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# Energy Stored in a Magnetic Field

Author: E.E. Kimberly

When a solenoid is energized by a current, part of the energy input is expended in heating the conductor while the other part is expended in building up the magnetic field and is stored in it. After a voltage v is applied to the solenoid and produces a current i, the work done in a time dt is

This work may be divided into two parts,

as follows:

 Fig. 7-12. Magnetization Curve for Example 7-2

The last term of this equation represents the energy stored in the magnetic field in a time dt. By integrating that term between the limits zero and /, the energy stored in a given time may be found. Thus,

or

(7-9)

This equation of energy is correct only if the inductance L of the circuit is constant.

When the magnetic circuit contains iron, the inductance is not constant and the stored energy is not so easily found. To find the energy in such a field, the saturation curve like that given in Fig. 7-6 (b) must be available. .

Example 7-2. - The field winding of a two-pole d-c generator has 1000 turns per pole. With a field current of 1.2 amp, the flux per pole is 1,500,000 lines. Calculate the energy stored. The magnetization curve is as shown in Fig. 7-12.

Solution. - Draw a line through the origin tangent to the curve A D, and let it intersect FD extended at B. If the inductance of the circuit had remained constant as the current was increased from zero, the inductance L would have been

and the stored energy would

have been

This energy is represented by (proportional to) the area ABC. However, with a current //= 1.2 amp, the flux obtained was AE instead of AC; hence, the area ADE represents the actual work done. The following is a proof of this statement.

or •But

and

Therefore, the energy W is proportional to , which is area ADE. This area may be measured with a planimeter. The energy

then is

Stored energy in a magnetic circuit is used in one method of welding thin sheets of metal by impulse. Stored energy presents a problem when interrupting an inductive circuit carrying direct current, because the energy must be dissipated in the arc and the heat produced by the arc is destructive to the opening contact points. In case the amount of energy is relatively small, it is feasible to provide a condenser across the opening points (as at the breaker points of an automobile distributor) to receive the energy instead of permitting it to burn the points.

Last Update: 2010-10-06