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In addition to the revision notes for Energy Stored in a Magnetic Field. Energy Density of a Magnetic Field. Mutual Induction on this page, you can also access the following Magnetism learning resources for Energy Stored in a Magnetic Field. Energy Density of a Magnetic Field. Mutual Induction
| Tutorial ID | Title | Tutorial | Video Tutorial | Revision Notes | Revision Questions | |
|---|---|---|---|---|---|---|
| 16.13 | Energy Stored in a Magnetic Field. Energy Density of a Magnetic Field. Mutual Induction |
In these revision notes for Energy Stored in a Magnetic Field. Energy Density of a Magnetic Field. Mutual Induction, we cover the following key points:
If we bring the opposite poles of two magnets near each other, they are attracted and we must do some work to move them apart. This means the system of magnets is storing energy in the form of magnetic potential energy.
The rate of potential energy delivered by magnetic field (i.e. the power) is calculated by
The (magnetic) potential energy stored in an inductor L when a current I flows through it, is
This equation is similar to that of the energy stored in a capacitor
where the inductance L of inductor is analogue to the inverse of capacitance 1/C of capacitor and the current I flowing through the inductor is analogue to the charge Q stored in the capacitor.
The inductance per unit length near the middle of solenoid is
The energy per unit volume w stored in the solenoid, is
This energy per unit volume stored in the inductor represents the energy density of magnetic field. It is
Or
The above equation is true not only for solenoids but for all types of magnetic fields.
The process of producing a current through a variable magnetic field is called induction. The induction by which electric current is produced in one coil by changing the magnetic field of the other coil requires the presence of two coils. If one coil is moved away, no current is induced in the other coil due to the long distance. Therefore, the current (and the resulting magnetic field) in one coil produced by this mutual interaction is known as mutual induction.
The mutual induction differs from the self-induction of an inductor, as in the case of inductor the presence of a single solenoid is enough to induce a magnetic field inside it.
The mutual inductance of the coil 2 on the coil 1 is denoted by m21. It is calculated by
If we change slightly the value of resistance R in the circuit containing the source, we obtain a variation of current, so we can write
From the Faraday's Law, the right side of the above equation represents the emf induced in the coil 2 due to the change in current in the coil 1. Since it opposes the current I1, we obtain
This reasoning can be used for the emf induced in the first coil as well (due to the law of conservation of energy). Therefore, we can write
Experiments show that m12 = m21. Thus, we can write the mutual inductance simply by M. in this way, the two above equations become
and
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