A beam of electrons passes un-deflected through mutually perpendicular electric and magnetic fields. Where do

Question

A beam of electrons passes un-deflected through mutually perpendicular electric and magnetic fields. Where do the electrons move if the electric field is switched off and the same magnetic field is maintained?

Accepted Answer

1. **Initial State (Undeflected):** When the electron beam passes undeflected, the electric force ($F_E = qE$) balances the magnetic force ($F_B = qvB$). This implies the velocity vector $\vec{v}$, electric field $\vec{E}$, and magnetic field $\vec{B}$ are mutually perpendicular.
2. **Final State (E switched off):** When the electric field is removed, only the magnetic force acts on the electrons: $\vec{F} = q(\vec{v} 	imes \vec{B})$.
3. **Resulting Motion:** Since the velocity $\vec{v}$ is perpendicular to the magnetic field $\vec{B}$, the magnetic force acts as a centripetal force ($F = qvB$), perpendicular to both $\vec{v}$ and $\vec{B}$ at all instants. This causes the electrons to move in a uniform **circular orbit** .

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