1. Use the magnetic force as centripetal force

For a charged particle moving perpendicular to a uniform magnetic field $B$, the magnetic force is

$F = qvB$

This provides the centripetal force needed for circular motion:

$qvB = \frac{mv^2}{r}$

From this,

$r = \frac{mv}{qB}$

2. Write the time period of circular motion

The time period is

$T = \frac{2\pi r}{v}$

Substitute $r = \frac{mv}{qB}$:

$T = \frac{2\pi}{v} \cdot \frac{mv}{qB}$

$T = \frac{2\pi m}{qB}$

3. Check dependence of $T$

From

$T = \frac{2\pi m}{qB}$

we see that the time period depends on:

• mass $m$
• charge $q$
• magnetic field $B$

and is independent of speed $v$.

4. Evaluate options

• A: speed — independent ✅
• B: mass — dependent ❌
• C: charge — dependent ❌
• D: magnetic induction — dependent ❌

Therefore, the correct answer is A.