chapter 1 part 2

II.   Eddy Current Loss

1.         A time-changing flux induces voltage within a ferromagnetic core.

2.         These voltages cause swirls of current to flow within the core – eddy currents.

3.         Energy is dissipated (in the form of heat) because these eddy currents are flowing in a resistive material (iron)

4.         The amount of energy lost to eddy currents is proportional to the size of the pathsthey follow within the core.

5.         To reduce energy loss, ferromagnetic core should be broken up into small strips, or laminations, and build the core up out of these strips. An insulating oxide or resin is used between the strips, so that the current paths for eddy currents are limited to small areas.

Conclusion:

Core loss is extremely important in practice, since it greatly affects operating temperatures, efficiencies, and ratings of magnetic devices.

3.   How Magnetic Field can affect its surroundings

3.1  FARADAY’SLAW – Induced Voltage from a Time-Changing Magnetic Field

Before, we looked at the production of a magnetic field and on its properties. Now, we will look at the various ways in which an existing magnetic field can affect its surroundings.

1.         Faraday’s Law:

‘If a flux passes through a turn of a coil of wire, voltage will be induced in the turn of the wire that is directly proportional to the rate of change in the flux with respect of time’

                                                          

If there is N number of turns in the coil with the same amount of flux flowing through it, hence:

where:     N – number of turns of wire in coil.

 Note the negative sign at the equation above which is in accordance to Lenz’ Law which states:

‘The direction of the build-up voltage in the coil is as such that if the coils were short circuited, it would produce current that would cause a flux opposing the original flux change.’

Examine the figure below:

§ If the flux shown is increasing in strength, then the voltage built up in the coil will tend to establish a flux that will oppose the increase.

§ A current flowing as shown in the figure would produce a flux opposing the increase.

§ So, the voltage on the coil must be built up with the polarity required to drive the current through the external circuit. So, -e_ind

§ NOTE: In Chapman, the minus sign is often left out because the polarity of the resulting voltage can be determined from physical considerations.

2.         Equation  e_ind = -d/dt assumes that exactly the same flux is present in each turn of the

coil. This is not true, since there is leakage flux. This equation will give valid answer if the windings are tightly coupled, so that the vast majority of the flux passing thru one turn of the coil does indeed pass through all of them.

3.         Now consider the induced voltage in the ith turn of the coil,

Since there is N number of turns,

            The equation above may be rewritten into,

where l (flux linkage) is defined as:

  (weber-turns)

4.         Faraday’s law is the fundamental property of magnetic fields involved in transformer operation. 

5.         Lenz’s Law in transformers is used to predict the polarity of the voltages induced in transformer windings.

3.2  Production of Induced Force on a Wire.

1.        A current carrying conductor present in a uniform magnetic field of flux density B, would produce a force to the conductor/wire. Dependent upon the direction of the surrounding magnetic field, the force induced is given by:

where:

        i – represents the current flow in the conductor

        l – length of wire, with direction of l defined to be in the direction of current flow

        B – magnetic field density

2.        The direction of the force is given by the right-hand rule. Direction of the force depends on the direction of current flow and the direction of the surrounding magnetic field. A rule of thumb to determine the direction can be found using the right-hand rule as shown below:

      Right Hand rule

3.        The induced force formula shown earlier is true if the current carrying conductor is perpendicular to the direction of the magnetic field. If the current carrying conductor is position at an angle to the magnetic field, the formula is modified to be as follows:

 Where:   q - angle between the conductor and the direction of the magnetic field.

4.        In summary, this phenomenon is the basis of an electric motor where torque or rotational force of the motor is the effect of the stator field current and the magnetic field of the rotor.

see part 3

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