In this topic, you study Magnetic Energy.
We know that the energy is always required to raise a weight (W) through a certain height (h) but not to maintain it in its raised position. The energy expended in raising the weight (given by W x h joules) is ultimately stored in it as a potential energy and can be utilized in many ways.
Similar is the case of the magnetic field. Energy is always required for establishing a magnetic field but no energy is required to maintain it. The energy expended in establishing the flux is then stored in it as a potential energy and is, later on, recovered when the field collapses.
To understand this more clearly, consider the inductive coil shown in Fig. 5.6. Assume that its inductance (L) is constant and resistance is negligibly small. When the current in it is gradually increased from zero to a certain maximum value I so as to establish corresponding flux in its magnetic circuit, then this is opposed at every stage by the self-induced e.m.f. produced by the changing flux linkages of the coil. Energy is needed to overcome this opposition. This energy is initially drawn from the source. Once the current attains its maximum value I and the flux its corresponding value the self-induced e.m.f. reduces to zero. There being no further opposition, no additional energy is required to maintain this flux in the magnetic circuit. The energy taken initially from the source to establish the flux in the magnetic circuit is stored as a potential energy in the magnetic field itself. When the current in the coil is decreased, the collapsing field induces the e.m.f. in the coil in such a direction as to maintain the current. The coil thus acts as an instantaneous source and delivers the energy to the circuit.
Thus, the energy stored in the magnetic field during the period when the current increases is returned back to the circuit during the period when the current decreases. The value of this stored magnetic energy may be found as follows:
At an instant ‘t’ seconds after the closure of the switch (Fig. 5.6), let the current be ‘i’ amperes. If this current increases by di amperes in dt seconds, then from Equation (5.7), the e.m.f. induced in the coil,
This e.m.f. opposes the current and energy drawn from the source to overcome this opposition is ultimately stored in the magnetic field. Component of the applied voltage to neutralize the induced e.m.f.
Energy absorbed by the magnetic field during time dt seconds
— Power x Time
Hence, total energy E absorbed by the magnetic field when the current increases from 0 to its final value of I amperes is given by