Do magnetic lenses do work on particles flowing through them?

[BrandonBerchtold]

Do magnetic lenses do work on charged particles flowing through them?

Intuitively I would think yes because the magnetic field produced by the electric current in the coil is applying a force on the particles flowing through the lens, so therefore an electric current (the beam of particles to be focused) flowing through the lens should apply an equal and opposite force on the current in the coil, right?

 

[Dale]

Do magnetic lenses do work on charged particles flowing through them?

We can write the instantaneous force from the magnetic lens as $\vec F = q \vec v \times \vec B$. The instantaneous work is $P=\vec v \cdot \vec F$. So $P=\vec v \cdot ( q \vec v \times \vec B) = 0$