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 [ML2 T-2 A-2].

→ The magnetic flux is a scalar quantity and has the dimensions of [ML2 T-2 A-1].

→ The inductance of a coil depends on the

1. across of cross-section of the coil.
2. no. of turns in the coil.
3. 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 = Tm2 = 1 Tesla × 1 m2.

→ 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 = Φ2 – Φ1 = B2A – B1A = (B2 – B1)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. .
e0 = NBAω = max. e.m.f. induced.

→ Self inductance of a long solenoid is given by
L = μ0 n2 Al = $$\frac{\mu_{0} \mathrm{~N}^{2} \mathrm{~A}}{l}$$

→ Mutual inductance of two coils is given by
M = μ0 n1 n2 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 = L1 + L2 + L3 + …………

→ 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 = $$\frac{\mathrm{NA}}{\mathrm{R}}$$(B1 – B2)

→ 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 = $$\frac{1}{2}$$ LI2.

→ ‘e’ produced between the ends of a rod rotating about an end perpendicular to the magnetic field is given by
e= $$\frac{1}{2}$$ BWl2 = BA.f, f=frequency.