Motion of an Electron in a uniform magnetic field
Charged particles move in circles at a constant speed if projected into a magnetic field at right angles
to the field. Charged particles move in straight lines at a constant speed if projected into a magnetic field along the direction
of the field. If the electron enters the field at an angle to the field direction the resulting path of the electron
(or indeed any charged particle) will be helical as shown in figure
Magnetic fields exert forces on moving charges. This force is one of the most basic known.
The direction of the magnetic force on a moving charge is perpendicular to the plane formed by v and B and follows right hand rule. The magnitude of the force is proportional to q, v, B, and the sine of the angle between v and B.
The force on a charged particle due to an electric field is directed parallel to the electric field vector in the case of a positive charge, and anti–parallel in the case of a negative charge. It does not depend on the velocity of the particle.
In contrast, the magnetic force on a charge particle is orthogonal to the magnetic field vector, and depends on the velocity of the particle. The right hand rule can be used to determine the direction of the force.
The Lorentz force is the combination of the electric and magnetic force, which are often considered together for practical applications. Electric field lines are generated on positive charges and terminate on negative ones. The field lines of an isolated charge are directly radially outward. The electric field is tangent to these lines.
Magnetic field lines, in the case of a magnet, are generated at the north pole and terminate on a south pole. Magnetic mono poles do not exist in isolation. Like in the case of electric field lines, the magnetic field is tangent to the field lines. Charged particles will spiral around these field lines.