In an electric circuit, energy is required to maintain the flow of current but in magnetic circuit no energy is required to maintain the magnetic flux. Energy is only required in creating the magnetic flux and energy supplied to create a flux is stored in the magnetic field.

Consider a coil of self inductance L henrys. When the current in this coil is increased from zero to finite value I, then self induced e.m.f. is produced in the coil due to increase in current. This induced e.m.f, opposes the increase of current and energy will be required to overcome this opposition.

Let at any instant current flowing through the coil be I amperes, and applied voltage across this coil be e volts.

Applied voltage will be just equal and opposite in direction to the self induced e.m.f. in the coil due to change of current in it, so that it may counter-balance the self induced e.m.f.

i.e. applied e.m.f., e = - self induced e.m.f.

= -(-L di ) where di  is the rate of change of current
        dt            dt

= L  di
      dt

Energy supplied to the coil in short time dt

dw = ei dt Joules = L di x i x dt = Lidi
                               dt

Total energy supplied to the coil in increasing the current from 0 to I amperes



Energy stored in the coil = Energy Supplied =  1 LI² joules.
                                                                  2

For more help in Energy of Magnetic Field click the button below to submit your homework assignment