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If the speed of a charged particle moving through a magnetic field is increased, then the radius of curvature of its trajectory will ______.

Asked in GSEB Board July 2015 · Circular motion: radius, period and energy

Answer: (2) increases

Step-by-step solution

Idea: the magnetic force provides the centripetal force, qvB=(mv²)/r.

Cancelling one factor of v gives r=(mv)/(qB).

With m, q and B fixed, r∝ v.

So raising the speed increases the radius of curvature. The period T=(2π r)/v=(2π m)/(qB) is unchanged — the particle simply goes round a bigger circle in the same time.

Why the other options are wrong

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