The diagram above illustrates an arrangement of a cathode ray from an electron gun and a bar magnet placed perpendicularly to the direction of the ray. Will...

Answer Details

From the diagram: the electron gun fires the cathode ray horizontally to the right, and the bar magnet stands vertically to the right of the beam with its S pole at the top and its N pole at the bottom, so its axis is perpendicular to the ray.

Direction of the magnetic field. In the region in front of the magnet the field lines run from the N pole to the S pole, that is, vertically upward (from the bottom N pole to the top S pole), in the plane of the paper.

Nature of the beam. A cathode ray is a stream of negatively charged electrons. Taking the electron velocity to the right as \(v\) and the field upward as \(B\), the magnetic force on each electron is

\[ \vec{F} = -e\,(\vec{v} \times \vec{B}) \]

Both \(\vec{v}\) (horizontal, to the right) and \(\vec{B}\) (vertical, upward) lie in the plane of the paper and are mutually perpendicular. Their cross product \(\vec{v}\times\vec{B}\) therefore points out of the paper, and because the electron charge is negative, the force \(\vec{F}\) points into the plane of the paper.

Conclusion. The ray is not simply pushed up or down within the plane of the diagram. It is deflected perpendicular to the paper (into the page, away from the reader), because the deflecting force is at right angles to both the ray and the vertical field. Had the ray moved in the same direction and the field been directed into the page, the electrons would then be deflected downward; with the field as drawn (upward, in the plane of the paper) the deflection is out of the plane.