Question

Time period of a charged particle undergoing a circular motion in a uniform magnetic field is independent of (a) speed of the particle (b) mass of the particle (c) charge of the particle (d) magnetic field

Answer 1

Time period of a ‘charged particle’ undergoing a ‘circular motion’ in a ‘uniform magnetic field’ is independent of the ‘speed of the particle’.

Option: (a)

Explanation:  

If we consider m as the mass of the particle, q as the charge, v as the velocity B the magnetic field, r the radius of the ‘circular path’.

Then the ‘centripetal force’ is equal to the pull of the particle from the centre. Thus,

$\begin{array}{l}{\frac{m v^{2}}{r}=q v B} \\ \\{\text { Or } r=\frac{m v}{B q}} \\ \\{\text { So } T=\frac{2 \pi r}{v}}\end{array}$

Putting the value, $r=\frac{m v}{B q}$

Or $T=\frac{2 \pi m}{B q}$

So, ‘time period’ of the rotation is not dependent on velocity of charge.

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