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Moving Charges in Magnetic Fields

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David Burrows

on 21 October 2014

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Transcript of Moving Charges in Magnetic Fields

Moving charges in magnetic fields
Moving Charges
An electric current is the result of a flow of charge. Therefore, if a current in a conductor
experiences a force due to the presence of a magnetic field, then so should a single charge as
it moves through a field.

This is the principle used by particle accelerators like the one at CERN.

The direction of movement of a beam of negative electrons in a magnetic field can be predicted using the right-hand motor rule, but remember that electrons move in a direction opposite to that of conventional positive charges, so you must point your extended thumb in the opposite direction to the travel of the electron beam.
The size of the force exerted is found to depend on:

the size of the charge C in coulombs

the velocity of the charges in m/s

the strength of the field B, in Tesla.

Recall that the maximum force produced on a current-carrying conductor is:

In the diagram, the charged particles are protons of mass 1.67 × 10^–27 kg. They enter the magnetic field of strength B = 3.0 × 10^–2 T at a velocity of 2.5 × 10^5 m s–1.


(a) the force acting on the protons

(b) the radius of curvature of their path in the field.

And current can be expressed as I=q/t
This gives us:
Because l/t=v (distance over time)
The force on the moving charge will be acting constantly to change its direction of travel. In fact, the force is always directed at right angles to the instantaneous direction of travel. This is centripetal motion. Thus, if a moving charge enters a magnetic field it will be curved into a circular path of travel. If the strength of the field is strong enough the charged particle may be constrained to move in a completely circular path within the field and may never escape.
Note that this effect will occur for all charged particles, not just simple electrons. This
effect has very useful practical applications, especially where charged particles or ions
are concerned.
do Qs 18,19,20 on page 572
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