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An alpha particle of mass m moves on a circular path of radius r in a plane normal to a uniform magnetic field B. The time taken by this particle to complete one revolution is ______.

Asked in GUJCET 2016 · Circular motion: radius, period and energy

• (1) (2π m)/(eB)
• (2) (π m)/(2eB)
• (3) (eB)/(π m)
• (4) (π m)/(Be)

Step-by-step solution

Why the other options are wrong

• (1) (2π m)/(eB) is the period of a particle carrying charge e. An alpha particle is a helium nucleus, so its charge is 2e and its period is half of this.
• (2) Here the 2 has been divided out twice — once for the charge 2e and once more from the 2π. T=(2π m)/(qB) with q=2e leaves π m on top, not (π m)/2.
• (3) This is the reciprocal of the period, that is the revolution frequency. Read it as a time and it says a heavier particle goes round faster, which is the wrong way about.

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