Velocity of undeflected charged particle in crossed fields – Rankers Physics
Topic: Magnetic Effects of Current
Subtopic: Force Acting on Moving Charges

Velocity of undeflected charged particle in crossed fields

In crossed electric and magnetic field, the velocity of charged particle which passes undeflected through the region may be (where \(E\) is electric field and \(B\) is magnetic field)
\(v = E^2B\)
\(v = \frac{E}{B}\)
\(v = \frac{E^2}{B}\)
\(v = \frac{B}{E}\)

Solution:

For a charged particle to pass undeflected in crossed electric and magnetic fields, the net Lorentz force must be zero. Hence, \(qE = qvB ⇒ v = \frac{E}{B}\).

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