# Energy Stored in Magnetic Field – How Does It Works?

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How does magnetic field store energy? In an inductor, energy is stored within a magnetic field. Energy stored in magnetic field can be calculated with formula E = 1/2 LI2. The energy stored in magnetic is equal to the work needed to produce a current through the inductor. Magnetic field can be of permanent magnet or electro-magnet. Both magnetic fields store some energy.

Permanent magnet always makes the magnetic flux and it doesn’t shift upon the other outer components. But electromagnet creates its variable magnetic fields based on how much current it carries.

# Energy Stored in Magnetic Field – How Does It Works?

The dimension of this electro-magnet is responsible to create the strength the magnetic field and hence the energy stored in this electromagnet.

First we consider the magnetic field is due to electromagnet i.e. a coil of several no. turns. This coil or inductor is conveying current I when it is associated over a battery or voltage source through a switch.

Suppose battery voltage is V volts, value of inductor is L Henry, and current I will flow at steady state. Now, we will discuss energy stored in magnetic field formula and due to permanent magnet. Let’s see below.

## Energy Stored in Magnetic Field Formula

The formula for the energy stored in a magnetic field is E = 1/2 LI2. Energy is stored in a magnetic field. Energy density can be written as . A device or circuit component that exhibits significant self-inductance; a device which stores energy in a magnetic field.

When the switch is ON, a current will flow from zero to its steady value. But due to self induction a induced voltage appears which is:

This E always in the opposite direction of the rate of change of current.

Now here the energy or work done due to this current passing through this inductor is U. As the current begins from its zero value and flowing against the induced emf E, the energy will grow up step by step from zero value to U.

See Also: Energy Stored in a Capacitor

dU = W.dt, where W is the small power and W = – E.I So, the energy stored in the inductor is given by:

Now integrate the energy from 0 to its final value.

Again,

As per dimension of the coil, where N is the number of turns of the coil, A is the effective cross-sectional area of the coil and l is the effective length of the coil. Again,

Where:

• H is the magnetizing force,
• N is the number of turns of the coil, and
• l is the effective length of the coil.

Now putting expression of L and I in equation of U, we get new expression i.e.

So, the stored energy in a electromagnetic field i.e. a conductor can be determined from its measurement and flux density. Now let us start discussion about energy stored in the magnetic field due to permanent magnet.

## Energy Stored in The Magnetic Field Due to Permanent Magnet

Total flux flowing through the magnet cross-sectional area A is φ. Then we can write that φ = B.A, where B is the flux density.

Now this flux φ is of two types, (a) φr this is remanent flux of the magnet and (b) φd this is demagnetizing flux. So:

As per conservation of the magnetic flux Law.

Again, Bd = μ. H, here H is the magnetic flux intensity. Now MMF or Magneto Motive Force can be calculated from H and dimension of the magnet.

Where l is the effective distance between two poles.

Now to calculate energy we have to first go for the hesitance of the magnetic flux path. Magnet’s internal reluctance path that is for demagnetizing is denoted as Rm, And

Now Wm, is the energy stored in the magnet’s internal reluctance.

Now energy density:

Look at the model below. Dotted lined box is the magnet and one reluctance path Rl for the mechanical load is connected across the magnet.

Now apply node equation and loop equation, we get

Now, If we do any mechanical work inside a magnetic field, then the energy required W.

Again, if we place an electromagnetic coil in the region of a permanent magnet, then this coil will encounter a power. To move this coil some work is done.

This energy density is the co-energy with respect to the permanent magnet and the coil magnet. Magnetizing flux intensity for the permanent magnet is H and for the coil is HC.

This co-energy is denoted as:

Where, B is the flux density at the coil position near the permanent magnet.