The motor effect is really a force on each moving charge. Because that force stays at right angles to the velocity, it curves the path into a circle without ever speeding the charge up.
A charge moving through a magnetic field feels a force F = BQv sinθ, always perpendicular to its velocity. A perpendicular force does no work, so the speed is constant and the path is a circle with r = mv / BQ. Cross the magnetic field with an electric one and only the speed v = E / B passes straight through, a velocity selector.
In the magnetic field, the force points to the centre and the charge loops round; change the speed or the field and watch the radius follow r = mv / BQ. Switch to the velocity selector to see crossed fields let just one speed through.
A current in a slab sits in a field pointing into the page. The carriers are pushed sideways and pile up on one face until the electric field they build balances the magnetic force. Increase B or the current and the Hall voltage grows; switch to the semiconductor, with far fewer carriers, and it jumps, Vₐ = BI / (ntq).
The force on a wire and the force on a charge are the same physics seen two ways.
The magnetic force does no work: it changes direction, not speed, so the path is a circle, not a spiral that speeds up. In r = mv / BQ the radius is proportional to speed and inversely proportional to B. A velocity selector passes v = E / B regardless of charge or mass. Keep the Hall voltage (across the slab) separate from the driving p.d. (along it).
Four quick checks on the force on a moving charge. Each correct answer earns XP and lights this skill on your star map.
The magnetic force on a charge moving through a field does no work on it because the force is always:
A charged particle moves in a circle in a uniform magnetic field. If its speed is doubled while B, charge and mass are unchanged, the radius:
In a velocity selector with crossed electric and magnetic fields, a charged particle travels straight through only when its speed equals:
A Hall probe is an instrument used to measure:
To find the speed of a particle after acceleration through a p.d. V, use the energy gained QV = ½mv² before substituting into r = mv / BQ. State the direction of the force from F = BQv with the left-hand rule, remembering that for a negative charge the conventional current is opposite to the velocity.
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