MHT CET · Physics · Magnetic Effects of Current
Under the influence of a uniform magnetic field a charged particle is moving in a circle of radius \(R\) with constant speed \(v\). The time period of the motion
- A depends on \(v\) and not on \(R\)
- B depends on both \(R\) and \(v\)
- C is independent of both \(R\) and \(v\)
- D depends on \(R\) and not on \(v\)
Answer & Solution
Correct Answer
(C) is independent of both \(R\) and \(v\)
Step-by-step Solution
Detailed explanation
When magnetic field is perpendicular to motion of charged particle, then Centripetal force \(=\) magnetic force
ie, \(\frac{m v^{2}}{R}=B q v\)
Or
\(
R=\frac{m v}{B q}
\)
Further, time period of the motion
or
\(
\begin{array}{l}
T=\frac{2 \pi R}{v}=\frac{2 \pi\left(\frac{m v}{B q}\right)}{v} \\
T=\frac{2 \pi m}{B q}
\end{array}
\)
It is independent of both \(R\) and \(v\).
ie, \(\frac{m v^{2}}{R}=B q v\)
Or
\(
R=\frac{m v}{B q}
\)
Further, time period of the motion
or
\(
\begin{array}{l}
T=\frac{2 \pi R}{v}=\frac{2 \pi\left(\frac{m v}{B q}\right)}{v} \\
T=\frac{2 \pi m}{B q}
\end{array}
\)
It is independent of both \(R\) and \(v\).
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