NCERT Solution Class 12th Physics Chapter – 6 Electromagnetic Induction
| Textbook | NCERT |
| class | Class – 12th |
| Subject | Physics |
| Chapter | Chapter – 6 |
| Chapter Name | Electromagnetic Induction |
| Category | Class 12th Physics Notes |
| Medium | English |
| Source | last doubt |
NCERT Solution Class 12th Physics Chapter – 6 Electromagnetic Induction
?Chapter – 6?
✍Electromagnetic Induction✍
?Notes?
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
- 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 = 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 ∝ dϕ/dt
or
e = – dϕ/dt
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 = B→ . A→ = BA cos θ
where Φ = magnetic flux,
A→ = surface area,
B→ = magnetic field.
E or e = – dϕ/dt for one turn and e – Ndϕ/dt for N. turn of a coil.
Induced current is given by
I = e/R=−N/R⋅dϕ/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 = dϕ/R= Change in magnetic flux / Resistance of circuit
Motional e.m.f. is: e = Blυ.
Induced current produced = Blυ/R
ε = – L dI/dt; L = Self-inductance
Force required to pull a rod out of magnetic field is
F = B2l2vR
e = – M dI/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 = μ0 N2 A/l
Mutual inductance of two coils is given by
M = μ0 n1 n2 Al
= μ0 N1 N2 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
1LP=1L1+1L2+1L3+…
Induced charge in terms of B is given by –
q = NBA/R
Induced current is given by
I = NA/R(B1 – B2)
Also induced charge is given by
q = It = =e/R t
If two coils of inductances L1 and L2 are coupled together, then
M = k 
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 = 1/2 LI2.
‘e’ produced between the ends of a rod rotating about an end perpendicular to the magnetic field is given by
e= 1/2 BWl2 = BA.f, f=frequency.