# Where is the energy stored in an inductor?

In an inductor,

Most text books say that the $(1/2)Li^2$ is stored in the magnetic field.

But is there another way to explain this?

In a capacitor I understand that all the energy that the battery provides is used up to seperate the two oppositely charged plates.

Is there an analogy for Inductors? OR Could you explain how energy can be stored in a

magnetic field? Does that mean energy is stored in an electric field produced by a point charge?

Does that mean energy is stored in an electric field produced by a point charge?

The classical self energy of a point charge is formally infinite and, thus, somewhat of an embarrassment.

Could you explain how energy can be stored in a magnetic field?

It's clear that energy is stored in a magnetic field so I'm not sure what you're looking for here.

When work is done, energy is converted from one form to another. Work is being done by the battery when the current through an inductor is increasing.

This is simply due to the fact the product of voltage and current is power, the rate at which work is done.

And, when the magnetic field threading the inductor coils is changing, there is a voltage across the inductor.

Thus, when the current through the inductor is increasing, there is a voltage across, proportional to the rate of change of current, and thus, an associated power

$$p_L = i_L \cdot v_L = i_L \cdot L \frac{di_L}{dt}$$

Further, when the current is decreasing, work is being done by the inductor on the circuit. So, the work done increasing the current (and associated magnetic field) is stored as energy in the magnetic field.

• Does storing Energy in the Magnetic Field mean the Potential Energy? – Transcend97 Mar 3 '15 at 14:42

Magnetic fields have a energy density associated to them which is proportional to the square of their magnitude. To create a field one then needs to spend energy in order to create such energy distribution in space, similar to the case of electric fields in capacitors.

• But an electron produces an electric field without spending energy. Why do need to spend energy here? – Transcend97 Mar 3 '15 at 11:47

In a capacitor I understand that all the energy that the battery provides is used up to seperate the two oppositely charged plates.

Is there an analogy for Inductors?

Yes, there is.

The changing magnetic field through a circuit induces an emf in the circuit; this induced emf tries to oppose the change.

Thus the induced emf opposes the increasing current and work must be done against this emf by the voltage source in order to establish the current in the inductor. This work done is stored in the magnetic field.

### Reference:

Energy Stored in an Inductor