inertia. It is the electromagnetic analogue of mass in mechanics.So, work needs to be done against the back emf  in establishing the current. This work done is stored as magnetic potential energy. 

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