1Electromagnetic induction. Magnetic flux and flux linkage
1Electromagnetic induction. Magnetic flux and flux linkage.docx
Discussion and demonstration: Induction effects The first two demonstrations involve
moving a wire in a magnetic field and then a permanent magnet into and out of a
small coil. In both it is important to emphasise that:
Ø‘electricity’ is only produced while
something is moving
Øthe faster the movement, the more ‘electricity’ we
Cutting magnetic field lines
Start by thinking about a
simple bar magnet. It has a magnetic field in the space around it. We represent
this field by magnetic field lines. Now think about what happens when a wire is
moved into the magnetic field (Figure). As it moves, it cuts across the magnetic field. Remove the wire
from the field, and again it must cut across the field lines, but in the
opposite direction. We think of this cutting of a magnetic field by a conductor
as the effect that gives rise to an induced current in the conductor. It
doesn’t matter whether the conductor is moved through the field or the magnet
is moved past the conductor, the result is the same – there will be an induced
For a coil of N turns, the effect is N times greater than for a
single turn of wire.
When the coil is outside the field, there are no magnetic field
lines linking the coil.
When it is inside the field, field lines link the coil. Moving the
coil into or out of the field changes this linkage, and this induces an e.m.f.
across the ends of the coil.
Magnetic flux and magnetic
Magnetic flux density B is defined
by the equation
Now we can go on to define
magnetic flux as a quantity.
We picture magnetic flux
density B as the number of magnetic field lines passing through a region
per unit area.
Similarly, we can picture
magnetic flux as the total number of magnetic field lines passing through an
area A. For a magnetic field normal to A, the magnetic flux Φ must
therefore be equal to the product of magnetic flux density and the area A.
a The magnetic flux is equal
to BA when the field
is normal to the area.
magnetic flux becomes Bacosθwhen the field is at an angle θ to
the normal of the area.
The magnetic flux Φ
through area A is defined as:
where B is the component of
the magnetic flux density perpendicular to the area.
can we calculate the magnetic fl ux when B is not perpendicular to A?
When the field is parallel to
the plane of the area, the magnetic flux through A is zero. To find the
magnetic flux in general, we need to find the component of the magnetic
flux density perpendicular to the area.
flux = (B cos θ) × A
flux = BA cos θ
that, when θ = 90°, flux = 0 and when θ = 0°,
For a coil with N turns,
the magnetic flux linkage is defined as the product of the magnetic flux
and the number of turns; that is:
flux linkage = NΦ
flux linkage = BAN cos θ
The unit for magnetic flux or
flux linkage is the Weber (Wb).
One weber (1 Wb) is the flux
that passes through an area of 1 m2 when the magnetic flux density
is 1 T.
1 Wb =
1 T m2.
An e.m.f. is induced in a
circuit whenever there is a change in the magnetic flux linking the circuit.
Since magnetic flux is equal to BA cos θ, there are three ways an
e.m.f. can be induced: