An electron (mass $9 imes 10^{-31} \mathrm{~kg}$ and charge $1.6 imes 10^{-19} \mathrm{C}$ ) mov

Question

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

Professor PC Thomas Classes · Answer

(d) : For an electron to move undeflected through perpendicular electric and magnetic fields, the net force on it must be zero. \ $ 	ext { i.e., } F_B=F_E $ \ $\begin{array}{ll}	ext { or } & q v B=q E \ 	ext { or } & E=v B=\frac{c}{100} 	imes 9 	imes 10^{-4} \ & =\frac{3 	imes 10^8}{100} 	imes 9 	imes 10^{-4}=27 	imes 10^2 \mathrm{~V} / \mathrm{m}\end{array}$