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Magnetic flux
It is the number of magnetic lines of force passing through the given area.
Magnetic flux through small area is given as,
๐ต
Magnetic flux through large area is given as,
๐ต
๐ด
0
๐ต
๐ด
0
๐ต
๐ด
0
[ ษธ
๐ต
= ๐ต๐ด๐๐๐ ๐ ]
Magnetic flux through closed area is given as,
[ ษธ
๐ต
. ๐๐ด ]
Note:
โ If B is perpendicular to the area then magnetic flux will be maximum.
โ If B is parallel to the area then magnetic flux will be zero.
โ Magnetic flux is a scalar quantity.
โ S.I. unit of magnetic flux is Tm
2
also called weber (wb).
โ Magnetic flux is out from the area is taken +ve.
โ Magnetic flux is into the area is taken - ve.
Faraday's law of Electromagnetic Induction
According to Faraday's law of Electromagnetic Induction if we change magnetic flux through any closed
conducting loop then there induces an emf in the loop which is proportional to the rate of change of magnetic flux
through the loop.
Lenz law
According to Lenz law direction of induced EMF is in such a way that it opposes the change which creates it
Combining Lenz law and Faraday's law
[ ๐ = โ
๐ต
]
Note
โ If induced emf is positive then current in the loop is anticlockwise direction looking from +ve direction of
area.
โ if induced emf is negative the current in the loop is in clockwise direction looking from +ve direction of
area.
โ Always find ACW or CW loking from the direction of area vector.
Motional emf
- When a conductor moves inside magnetic field free charge inside conductor experience magnetic force and
it collects at the end of conductor which creates electric field inside conductor and a situation comes when
electric force balance is magnetic force inside conductor.
- But in this situation there developed potential difference across the ends of conductor called motional emf.
At equilibrium,
F
E
= F
B
QE = QUBsin
0
QE = QuB
E = uB
[
]
Note:
โ Positive terminal will be in the direction of uโ x B
โ Motional emf is equal to the product of area sweep per second and the magnitude of magnetic filed
perprndicular to the sweeped area. It is given as,
[ v o
= A
sweep
B
perpendicular
]
Energy conservation in Electromagnetic Induction
Let wire is moving with constant velocity u inside uniform magnetic field. There induces motional emf creates a
current in the circuit and the magnetic field applies force on the current carrying wire. To move wire AB with
constant velocity external force is applied to balance the magnetic Force.
๐
๐ข๐๐
๐
2
2
2
2
2
[๐ =
2
2
2
]
- Force due to external agent
๐๐ฅ๐ก
๐ต
0
๐๐ฅ๐ก
๐๐ฅ๐ก
๐๐ฅ๐ก
[๐
๐๐ฅ๐ก
๐ข
2
๐
2
๐ต
2
๐
]
Here electrical power is equal to power given by external agent so
energy is conserved.
Eddy current
When magnetic flux changes through any conductor due to Electromagnetic
Induction there induces electric current in the circular loops of different size.
The current is called Eddy current.
12
1
1
2
0
2
2
Mutual inductance of solenoid 1 due to current in solenoid 2.
12
โ
12
๐ผ 2
( ๐ 1
๐
) ๐๐
1
2
(๐ 0
๐ 2
๐ผ 2
)
๐ผ 2
[ ๐
12
1
2
0
1
2
๐ ]
- Mutual inductance of solenoid 2 due to current in solenoid 1.
Flux in solenoid 1 due to current in solenoid 2
21
2
1
2
0
1
1
Mutual inductance of solenoid 1 due to current in solenoid 2.
21
21
2
2
1
2
0
1
1
1
[ ๐
12
1
2
0
1
2
๐ ]
Note
โ Mutual inductance of loop 1 due to curent in loop 2 is always equal to mutual inductance of loop 2 due to
current in loop 1.
โ Inductor is represented as
โ S.I. unit of inductance is Henery ( H )
Voltage across inductor
๐ต
[ ๐ = โ๐ฟ
๐๐ผ
๐๐ก
]
Energy stored inside inductor
Total energy stored inside inductor in time internal 0 to t in which current varies from 0 to I is
๐ก
0
where I is current through inductor and V is voltage across inductor
๐๐ผ
๐๐ก
๐ก
0
since we know voltage across indctor is ๐ฟ
๐๐ผ
๐๐ก
๐ผ
0
๐ผ
0
๐ธ = ๐ฟ [
2
]
0
๐ผ
2
2
[ ๐ธ =
2
]
AC Generator
AC Generator is a device that converts mechanical nergy into electrical
energy. AC generator is working on the principal of Faradays law of
Electromagnetic Induction.
Construction
There is a horse shoe magnet between which coil is present which can rotate
about its axis. Ends of the coil is connected to the slip rings. Output voltage
is taken from carbon brush which is in contact with slip rings.
Working
When the coil is rotates between the poles of the magnet magnetic flux through the coil changes and there induces
an emf in the coil from Faraday's Law of electromagnetic induction.
- Flux through coil at any time t is given as
[ ๐ฃ = ๐ฃ
0
๐ ๐๐๐๐ก ]
where ๐ฃ 0
