The flow of an electric current down a conducting wire is ultimately due to the motion of electrically charged particles (in most cases, electrons) through the conducting medium. It seems reasonable, therefore, that the force exerted on the wire when it is placed in a magnetic field is really the resultant of the forces exerted on these moving charges.
The Lorentz force is the force on a point charge due to electromagnetic fields. It is given by the following equation in terms of the electric and magnetic fields:
where F is the force (in newtons)
E is the electric field (in volts per metre)
B is the magnetic field (in teslas)
q is the electric charge of the particle (in coulombs)
v is the instantaneous velocity of the particle (in metres per second)
× is the vector cross product.
The implications of this expression include:
1. The force is perpendicular to both the velocity v of the charge q and the magnetic field B.
2. The magnitude of the force is F = qvB sinθ where θ is the angle < 180 degrees between the velocity and the magnetic field. This implies that the magnetic force on a stationary charge or a charge moving parallel to the magnetic field is zero.
3. The direction of the force is given by the right hand rule. The force relationship above is in the form of a vector product.
Example :
A long length of wire is suspended horizontally between the poles of a magnetron magnet. When a large current from a 12V storage battery is passed through the wire, the wire jumps out of the magnetic field. When the direction of the current is switched, the wire jumps the opposite direction.
The magnetron magnet in this demonstration was originally used in MIT's groundbreaking research developing radar during and after World War II. Microwave emitting cavity magnetrons need strong magnetic fields, which were often created by powerful permanent magnets like the one used in this demo.
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