An electron with mass ' m ' with an initial velocity (t=0) v⃗=v₀ î(v₀>0) enters a magnetic field B⃗=B₀ ĵ. If the initial de-Broglie wavelength at t=0 is λ₀ then its value after time ' t ' would be :

Solution

Physics sir · 3 steps

A magnetic force only turns the electron, it never speeds it up, so λ stays exactly λ₀.

1. Force is sideways. The magnetic force is F⃗ = -e v⃗ × B⃗. A cross product is always perpendicular to v⃗, so this force can bend the path but cannot push along it.
2. No work done. A force perpendicular to the velocity does zero work. The kinetic energy stays fixed, so the speed stays v₀ at every instant while the electron moves on a circle in the xz-plane.

   λ = h/p = h/(m v₀) = λ₀

3. So. The de Broglie wavelength depends only on the magnitude of momentum, mv₀, which never changes. The wavelength after time t is still λ₀, option (b).

The idea to keep. A pure magnetic field changes only the direction of a charge's velocity, never its speed. So the kinetic energy, the size of the momentum and the de Broglie wavelength all stay constant.

Answer from the NTA final answer key. Solution by PrepWiser.