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6.3 - Electromagnetism

Definitions and Core Info

A magnetic field is a field in which a charged particle experiences a force. Its direction is determined by the force experienced by a positive test charge.

Field Lines

Uniform:

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Bar magnet or solenoid:

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Around a current carrying wire (direction determined with right hand grip rule):

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Magnetic Force

Flemings' left hand rule:

  • Thumb: Thrust (force)
  • Index/First finger: Magnetic field
  • Middle/Second: Current

Right hand grip rule:

  • Thumb: Direction of magnetic field.
  • Grip: Direction of current in the coil.

The "thrust" represents the magnetic force on a current-carrying wire/moving charge:

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In a magetic field, a moving charge moves in circular motion. The radius is derived as:

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... where m is the mass of the particle, v is its velocity, B is the magnetic flux density it is going through, and q is its charge.

This can be used to perform selection of certain particles by their velocity.

  1. Particles are charged such that they all have the same charge.
  2. They are accelerated through an electric field on top of a magnetic field through a vacuum.
  3. F = BQv, F = Eq, => E = Bv
  4. Particles with the incorrect velocity will have unbalanced forces, causing them to undergo circular motion upwards or downwards as they pass through the vacuum.
  5. Particles with the correct velocity will pass through the window.

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Electromagnetic Induction

Magnetic Flux

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... where B is the magnetic flux density, A is the cross sectional area of the coil, and theta is the angle of the coil from the vertical of the cross section.

Flux linkage:

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... where N is the number of turns in the coil.

Faraday's Law

The EMF induced in a coil is equal to the rate of change of magnetic flux linkage.

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Lenz's Law

If the magnetic flux linkage through a coil changes, it will induce a current to oppose the change. This opposition occurs due to the generation of an equal and opposite magnetic field. This is due to conservation of energy.

Transformers

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An alternating current is passed through the primary coil, causing an alternating magnetic field to be generated, along with alternating magnetic flux lines through the soft iron core, which maximises retainment of magnetic flux lines due to magnetic shielding. This generates an alternating EMF in the secondary coil due to Faraday's law.

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... where Vs and Ns are the EMF and number of turns in the secondary coil, and p is likewise for the primary coil.

Transformers can be >95% efficient, with some reaching over 98.5% efficiency.

An Eddy current can be created in the soft iron core due to the magnetic field from the primary coil. This creates an opposing magnetic field and releases energy into the core as heat, reducing efficiency. This is mitigated by

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