# Energy Stored in an Inductor

## Energy Stored in an Inductor

We know from Lenz’s law that inductances oppose changes in current. There is an alternative way to look at this opposition that is based on energy. Energy is stored in a magnetic field. It takes time to build up energy, and it also takes time to deplete energy; hence, there is an opposition to rapid change. In an inductor, the magnetic field is directly proportional to current and to the inductance of the device. It can be shown that the energy stored in an inductor $${E}_{\text{ind}}$$ is given by

$${E}_{\text{ind}}=\cfrac{1}{2}{\text{LI}}^{2}\text{.}$$

This expression is similar to that for the energy stored in a capacitor.

### Example: Calculating the Energy Stored in the Field of a Solenoid

How much energy is stored in the 0.632 mH inductor of the preceding example when a 30.0 A current flows through it?

Strategy

The energy is given by the equation $${E}_{\text{ind}}=\cfrac{1}{2}{\text{LI}}^{2}$$, and all quantities except $${E}_{\text{ind}}$$ are known.

Solution

Substituting the value for $$L$$ found in the previous example and the given current into $${E}_{\text{ind}}=\cfrac{1}{2}{\text{LI}}^{2}$$ gives

$$\begin{array}{lll}{E}_{\text{ind}}& =& \cfrac{1}{2}{\text{LI}}^{2}\\ & =& 0.5(0.632×{\text{10}}^{-3}\phantom{\rule{0.25em}{0ex}}\text{H})(\text{30.0 A}{)}^{2}=\text{0.284 J}\text{.}\end{array}$$

Discussion

This amount of energy is certainly enough to cause a spark if the current is suddenly switched off. It cannot be built up instantaneously unless the power input is infinite.

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