# Derive an expression for energy stored in a magnetic field .

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Derive an expression for energy stored in a magnetic field .

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Expression for energy stored in a magnetic field: The energy is stored in magnetic field when current increases and return back when the current decreases. At instant ‘t’ seconds after closer of switch (Refer Fig.), let the current be ‘I’ amperes. If current increases by di amperes in dt seconds, then e.m.f. induced in the coil is given by,

e = - L (di/ dt) volts

The e.m.f. opposes the current and energy drawn from the source. Component of applied voltage to neutralize the induced e.m.f. = - e volts.

Therefore Energy absorbed by the magnetic field during dt seconds = Power x Time = (-e) idt = L ( di/dt) × i × dt = L i di joules Hence total energy absorbed by the magnetic field when current increases from 0 to I amperes

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