Chapter 6 - Electromagnetic Induction
Faraday's first law of electromagnetic induction
Whenever there is a change of flux linked with a CLOSED coil/conductor , an EMF is INDUCED in it.
eddy currents are produced when
a metal is kept in varying magnetic field
motional emf formula
E = ( V X B ) . L When all mutually perpendicular, E = BLV
SI unit of magnetic flux
Weber (Wb) (Tm^2)
cases when flux changes
when area changes when radius changes when theta changes when magnetic field changes
When any component of conductor ( B , L , V) are parallel to each other then motional emf is
zero
flux in terms of mutual conductance formula
Φ1= Mi2 Φ2=Mi1
flux in terms of Self inductance formula
Φ= -L di/dt
flux when coil rotates with angular velocity ω in magnetic field
Φ= NBAcosωt
Introduction of Faraday's Laws
Faraday stated that electrical energy can be made from converting from mechanical energy
Rail Problem: Force on moveable arm =
Fm = BiL = B2L2v/R
SI unit of Self Inductance
Henry = Wb/A
Rail Problem: Induced Current when rod has an internal resistance r
I = e/r+R
when the coils are separated by an air gap then the coefficient of coupling is
K < 1
when flux is 100% linked the coefficient of coupling is?
K = 1
coefficient of coupling formula
K = M/root L1L2
self inductance of coil formula
L= µ0N^2πR/2
self inductance of solenoid
Lsol = µ0n^2V = µ0N^2Al
mutual inductance of concentric coils formula
M = µ0N1N2πr^2/2R
mutual inductance of coaxial solenoids
M = µ0N1N2πr^2/l r is for inner solenoid
CGS unit of magnetic flux
Maxwell (Mx)
A coefficient of coupling of 0 indicates:
No lines of flux cut the secondary windings.
When north pole of magnet is brought towards coil, face of coil acts as
North pole
Rail Problem: Power Input/ Output
Pin= F.V = B2L2v2/R Pout= i^2R = B2L2V2/R
When north pole of magnet is moved away from coil, face of coil acts as
South Pole
Lenz's Law
The direction of an induced current is such that it opposes the change causing it.
Faraday's second law of electromagnetic induction
The emf induced is DIRECTLY PROPORTIONAL to the RATE of CHANGE of MAGNETIC FLUX E = -dΦ/dt
motional emf
The emf produced across a conductor due to its motion through a magnetic field
self-inductance
The property of a wire, either straight or in a coil, to create an induced EMF due to changing current, that opposes the change in the potential difference across the wire.
emf induced across ends of rod rotating in magnetic field
Vo-Vp = BLVcom = BwL2/2
When bar magnet is dropped to a metal ring, its acceleration when compared to g is
a<g
undesirable effects of eddy currents
causes unnecessary heating and thus wastage of power
Faraday's laws are based on
conservation of energy
Lenz's Law is based on
conservation of energy
magnetic flux
BAcosθ
Rail Problem: Find induced emf
E = Blv
induced emf and maximum induced emf when coil rotates with angular velocity ω
dΦ/dt = NBA d(coswt)/dt e = NBAωsinωt e0 = NBAω => e = e0sinωt
emf when radius changes formula
e= 2piRB dR/dT
MUTUAL INDUCTANCE
induced emf/current in a coil due to the changing current in the neighboring coil
area under i-t curve
integral idt = charge
charge in terms of Φ formula
q= ΔΦ/R
induced emf does not depend on
resistance and nature of coil
how many times does current and emf change when wire is rotated in magnetic field
twice per cycle
How can eddy currents be minimized?
using laminated core
