Electromagnetism

In the case of a solenoid, B equals the permeability of free space constant multiplied by the charge and multiplied by the number of loops per unit length. Note again that this is not related to the diameter of the coils or any distance inside the coils as this is uniform. This can be a large magnetic field strength that is utilized by the medical field in magnetic resonance imaging or MRI scanners. Superconducting wires are used so that not a lot of heat is generated by the current necessary to create large magnetic fields.

ELECTROMAGNETISM

What is true of magnetic currents and electricity is that it is the change in magnetic field that generates a current and not the absolute value of the magnetic field. If you put a magnetic bar through a circular coil, you will get a galvanometric reading that will change, depending on the rate of change of the bar’s magnetic field within the coil. If the magnetic bar is held stable, there will be no current and no reading on the galvanometer. This ability to cause an emf and a current in a wire is called induction.

This leads to the concept of magnetic flux. The magnetic flux is the magnetic field multiplied by the area it is applied to multiplied by the cosine of theta, which is the angle of the field as it is applied to the area. It is greatest when the field is perpendicular to the area. The change in magnetic flux is what produces the EMF.

The EMF is directly proportional to the change in flux and inversely proportional to time. The faster the change in flux, the greater will the EMF generated be. If the coil has N turns, the EMF will be N times greater than for a single coil. This leads to an EMF that is N multiplied by the change in flux divided by the change in time. This is called Faraday’s law of induction. The units for EMF are in volts, which is typical for EMF. There is a minus sign in this law because the emf will create a current and a magnetic field that oppose the change in flux. This opposition is laid out in the form of Lenz’s law.

Lenz’s law is an example of the conservation of energy. The induced emf produces a current in direct opposition to the change in flux because a change in flux means a change in energy. The energy in the system can enter or leave but there is resistance to that. If Lenz’s law wouldn’t be true, and if the induced EMF were in the same direction

of flux, energy would increase without an apparent source and the conservation of energy would be violated.

Motional EMF is induced whenever a conductor moves in a magnetic field or whenever a magnetic field moves relative to a conductor. This can create a sort of current loop in the conductor called the “eddy current”. These currents can produce a significant drag (called magnetic damping) on the motion involved. If a metal pendulum is passed through a magnetic field, there is a significant drag on the bob of the pendulum that isn’t present if the bob is made from an insulating material. There will be drag in both directions of the pendulum. This only happens as the pendulum is entering and leaving the magnet’s field in keeping with induction and the change in magnetic flux causing a current in the metal bob. The bob needs to be a solid plate in order to generate a circular current within the bob; it isn’t seen as much when the bob is slotted and can’t be induced as much.

These eddy currents and magnetic damping are used in trash separation at recycling centers. The metals and nonmetals are passed down a ramp, the metals will be dragged down by metal damping. Nonmetals will not be affected. Metal detectors work best when they are continually moved because they detect the eddy current from a metal near the detector.

Magnetic braking works for large trains but cannot stop the train altogether because they become less effective at slow speeds. The magnetic eddy effect is seen only when there is movement. Braking of roller coasters happens with magnetic braking systems. Induction cooktops use a varied magnetic field to produce an eddy current that heats up the cooking pot but only if the cooking pot is metallic. It won’t work if the pot is ceramic.