By going through these CBSE Class 12 Physics Notes Chapter 6 Electromagnetic Induction, students can recall all the concepts quickly.

## Electromagnetic Induction Notes Class 12 Physics Chapter 6

→ An induced e.m.f. is produced in a conductor when it moves through a magnetic field.

→ The induced e.m.f. may also be produced when a stationary conductor is placed in a changing magnetic field.

→ Lenz’s law explains the cause of induced e.m.f.

→ Electromagnetic induction (E.M.L) converts mechanical energy into electrical energy.

→ inductance in the electrical circuit is equivalent to the inertia or mass in mechanics.

→ The dimensional formula of inductance is [ML^{2} T^{-2 }A^{-2}].

→ The magnetic flux is a scalar quantity and has the dimensions of [ML^{2 }T^{-2 }A^{-1}].

→ The inductance of a coil depends on the

- across of cross-section of the coil.
- no. of turns in the coil.
- permeability of the core of the coil.

→ The direction of induced current can be obtained by Fleming’s right rule.

→ When the magnetic flux through a circuit changes, an induced e.m.f. is produced in it and it lasts so long as the change in the magnetic flux takes place.

→ Eddy currents are set up in any conducting material placed in a varying magnetic field.

→ Eddy currents produce heat at the cost of electrical power and thus reduce power efficiency.

→ Eddy currents can be minimized by using eddy currents.

→ S.I. unit of Φ is weber (Wb).

I Wb = Tm^{2} = 1 Tesla × 1 m^{2}.

→ S.L. unit of L and M is henry (H).

→ 1 H = 1 VA^{-1} s.

→ The mutual inductance of two coils depends upon the shape, size, or geometry of two coils and the no. of turns in the two coils.

→ The area of cross-section and length of two coils affect the ‘M’ between two coils.

→ No current flows in a rectangular closed loop moving horizontally in a uniform magnetic field as long as the loop is completely in the magnetic field.

→ Eddy currents don’t cause sparks.

→ Faraday’s flux rule: It states that the induced e.m.f. produced in a closed circuit is directly proportional to the rate of change of the magnetic flux linked with it.

i.e., e ∝ \(\frac{\mathrm{d} \phi}{\mathrm{d} \mathrm{t}}\)

or

e = – \(\frac{\mathrm{d} \phi}{\mathrm{d} \mathrm{t}}\)

when – ve sign shows that ‘e’ acts in a direction opposite to the direction of change in magnetic flux.

→ Lenz’s law: It states that the induced e.m.f. always acts in such a direction so as to opposite the very cause producing it.

→ Self-induction: It is defined as the property of an electrical circuit due to which it opposes the change in the current in the circuit.

→ Self-inductance of a coil: 11 is defined as the magnetic flux linked with a coil when unit current flows through it. It is also equal to the induced e.m.f. produced in the coil when the rate of change of current is unity through it.

→ Mutual inductance of two coils: It is the property of producing induced e.m.f. in a coil by changing the current or magnetic flux linked with the neighboring coil.

→ Coefficient of Mutual induction: It is equal to induced e.m.f. of one coil when the rate of change of current is unity in the neighboring coil.

**Important Formulae**

→ Φ = \(\overrightarrow{\mathrm{B}}\) . \(\overrightarrow{\mathrm{A}}\) = BA cos θ

where Φ = magnetic flux,

\(\overrightarrow{\mathrm{A}}\) = surface area,

\(\overrightarrow{\mathrm{B}}\) = magnetic field.

→ E or e = – \(\frac{\mathrm{d} \phi}{\mathrm{dt}}\) for one turn and e – \(\frac{\mathrm{Nd} \phi}{\mathrm{dt}}\) for N. turn of a coil.

→ Induced current is given by

I = \(\frac{\mathrm{e}}{\mathrm{R}}=-\frac{\mathrm{N}}{\mathrm{R}} \cdot \frac{\mathrm{d} \phi}{\mathrm{dt}}\)

→ When the magnetic field is parallel to the outward normal to the surface of the coil, then the change in the magnetic flux due to change in field is:

dΦ = Φ_{2} – Φ_{1} = B_{2}A – B_{1}A = (B_{2} – B_{1})A

→ Charge induced in a circuit is

q = \(\frac{\mathrm{d} \phi}{\mathrm{R}}=\frac{\text { Change in magnetic flux }}{\text { Resistance of circuit }}\)

→ Motional e.m.f. is: e = Blυ.

→ Induced current produced = Blυ/R

→ ε = – L \(\frac{\mathrm{dI}}{\mathrm{dt}}\); L = Self-inductance

→ Force required to pull a rod out of magnetic field is

F = \(\frac{B^{2} l^{2} v}{R}\)

→ e = – M\(\frac{\mathrm{dI}}{\mathrm{dt}}\), M = Mutual inductance.

→ Induced e.m.f. in a coil rotating with angular speed ω in a magnetic field B is e = NBA ω sin ωt. .

e_{0} = NBAω = max. e.m.f. induced.

→ Self inductance of a long solenoid is given by

L = μ_{0} n^{2} Al = \(\frac{\mu_{0} \mathrm{~N}^{2} \mathrm{~A}}{l}\)

→ Mutual inductance of two coils is given by

M = μ_{0} n_{1} n_{2} Al

= \(\frac{\mu_{0} \mathrm{~N}_{1} \mathrm{~N}_{2} \mathrm{~A}}{l}\)

where l = length of primary coil.

A = Area of a cross-section of each coil.

→ The inductance of coils in series is given by

L = L_{1} + L_{2} + L_{3} + …………

→ The inductance of coils in parallel is given by

\(\frac{1}{L_{P}}=\frac{1}{L_{1}}+\frac{1}{L_{2}}+\frac{1}{L_{3}}+\ldots\)

→ Induced charge in terms of B is given by:

q = \(\frac{\mathrm{NBA}}{\mathrm{R}}\)

→ Induced current is given by

I = \(\frac{\mathrm{NA}}{\mathrm{R}}\)(B_{1} – B_{2})

→ Also induced charge is given by

q = It = \(=\frac{\mathrm{e}}{\mathrm{R}}\) t

→ If two coils of inductances L1 and L2 are coupled together, then

M = k \(\sqrt{\mathrm{L}_{1} \mathrm{~L}_{2}}\)

where k is called coupling constant,

→ k = 1 for perfectly coupled coils.

→ Two coils are said to be perfectly coupled when the magnetic flux of one coil is completely linked with the second coil.

→ Magnetic energy stored in a coil of inductance L is given by

U = \(\frac{1}{2}\) LI^{2}.

→ ‘e’ produced between the ends of a rod rotating about an end perpendicular to the magnetic field is given by

e= \(\frac{1}{2}\) BWl^{2} = BA.f, f=frequency.