An electron of mass m and charge e moves in a circular path in a magnetic field of flux density B. How long does it take to complete one orbit?

Analyze the question: A charged particle moves in a circle because the magnetic force acts as the centripetal force. We need the time for one complete orbit, which is the period T.

Concept: The magnetic force on a charge moving perpendicular to a field is F = Bev. The centripetal force needed for circular motion is F = mv²/r.

Solution:

1. Equate the two forces: Bev = mv²/r

2. Solve for the radius: r = mv/(Be)

3. The period is the circumference divided by the speed: T = 2πr/v

4. Substitute r: T = 2π(mv/(Be))/v = 2πm/(Be)

The speed v cancels, so the period does not depend on how fast the electron moves or on the size of the orbit.

Checking the options:

• A and B have the wrong variables in the wrong places (B or m and e in the same part of the fraction), so they don't match.
• D, Be/(2πm), is the frequency (f = 1/T), not the period.
• C, 2πm/(Be), matches our result.

Tip: Remember that T = 2πm/(Be) is the period and f = Be/(2πm) is the frequency. Period is "time", so the mass (m) sits on top. If an option looks like the inverse, it is the frequency, a common trap in WASSCE and JAMB questions.