Answer to Question #181497 in Physics for Jacob

Question

An alpha particle, with 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 35 N/C and a uniform magnetic field. The magnetic field makes an angle of 45° with the particle’s velocity vector and is such that it causes the alpha

particle to pass through the region of space undeflected.

What will be the magnitude of the magnetic field that is required to cause the alpha particle to pass through undeflected?

Answer 1

Find electrical force:

$$F=qE.$$

To remain undeflected, the magnetic force must be equal in magnitude and opposite in direction:

$$F=qvB\sin\theta=qE,\\\space\\ B=\frac{E}{v\sin\theta}=0.1\text{ T}.$$