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GR9277 #60
Problem
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\prob{60}
An electron in a metal has an effective mass $m^*=0.1m_e$. If this metal is placed in a magnetic field of magnitude 1 tesla, the cyclotron resonant frequency, $\omega_c$, is most nearly

1. 930rad/s
2. 8.5E6rad/s
3. 2.8E11rad/s
4. 1.8E12rad/s
5. 7.7E20rad/s

Electromagnetism$\Rightarrow$}Cyclotron Frequency

The cyclotron frequency is given by $F=qvB = mv^2/r \Rightarrow qB=mv/r = m\omega$, where one merely equates the Lorentz Force with the centripetal force using $v=r\omega$ to relate angular velocity with velocity.

So, $\omega = qB/m$. Plug in the quantities to get choice (D).

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Comments
pgre
2013-10-15 21:20:06
Shouldn't cyclotron frequency be

$\frac{bq}{2 \pi m}$ ?
 hipparcos2018-04-05 15:24:41 The problem is asking for angular frequency.
Kabuto Yakushi
2010-09-04 13:32:01
We have to be careful here, for m we can't use the mass of an electron: $\m_e$= $\9\cdot10^{-31}$ or else we will get
$\approx$ $10^{11}$ which is wrong. We have to use the effective mass supplied by by the question of m=.1$\m_e$.

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