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Magnetic Flux and Faraday’s
Law of Electromagnetic
Induction
f = B dS⋅ ∫
In Uniform magnetic field the above expression can be written
as
f = B A⋅
The total magnetic flux linked with the coil is the flux
linked with each turn multiplied by the number of turns.
Thus,
f = BAN cos θ
Where θ is the angle between normal to the plane of the
coil and the direction of the magnetic field.
Faraday’s Laws of Electro Magnetic
Induction
1. Whenever the magnetic flux linked with a conducting
loop or coil changes, an e.m.f is induced in it.
2. The induced emf is directly proportional to the rate of
change of magnetic flux through the coil.
d e N dt
f = − ×
Here e is the induced emf
N is the number of turns
f is the magnetic flux linked with each turn of the coil.
The negative sign indicates that the induced emf
opposes the cause that produces it.
Lenz’s Law
Statement of lenz’s law: The direction of the induced emf is
always such as to result in opposition to the change producing it.
From Faraday’s second law and Lenz’s law induced emf is
given by
Nd e dt
− f
If R is the Resistance of the Coil then
Induced Current
induced emf 1 d I Resistance R dt
f = = −
Expression for induced charge
in
1 d d dq i dt dt R dt R
f f = = − = −
q R
Df D = −
Change in magnetic flux Q Resistance
Methods of Producing
Induced Emf
1. Motional e.m.f 2. Orientational e.m.f 3. E.m.f by time varying magnetic field
ELECTROMAGNETIC INDUCTION
Chapter
NCERT CRUX
2 CUET 2023-24 P
W
Motional EMF
When a conductor moves through a magnetic field so as
to cut the field lines, an induced emf will exist across its
ends, in accordance with Faraday’s law.
The direction of the induced emf and consequent
current can be deduced from Fleming’s right hand rule.
Fleming’s Right Hand Rule
The right hand is held with the thumb, index finger and
middle finger mutually perpendicular to each other (at
right angles), as shown in the diagram.
The thumb is pointed in the direction of the motion of
the conductor relative to the magnetic field.
The fore finger is pointed in the direction of the
magnetic field.
Then the middle finger represents the direction of the
induced or generated current within the conductor
(from the terminal with lower electric potential to the
terminal with higher electric potential, as in a voltage
source)
Fleming right hand rule
Explanation of EMF Induced in Rod on the
Basis of Magnetic Force
Motional EMF in Translatory motion :
By Faraday’s law
Let conductor PQ slides a distance D x in time D t , the change
in magnetic flux in this time
Df = BDA = B( l D x ) and
x e Bl t t
Df (^) D = = D (^) D
= Blv
1. Induced current (^) in
e Bvl i R R
2. Magnetic force on the conductor: Conductor PQ
experiences a force opposite to the direction of motion
2 2
m in
Bv B v F Bi B R R
l l l l
3. Power dissipated in moving the conductor:
2 2 2
agent^ agent.
dW B v P F v dt R
l = = =
4. Electrical power: Electrical power dissipated through
the resistance.
(^2 2 2 ) 2 thermal
Bv B v P i R R R R
^ l^ l = = =
EMF Induced in a Rotating Disc
Consider a disc of radius r rotating in a magnetic field B.
\ emf between the centre and the edge of the disc.
r (^2)
0
B r B xdx 2
ω ω = ∫
Self Induction
i.e., Nf ∝ I ⇒ Nf = LI
Where ‘L’ is the constant of proportionality and is known as
coefficient of self induction (or) self inductance.
Energy stored in an inductor: Because of its self
induced back emf, work must be done to increase the
current through a coil having self inductance (called
inductor) from zero to a value i. This work will be
stored as energy in the magnetic field established in the
coil and is given by
U Li 2
Self Inductance of a Solenoid
2 \ L = μ 0 n A l
since
2
0
N N
n , L A l l
= = μ
Thus self inductance (L) depends on
1. The number of turns(N) of the solenoid, 2. The length (l) of the solenoid, 3. The area of cross-section (A) of the solenoid, 4. Nature of material of the core of the solenoid.
Energy density in magnetic field
\ Energy density u
2
0
U B
V 2
μ
