Magnetic Force on a Current Carrying Conductor
When charged moving particles are placed in a magnetic field, they experience a magnetic force given by the Lorentz force equation. This states that the magnetic force felt by a charged particle is equal to the product of the charge of the particle, the velocity of the particle and the component of the velocity that is perpendicular to the magnetic field. The magnetic force is produced in a direction that is itself perpendicular to both the velocity and the magnetic field.
A right-hand rule is a useful tool for finding the direction of a cross-product. There are a number of ways to use this tool. One way is to point your fingers in the direction of the current I, and then curl your fingers in the direction of the external magnetic field (B). Your thumb will point in the direction of the magnetic force
We can see that the magnetic force (F) is directly proportional to the current (I) length of wire (L) in the external magnetic field, the external magnetic field magnitude (B), and the sin of the angle, between the current direction in the wire and the external magnetic field. Because of this, the magnetic force is greatest if the current direction in the wire is perpendicular to the external magnetic field and zero when it is parallel to the external magnetic field.
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