Energy Stored In An Inductor

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A current of 4 amperes flows steadily through a coil having a self-inductance of 0.5 henry. How much magnetic energy is stored in the field of this inductor while the current flows?

RankGuru · Accepted Answer

From NCERT Class 12, Chapter 6 (Electromagnetic Induction), the energy stored in the magnetic field of an inductor carrying current $I$ is $U = \frac{1}{2}LI^2$, which represents the work done against the back-emf to establish the current from zero. Substituting the values: $U = \frac{1}{2} 	imes 0.5 	imes 4^2 = \frac{1}{2} 	imes 0.5 	imes 16 = 4\ 	ext{J}$. The option 8 J omits the factor of one-half. The option 2 J uses the current linearly instead of squaring it, or drops another factor. The option 16 J forgets both the inductance and the one-half factor. A plausibility check confirms the units: $	ext{H} 	imes 	ext{A}^2 = 	ext{(V·s/A)} 	imes 	ext{A}^2 = 	ext{V·A·s} = 	ext{J}$, verifying an energy result. This stored energy is released back to the circuit if the current is interrupted, which is why suddenly breaking an inductive circuit can produce a large voltage spike as the field collapses.

Energy Stored In An Inductor

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