Electromagnetism.

Force on a Current-Carrying Conductor Placed in A Magnetic Field.

If a current-carrying conductor is placed in a magnetic field, it has a force exerted on it. The magnitude of this force is given by:

F=BIl

Where,

EMF generated in a conductor that cuts a magnetic field of uniform flux density.

An emf is generated by a conductor that cuts or is cut by a magnetic field. The magnitude of the emf generated is given by:

E=Blv

Where,

Definitions of the Tesla and the Weber.

The Tesla is defined as the density of a magnetic field such that a conductor carrying one ampere at right angles to the field has a force of one Newton per metre acting on it.

The Weber can be defined in two ways:

1. The amount of flux, when cut at a uniform rate by a conductor in one second, generates an emf of one Volt.
2. The magnetic flux linking one turn induces in it an emf of one volt when the flux is reduced to zero at a uniform rate in one second.

The Flux and Flux Density are related by the following formula:

(phi) = B x A

Where,

The induced voltage in a coil therefore depends on the total flux, the number of turns, and the time for the field to be reversed.

Magnetomotive Force.

A magnetic circuit consisting of a coil wound on either a magnetic or non-magnetic former can be compared with the electric circuit. In the electric circuit:

Current = emf / resistance

or

I = E/R

In the magnetic circuit:

Flux = mmf / Reluctance

or

(phi) = F/Rm

Magnetomotive force is measured in amperes, A, and is produced by the current in the magnetizing current where:

mmf = NI

Magnetic Field Strength.

The magnetic field strength, H, is the magnetomotive force per unit length in a magnetic circuit. It is given by:

H = mmf / l

where,

Permeability.

The ratio of the flux density B to the magnetic field strength H in vacuum is called the permeability of free space. It is measured in Henrys per metre and is given by:

The value of permeability for air and for many non-magnetic materials is almost the same as that of free space.

Relative and Absolute Permeabilities.

The amount of flux for a given magnetomotive force can be increased by the use of a magnetic core material. The ratio of the flux density with a core to that without, for the same magnetic field strength, is called the relative permeability. It is dimensionless and is given by:

The absolute permeability is then given by:

The value of the relative permeability tends to vary for different values of the magnetic field strength. The relationship between the flux density and the magnetic field strength is then usually represented by a graph:

The gradient of the graph gives the relative permeability at that point.