CLASS 12 ELECTROMAGNETIC INDUCTION
ELECTROMAGNETIC INDUCTION
✤ Magnet Flux -
The magnetic flux through any surface placed in a magnetic field is the total no. of magnetic lines of forces crossing this surface, normally.
Φ = BAcos θ [ML²A⁻¹T⁻²] = B. A (Wb/Tm²)
Here θ is the angle made by normal to the plane with magnetic field.
✤ Electromagnetic Induction:
The phenomenon of production of induced emf due to a change of magnetic flux linked with a closed circuit is called electromagnetic induction.
✤ Faraday's Law
i) First Law
Whenever the magnetic flux linked with a closed circuit, an emf is induced in it which lasts only so long as the change in flux is taking place.
for large deflection in galvanometer: -
(i) move the coil fast towards G.
(ii) switch off & on
We can use LED and bulb in place of galvanometer.
ii) Second Law
The magnitude of the induced emf is equal to the rate of change of magnetic flux linked with the closed circuit.
|E| = dΦ/dt or E = -dΦ/dt or E = -(Φ₂-Φ₁)/(t₂-t₁)
For N turns
|E| = -NdΦ/dt or E = -NdΦ/dt
e₁ = -IdΦ/dt = 12x10⁻³dt
e₂ = -IdΦ/dt = 30x10⁻³dt
(Scope of e₂ > e₁)
✤ Motional EMF:
The emf induced across the ends of a conductor due to its motion in a magnetic field is called motional emf.
E = Blv unit is Volt
here l = length of wire
V = velocity
✤ Lenz's Law
states that the direction of induced current is such that it oppose the cause which produced it.
I = E/R or I = (-dΦ/dt)/R (Ampere)
EMF Induced in a Rotating Rod in a uniform magnetic field
E= 1/2 Bℓ²ω² (volt)
Angular frequency
(W= v/t)
✤ AC generator
emf in generator E=NBAωsinωt
ωt=0, plane of coil is ⊥ to B then E=0
ωt = π/2, plane of coil is parallel to B, then, E=E₀
ωt=π, plane of coil is ⊥ to B then, E= 0
ωt = 2π, plane of coil is parallel to B then, E=-E₀
ωt=2π, plane of coil is ⊥ to B after completing 1 rotation then, E=0
N-S= horse shoe magnet.
S₁,S₂= slip rings to charge the direction of current
b₁,b₂ = carbon brush - transfer the current.
✤ Self – Induction
The phenomenon of production of induced emf in a coil when a changing current passes through it.
Φ = LI L = coefficient of (Henry) [ML²T-²A-²]
L = Φ/I self induction
Relation btw 'L' & induced EMF
E = -L dI/dt
Self- Inductance of a long Solenoid
L = µ₀N²A/l
I depend only physical construction.
✤ Mutual Induction:
Mutual Induction is the phenomenon of production of induced emf in 1 coil due to a change of current in the neighbouring coil.
Φ = MI M = Φ/I
coefficient of mutual induction (Henry)
✤ Relation blw mutal induction & EMF
E=M dI / dt
✤ Mutal Inductance of 2 Long Solenoids
M = µ₀N₁N₂A / l N₁,N₂ - No. of turns in solenoids.
A - area (m²)
l - length of solenoid
Factorise on which mutual inductance depends.
No. of twins.
Common cross-sectional area.
Relative separation.
Relative orientation of the 2 coils.
Permeability of the core material.
1. Current induced in the loop. I = Blv / r
2. force on the current conductor in magnetic field f = BIv
3. direction of force is opposite to velocity.
4. Power required to push the conductor p = B2I²v2 / r
5. The mechanical energy dissipated per second
p = B²l²v² / r
Sketch the variation of magnetic flux, induced emf current, power dissipated as Joule heat as function of time.
sketch the variation of flux when instead of rectangular loop circular loop is used.
F = qE + q(v x B)
Energy density (energy/vol) = 1/2 B²/2 μ₀
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