Question
A charged particle enters a region of space where uniform electric and magnetic fields are present. If the particle enters this region with velocity v in the direction indicated by arrow 1 in the diagram, it moves uniformly and in a straight line. If the particle enters the region of the electric and magnetic fields with the same speed but in the direction indicated by arrow 2, it also moves uniformly and in a straight line. The magnitude of the electric field is E. Find the magnetic induction B. The directions indicated by arrows 1 and 2 are mutually perpendicular.
Answer Key
Solution
The electric field vector is directed perpendicular to the plane of the figure (either "towards us" or "away from us"). The magnetic induction vector lies in the plane of the figure, at an angle of 45° to the velocity of the first electron and 135° to the velocity of the second electron (or vice versa). The ratio of the magnitudes of the electric field intensity to the magnetic induction is given by the relationship: