An electron beam moving with a speed of \( 2.5\times10^{7}\,\mathrm{m\,s^{-1}} \) enters a magnetic field of \( 4\times10^{-3}\,\mathrm{T} \) directed perpendicular to its direction of motion. What is the magnitude of the electric field that must be applied so that the beam passes undeflected?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 10^{5}\,\mathrm{N\,C^{-1}} \)
The beam passes undeflected when the electric force \( eE \) and the magnetic force \( evB \) on each electron are equal and opposite. The total Lorentz force is then zero. The electric field is applied perpendicular to both the beam and the magnetic field.
\( eE=evB \)
\( \begin{aligned} E &= vB \\ &= 2.5\times10^{7}\,\mathrm{m\,s^{-1}}\times4\times10^{-3}\,\mathrm{T} \\ &= 10^{5}\,\mathrm{N\,C^{-1}} \end{aligned} \)