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A linear inductor stores magnetic-field energy proportional to the square of its current.
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Formula
W in J; L in H; I in A
| Symbol | Meaning | Unit |
|---|---|---|
| Stored magnetic-field energy | J | |
| Inductance | H | |
| Instantaneous coil current | A |
W_L=\frac{1}{2}LI^2Integrating p=Li(dI/dt) gives this expression when L is constant. It applies to a linear inductor without saturation; nonlinear magnetization requires integrating the flux-current curve. Interrupting current can release stored energy as a high voltage transient.
Integrating p=Li(dI/dt) gives this expression when L is constant. It applies to a linear inductor without saturation; nonlinear magnetization requires integrating the flux-current curve. Interrupting current can release stored energy as a high voltage transient.
A linear inductor stores magnetic-field energy proportional to the square of its current.
Base equation for the target quantity
Preserve signs, boundary conditions and units when rearranging.
Work through the numerical example for “Magnetic energy stored in an inductor” and check its unit and magnitude.
A 20 mH coil carrying 3 A stores 0.5·0.020·9=0.09 J.
Substituting a related quantity that shares the same symbol.
Use variable definitions and check: W in J; L in H; I in A.
Formula cluster
A linear inductor stores magnetic-field energy proportional to the square of its current.
A 20 mH coil carrying 3 A stores 0.5·0.020·9=0.09 J.
Estimate energy available from coils and magnetic actuators.
Here is how to work through a typical Magnetic energy stored in an inductor (WL = ½LI²) task step by step:
Task
Work through the numerical example for “Magnetic energy stored in an inductor” and check its unit and magnitude.
Solution path
A 20 mH coil carrying 3 A stores 0.5·0.020·9=0.09 J.
For a linear inductor, voltage is proportional to current change. Power is Li·di/dt; integrating from zero to I gives ½LI2. Doubling current quadruples stored energy and the energy potentially released at switch-off. Assume constant inductance and provide a safe current path when switching off real inductive loads. Application: Estimate energy available from coils and magnetic actuators. The numerical example A 20 mH coil carrying 3 A stores 0.5·0.020·9=0.09 J anchors the idea in a concrete measurement case. The corresponding units are W in J; L in H; I in A. A 20 mH coil carrying 3 A stores 0.5·0.020·9=0.09 J. This checks that the reference quantities are compatible.
Under saturation, flux linkage is no longer proportional to current, so constant L is insufficient. Energy must be obtained by integrating voltage or the flux-current curve. A small-signal inductance from a datasheet may be inaccurate at high current. Assume constant inductance and provide a safe current path when switching off real inductive loads. The corresponding units are W in J; L in H; I in A. A 20 mH coil carrying 3 A stores 0.5·0.020·9=0.09 J. This checks that the reference quantities are compatible.
Inductor current cannot vanish instantaneously in the ideal model. The coil develops voltage to sustain current; without a path, that voltage can rise sharply. A flyback diode or clamp limits the transient but changes decay time and dissipation. Assume constant inductance and provide a safe current path when switching off real inductive loads. Scope: Integrating p=Li(dI/dt) gives this expression when L is constant. It applies to a linear inductor without saturation; nonlinear magnetization requires integrating the flux-current curve. Interrupting current can release stored energy as a high voltage transient. A practical application is Estimate energy available from coils and magnetic actuators.
Write the quantity and unit from the variable list next to every value: W in J; L in H; I in A. Substitute only after converting to a consistent unit system, and state sign or reference direction explicitly. The example A 20 mH coil carrying 3 A stores 0.5·0.020·9=0.09 J. is a calculation check: result, unit and order of magnitude must fit the described situation. Round after intermediate calculations so small contributions are not lost prematurely. Assume constant inductance and provide a safe current path when switching off real inductive loads.
The background states this starting condition: Integrating p=Li(dI/dt) gives this expression when L is constant. It applies to a linear inductor without saturation; nonlinear. That limits when the result is a valid model prediction. Compare the problem’s boundary conditions with this assumption before substituting values; real components, material properties or loads can introduce additional effects. The cited reference supports the relation used here but does not remove the need to check whether the specific case fits the model. Assume constant inductance and provide a safe current path when switching off real inductive loads.
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