A magnetic field of \( 5\times10^{-4}\,\mathrm{T} \) just balances a perpendicular electric field of \( 15\,\mathrm{kV/m} \) in their effect on an electron beam passing through the two fields in a direction perpendicular to both of them. What is the speed of the electrons?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 3\times10^{7}\,\mathrm{m/s} \)
The beam goes through undeflected when the electric force \( eE \) and the magnetic force \( evB \) on each electron are equal and opposite. Then the total Lorentz force is zero.
\( eE=evB \)
\( \Rightarrow\; v=E/B \)
\( E=15\,\mathrm{kV/m}=1.5\times10^{4}\,\mathrm{V/m} \)
\( \begin{aligned} v &= \frac{E}{B} \\ &= \frac{1.5\times10^{4}\,\mathrm{V/m}}{5\times10^{-4}\,\mathrm{T}} \\ &= 3\times10^{7}\,\mathrm{m/s} \end{aligned} \)