# Mutual Inductance

### After reading this section you will be able to do the following:

• Describe what mutual inducatance is and how it is related to self-inductance
• Explain what an Eddy Current is.
• Discuss the one requirement necessary for a current to be induced into an object.
• Understand the role mutual inductance plays in eddy current inspection, which is an NDT technique.

The magnetic flux through a circuit can be related to the current in that circuit and the currents in other nearby circuits, assuming that there are no nearby permanent magnets. Mutual inductance is a quantity that describes the effect of one coil's magnetic field on another coil's magnetic field. Consider the following two circuits that are close to each other: The magnetic field produced by circuit 1 on the left will intersect the coil in circuit 2 and create current flow. The induced current flow in circuit 2 will have its own magnetic field which will interact with the magnetic field of circuit 1. At some point P, the magnetic field consists of a part due to the current in circuit 1 (i1) and a part due to the current in circuit 2 (i2).

The inductors (coils) in the circuits are labeled L1 and L2 and this term represents the self inductance in henries (H) of each of the coils. The values of L1 and L2 depend on the geometrical arrangement of the circuit (i.e. number of turns in the coil) and the conductivity of the material. The constant M, called the mutual inductance of the two circuits, is dependent on the geometrical arrangement of both circuits. In particular, if the circuits are far apart, the magnetic flux through circuit 2 due to the current i1 will be small and the mutual inductance will be small. L2 and M are constants.

## Eddy Currents

Anytime a conductor is placed in a changing magnetic field electrical current is generated in the conductor. This conductor can be a piece of wire that is often wrapped into a coil, but the conductor does not need to be in the shape of a coil and does not even need to be wire. It could be a piece of flat steel, aluminum plate, or any other conductive object. The only requirement is that the object must be able to conduct electrical current.

When current is induced in a conductor such as the square piece of metal shown above, the induced current often flows in small circles that are strongest at the surface and penetrate a short distance into the material. These current flow patterns are thought to resemble eddies in a stream, which are the tornado looking swirls of the water that we sometimes see. Because of this presumed resemblance, the electrical currents were named eddy currents. Induced eddy currents generate their own magnetic field.

## Mutual Induction in Eddy Current Inspection In eddy current inspection, the eddy currents are generated in the test material due to mutual induction. The test probe is basically a coil of wire through which alternating current is passed. Therefore, when the probe is connected to an eddyscope instrument, it is basically represented by circuit 1 above. The second circuit can be any piece of conductive material. When alternating current is passed through the coil, a magnetic field is generated in and around the coil. When the probe is brought in close proximity to a conductive material, such as aluminum, the probe's changing magnetic field generates current flow in the material. The induced current flows in closed loops in planes perpendicular to the magnetic flux. They are named eddy currents because they are thought to resemble the eddy currents that can be seen swirling in streams. The eddy currents produce their own magnetic fields that interact with the primary magnetic field of the coil. By measuring changes in the resistance and inductive reactance of the coil, information can be gathered about the test material. This information includes the electrical conductivity and magnetic permeability of the material, the amount of material cutting through the coils magnetic field, and the condition of the material (i.e. whether it contains cracks or other defects.) The distance that the coil is from the conductive material is called liftoff, and this distance affects the mutual-inductance of the circuits. Liftoff can be used to make measurements of the thickness of nonconductive coatings, such as paint, that hold the probe a certain distance from the surface of the conductive material.

Eddy current inspection is discussed more in depth in the techniques portion of this website.

### Review:

1. Mutual inductance is the effect of one coil's magnetic field on another coil's magnetic field.
2. Mutual inductance is the basis of eddy current inspection.
3. Any electrically conductive object will conduct an induced current if it is placed in a changing magnetic field.
4. Eddy currents are circular induced currents.
5. Eddy currents generate their own magnetic fields.