The force on an object moving in a magnetic field is given by the equation
where q is the charge on the object, v is its velocity, B is the magnetic field, and F is the resultant force. The symbol ×, pronounced “cross”, is a special form of multiplication for vectors called the cross-product. The cross-product of two vectors is a third vector which is perpendicular to the plane formed both of the original vectors. The diagram below shows how to find this direction. Have your right hand in the direction of v and rotate the palm through the plane formed by v and B until it reaches the direction of B. The hard thing for most people is first orienting your hand so that it can swing easily in the plane from v to B.
There is a second complication in that v × B is multiplied by q to find F. Now q can be positive, negative, or neutral (zero). When q > 0, the force is in the same direction as v × B. When q < 0, the force is in the opposite direction to v × B. This is illustrated in the next diagram.
The size of the resultant vector found from the cross-product v × B is the same as the parallelogram formed by v and B.
Consider the three cases below. The area is maximum is when v and B are perpendicular. There will be zero area and no force when v and B are parallel or antiparallel.
Note