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What is Magnetic Flux?
The product of a magnetic field passing through a surface placed perpendicular
to the field is known as magnetic flux. More generally it is the scalar product of the magnetic
field and the area vector.
The magnetic flux through a surface is directly proportional to the
net density or number of magnetic
field lines passing through that surface. The magnetic flux is defined by the
integral of the magnetic field over the area of the surface. Where the
surface S is a planar surface with area A, and the magnetic field is constant with
magnitude B, a simplified version of the formula can be used:
If the surface is placed parallel to the magnetic field the area vector will form an angle
of 90 degrees with the field and as
a result the magnetic flux would be zero. If the surface is placed
perpendicular to the field the area vector forms an angle of 0 with the field
and hence the
magnetic flux would be greatest.
The integral of the magnetic flux through a surface S is defined as the integral of
magnetic field over the area of the surface S.
is the magnetic flux
B is the magnetic field,
S is the surface (area)
and '.' denotes the dot product,
Magnetic flux through a closed surface
According to Gauss’s law of magnetism, the total magnetic flux through a closed surface is equal to zero. A closed surface is a surface like
a sphere or disk.
for any closed surface S.
Magnetic flux through an open surface
In electromagnetism a magnetic flux
passing through an open surface is of great importance.
The electromotive force is produced when a changing magnetic
flux is passes through a conductive coil. According to Faraday’s law:
E is the EMF, and the derivative is of
Φ, the flux through a surface, with respect to
This is the principle on which an electrical generator works. Most common generators use
the principal of magnetic flux to produce electricity. A changing magnetic flux induces
emf in a coil. The emf causes the current to flow in the coil
hence producing electricity.
Measurement of Magnetic Flux
The apparatus used to measure magnetic flux is called a fluxmeter,it consists of coils and electronics which evaluate the voltage change in the coil to
measure the magnetic flux.