Eddy current

Eddy currents flow in closed loops within conductors, in planes perpendicular to the magnetic field.

This effect is employed in eddy current brakes which are used to stop rotating power tools quickly when they are turned off.

Thus eddy currents are a cause of energy loss in alternating current (AC) inductors, transformers, electric motors and generators, and other AC machinery, requiring special construction such as laminated magnetic cores or ferrite cores to minimize them.

The first person to observe eddy currents was François Arago (1786–1853), the President of the Council of Ministers of the 2nd French Republic during the brief period 10th May to June 24, 1848 (equivalent to the current position of the French Prime Minister), who was also a mathematician, physicist and astronomer.

This change in magnetic flux, in turn, induces a circular electromotive force (EMF) in the sheet, in accordance with Faraday's law of induction, exerting a force on the electrons in the sheet, causing a counterclockwise circular current

Since the electrons have a negative charge, they move in the opposite direction to the conventional current shown by the arrows.

The electrons collide with the metal lattice atoms, exerting a drag force on the sheet proportional to its velocity.

As described by Ampère's circuital law, each of the circular currents in the sheet induces its own magnetic field (marked in blue arrows in the diagram).

Another way to understand the drag is to observe that in accordance with Lenz's law, the induced electromotive force must oppose the change in magnetic flux through the sheet.

Eddy currents in conductors of non-zero resistivity generate heat as well as electromagnetic forces.

The electromagnetic forces can be used for levitation, creating movement, or to give a strong braking effect.

Eddy currents can also have undesirable effects, for instance power loss in transformers.

This Joule heating reduces efficiency of iron-core transformers and electric motors and other devices that use changing magnetic fields.

Electrons cannot cross the insulating gap between the laminations and so are unable to circulate on wide arcs.

So, by Lenz's law, the magnetic field formed by the eddy current will oppose its cause.

The faster the wheels are spinning, the stronger the effect, meaning that as the train slows the braking force is reduced, producing a smooth stopping motion.

the power lost due to eddy currents per unit mass for a thin sheet or wire can be calculated from the following equation:[4]

where This equation is valid only under the so-called quasi-static conditions, where the frequency of magnetisation does not result in the skin effect; that is, the electromagnetic wave fully penetrates the material.

Another application is on some roller coasters, where heavy copper plates extending from the car are moved between pairs of very strong permanent magnets.

Electrical resistance within the plates causes a dragging effect analogous to friction, which dissipates the kinetic energy of the car.

The same technique is used in electromagnetic brakes in railroad cars and to quickly stop the blades in power tools such as circular saws.

In a varying magnetic field, the induced currents exhibit diamagnetic-like repulsion effects.

This can lift objects against gravity, though with continual power input to replace the energy dissipated by the eddy currents.

As described in the section above about eddy current brakes, a non-ferromagnetic conductor surface tends to rest within this moving field.

[8] In some coin-operated vending machines, eddy currents are used to detect counterfeit coins, or slugs.

The coin rolls past a stationary magnet, and eddy currents slow its speed.

Eddy currents are used in certain types of proximity sensors to observe the vibration and position of rotating shafts within their bearings.

These sensors are extremely sensitive to very small displacements making them well suited to observe the minute vibrations (on the order of several thousandths of an inch) in modern turbomachinery.

[clarification needed] Widespread use of such sensors in turbomachinery has led to development of industry standards that prescribe their use and application.

[9][10][11] Eddy current techniques are commonly used for the nondestructive examination (NDE) and condition monitoring of a large variety of metallic structures, including heat exchanger tubes, aircraft fuselage, and aircraft structural components.

Eddy currents ( I , red ) induced in a conductive metal plate (C) as it moves to the right under a magnet (N) . The magnetic field ( B , green ) is directed down through the plate. The Lorentz force of the magnetic field on the electrons in the metal induces a sideways current under the magnet. The magnetic field, acting on the sideways moving electrons, creates a Lorentz force opposite to the velocity of the sheet, which acts as a drag force on the sheet. The blue arrows are counter magnetic fields generated by the circular motion of the charges.
Forces on an electron in the metal sheet under the magnet, explaining where the drag force on the sheet comes from. The red dot e 1 shows a conduction electron in the sheet right after it has undergone a collision with an atom, and e 2 shows the same electron after it has been accelerated by the magnetic field. On average at e 1 the electron has the same velocity as the sheet ( v , black arrow ) in the + x direction. The magnetic field ( B , green arrow ) of the magnet's North pole N is directed down in the − y direction. The magnetic field exerts a Lorentz force on the electron (pink arrow) of F 1 = − e ( v × B ) , where e is the electron's charge . Since the electron has a negative charge, from the right hand rule this is directed in the + z direction. At e 2 this force gives the electron a component of velocity in the sideways direction ( v 2 , black arrow ) The magnetic field acting on this sideways velocity, then exerts a Lorentz force on the particle of F 2 = − e ( v 2 × B ) . From the right hand rule, this is directed in the − x direction, opposite to the velocity v of the metal sheet. This force accelerates the electron giving it a component of velocity opposite to the sheet. Collisions of these electrons with the atoms of the sheet exert a drag force on the sheet.
Eddy current brake. The North magnetic pole piece (top) in this drawing is shown further away from the disk than the South; this is just to leave room to show the currents. In an actual eddy current brake the pole pieces are positioned as close to the disk as possible.
(left) Eddy currents ( I , red ) within a solid iron transformer core. (right) Making the core out of thin laminations parallel to the field ( B , green ) with insulation (C) between them reduces the eddy currents. Although the field and currents are shown in one direction, they actually reverse direction with the alternating current in the transformer winding.
Demonstration of Waltenhofen's pendulum, precursor of eddy current brakes. The formation and suppression of eddy currents is here demonstrated by means of this pendulum, a metal plate oscillating between the pole pieces of a strong electromagnet. As soon as a sufficiently strong magnetic field has been switched on, the pendulum is stopped on entering the field.
A cross section through a linear motor placed above a thick aluminium slab. As the linear induction motor 's field pattern sweeps to the left, eddy currents are left behind in the metal and this causes the field lines to lean.
Lamination of magnetic cores in transformers greatly improves the efficiency by minimising eddy currents
E-I transformer laminations showing flux paths. The effect of the gap where the laminations are butted together can be mitigated by alternating pairs of E laminations with pairs of I laminations, providing a path for the magnetic flux around the gap.