Motion in Combined Electric and Magnetic Fields

2025 1 question

1. An electron (mass $9 \times 10^{-31}\text{ kg}$ and charge $1.6 \times 10^{-19}\text{ C}$) moving with speed $c/100$ ($c =$ speed of light) is injected into a magnetic field $B$ of magnitude $9 \times 10^{-4}\text{ T}$ perpendicular to its direction of motion. We wish to apply a uniform electric field $\vec{E}$ together with the magnetic field so that the electron does not deflect from its path. Then (speed of light $c = 3 \times 10^8\text{ ms}^{-1}$):