AIEEE Concepts®: Magnetic Flux

Magnetic Flux

Magnetic lines of force passing through the area perpendicular to it is called magnetic flux through that area. If 'B' is flux density and 'A' is area perpendicular

tothe field, then the flux through the area is given by

= BA.

If 'B' makes angle with the normal drawn to the area 'A', then flux is given by = BA cos

.or

' is measured in weber (or) tesla-metre²

Whenever the magnetic flux linked with a coil (closed circuit) changes, emf is induced in the coil. The emf is called induced emf and the phenomenon is

called electromagnetic induction. This is Faraday's law. Induced emf is equal to negative rate of change of magnetic flux.

If

is change in magnetic flux in time 'dt' in each turn, emf induced in each turn is

Where the coil has 'N' turns.

According to Lenz's law, the direction of induced current is such as to oppose the change that causes the induced current. Lenz's law is a consequence of

law of conservation of energy.

The magnetic Flux through a coil is

= BAN cos

Where A = area of the face of the coil, B = Magnetic induction intensity

N = Number of turns

Motional EMF

When a conductor is moved in a magnetic field, induced current flows through it. Direction of induced current can be found using Fleming's right hand rule.

Fleming's right hand rule : Stretch the thumb, fore finger, and central finger of right hand in three mutually perpendicular directions. If the fore finger indicates the

direction of magnetic field, thumb indicates direction of motion of conductor, then central finger indicates direction of induced current.

When a conductor of length 'l', is made to move in a direction perpendicular to the magnetic field 'B' with uniform velocity 'v', e.m.f induced is given by

e = Blv

If R is resistance of conductor, induced current i =

If a rod of length 'l' is rotated in a plane perpendicular to magnetic field 'B' with angular velocity '

' e.m.f. induced is e =

.

When a disc of radius 'r' is rotating about its own axis in a plane perpendicular to magnetic field 'B', making 'n' revolutions per second, the emf induced is

e =

Self induction :

If current flowing in a coil changes, the magnetic flux around the coil changes. Then emf is induced in the coil called self induced emf and the phenomenon is called

self induction.

If 'i' is the current flowing through the coil and

is magnetic flux developed around the coil

Here 'L' is called coefficient of self induction of coil or self inductance of coil.

Self induced e.m.f. is given by e =

S.I. Unit of self inductance : Henry.

Mutual Induction :

When current in one coil changes, magnetic flux passing through the second coil. This Phenomenon is called mutual induction.

If 'ip' is current flowing in the primary coil, i magnetic flux linked with secondary coil then

Here 'M' is called coefficient of Mutual induction or mutual inductance.

Induced emf in secondary coil is

e =

= M

or, M =

S.I. unit : Henry

Dimensional formula of self inductance or mutual inductance is

Energy for an inductor

Magnetic potential energy stored with the current carrying coil is given by

The coefficient of self inductance of a coil is also numerically equal to twice the work required to establish a unit current in the coil is L = 2W. If i = 1. Energy in a

current carrying coil is stored in the form of magnetic field.

Note:-An inductance always has a resistance. i.e., one cannot have inductance without having resistance. An ideal inductance has no resistance.

Mutual inductance of two closed coils & coefficient of coupling

If two coils of self-inductances L₁ and L₂ are placed near each other, then mutual inductance

Where K is a constant, called coefficient of coupling

If flux linkage between coils is 100% then K = 1 and so,

Growth and Decay of Current in L-R Circuit

Growth in Series dC circuit

a) When switch 'S' is on, current gradually increases from 0 (zero) to maximum value i°; but inductance opposes the growth and a back emf is developed.