A particle of charge q and mass m moves in a circular orbit of radius r with an angular speed . The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on [2000]

Question

A particle of charge q and mass m moves in a circular orbit of radius r with an angular speed $ω$ . The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on [2000]

Smart Achievers · Accepted Answer

(3)

The angular momentum of the particle

$L = m v r = m r^{2} ω$ where $ω = 2 πn$ $[∵ v = r ω]$

$∴$ $Frequency n = \frac{ω}{2 π};$ $Further,$ $i = \frac{q}{t} = q \times n = \frac{ω q}{2 π}$

Magnetic moment, $M = i A = \frac{ω q}{2 π} \times π r^{2}$ $\Rightarrow M = \frac{ω q r^{2}}{2}$

$∴$ $\frac{M}{L} = \frac{ω q r^{2}}{2 m r^{2} ω} = \frac{q}{2 m}$

Solution

Q.
A particle of charge q and mass m moves in a circular orbit of radius r with an angular speed $ω$ . The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on [2000]

1 $ω$ and $q$

2 $ω, q$ and $m$

3 $q$ and $m$

4 $ω$ and $m$

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Solution

Q. A particle of charge q and mass m moves in a circular orbit of radius r with an angular speed ω. The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on [2000]

1 ω and q

2 ω, q and m

3 q and m

4 ω and m