Answer to Question #122741 in Electricity and Magnetism for Raydelle

Question

An alpha particle, of charge +3.2 × 10−19 C and velocity of magnitude 500 m/s, travels horizontally into a region of space in which there is an upward-directed uniform electric field of magnitude 20 N/C and a uniform magnetic field. The magnetic field makes an angle of 40° with the particle’s velocity vector, and is such that it causes the alpha particle to pass through the region of space undeflected.
Beginning with an explanation of what happens to the alpha particle in the presence of the electric field, explain clearly how the presence of the magnetic field causes the alpha particle to pass through undeflected.
Determine the magnitude of the magnetic field that is required to cause the alpha particle To pass through undeflected

Answer 1

The electric field causes the particle move upward, while the magnetic field causes the particle to move downward. Applying the left-hand rule, we see that the magnetic field is directed to the right (particle moves into the screen, electric field lines point upward).

The magnitude of the force created by the electric field is

$$F=qE.$$

The magnitude of the magnetic field is

$$F=qvB\text{sin}40°.$$

The magnetic field is

$$B=\frac{qE}{qv\text{ sin}40°}=\frac{E}{v\text{ sin}40°}=0.062\text{ T}.$$