ENERGY STORED IN MAGNETIC FIELD
When a coil is connected to an electric source, the current flowing in the circuit gradually increases from zero to its final value, and a magnetic field is established. Consequently, a portion of the electrical energy supplied by the electric source is stored as current, is dissipation from the magnetizing coil as heat. After the magnetic field has been established, and the current has attained its maximum or steady value, any more energy given to it will be dissipated as heat. In other words, no additional energy is required to maintain the field, once the steady-state has reached. If, however, the circuit of a stored in it will be spent in generating an induced emf or current.
Figure 1 depicts an iron-cored coil when the resistance of the resistance of the coil lumped outside so that the exciting coil is devoid of any resistance (pure, lossless). Let the exciting coil is devoid of any resistance (pure, lossless). Let the inductance of the coil be L Henrys and a current of I amperes be flowing through it at any instant t. At this instant the current is current is rising at the rate of amperes per second. This induces an emf e in the coil.
The induced emf in the coil is given by expression
Multiplying both sides of above equation by I, we have the power input to the coil,
Which is positive when both and di/dt have the same sign, else it is negative. If the coil current when zero at t=0 and has attained the value of I amperes at t=T, the energy input to the coil during this interval of T second is
It should be noted that the total stored energy in the magnetic field depends upon the final or steady-state value of the current and is independent of the manner in which the current has increase or time it has taken to grow.
Equation(1) can be written as
Corresponding the stored energy is
Equation (10.5) can also be written as
and energy stored
When S is the reluctance of the magnetic circuit and 0 is the flux established in the magnetic circuit.
In case of an airgap in the core, airgap reluctance being far larger than that of the core, portion of the field energy would reside in the airgap.
Energy Stored Per Unit Volume
Energy stored in a magnetic field of self-inductance L and carrying a current of I amperes
Energy stored in magnetic field
Now since the magnetising force and al=volume of the magnetic field in m3
joules in a medium
joule in air