An electric field E exerts a force on a charge q. A magnetic field B will also exert a force on a charge q, but only if the charge is moving (and not moving in a direction parallel to the field). The direction of the force exerted by a magnetic field on a moving charge is perpendicular to the field, and perpendicular to the velocity (i.e., perpendicular to the direction the charge is moving).
The equation that gives the force on a charge moving at a velocity v in a magnetic field B is:
This is a vector equation : F is a vector, v is a vector, and B is a vector. The only thing that is not a vector is q.
Note that when v and B are parallel (or at 180°) to each other, the force is zero. The maximum force, F = qvB, occurs when v and B are perpendicular to each other.
The direction of the force, which is perpendicular to both v and B, can be found using your right hand, applying something known as the right-hand rule. One way to do the right-hand rule is to do this: point all four fingers on your right hand in the direction of v. Then curl your fingers so the tips point in the direction of B. If you hold out your thumb as if you're hitch-hiking, your thumb will point in the direction of the force.
At least, your thumb points in the direction of the force as long as the charge is positive. A negative charge introduces a negative sign, which flips the direction of the force. So, for a negative charge your right hand lies to you, and the force on the negative charge will be opposite to the direction indicated by your right hand.
In a uniform field, a charge initially moving parallel to the field would experience no force, so it would keep traveling in straight-line motion, parallel to the field. Consider, however, a charged particle that is initially moving perpendicular to the field. This particle would experience a force perpendicular to its velocity. A force perpendicular to the velocity can only change the direction of the particle, and it can't affect the speed. In this case, the force will send the particle into uniform circular motion. The particle will travel in a circular path, with the plane of the circle being perpendicular to the direction of the field.
In this case, the force applied by the magnetic field ( F = qvB ) is the only force acting on the charged particle. Using Newton's second law gives:
The particle is undergoing uniform circular motion, so the acceleration is the centripetal acceleration:
a = v2 / r
so, q v B = m v2 / r
A factor of v cancels out on both sides, leaving
q B = m v / r The radius of the circular path is then: r = m v / (q B)
A particle that is initially moving at some angle between parallel and perpendicular to the field would follow a motion which is a combination of circular motion and straight-line motion...it would follow a spiral path. The axis of the spiral would be parallel to the field.
To understand this, simply split the velocity of the particle into two components:
The field does not affect v-parallel in any way; this is where the straight line motion comes from. On the other hand, the field and v-perpendicular combine to produce circular motion. Superimpose the two motions and you get a spiral path.
Information provided by: http://physics.bu.edu