Question

What will be the magnitude of a magnetic field that causes an alpha particle to pass through space undeflected if the particle has a velocity of magnitude 500m/s and travels horizontally in space in which there is an upward directed uniform electric field of magnitude 35N/C and a uniform magnetic field which the magnetic field makes an angle of 46⁰ with the particles velocity vector?

Answer 1

From the equilibrium between the electric and magnetic forces:

$$qE=qvB\sin\theta,\\\space\\ B=\frac{E}{v\sin\theta}=0.097\text{ T}.$$