GR 8677927796770177 | # Login | Register

GR9277 #60
Problem
 GREPhysics.NET Official Solution Alternate Solutions
\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

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).

Alternate Solutions
 There are no Alternate Solutions for this problem. Be the first to post one!
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$\m_e$.

LaTeX syntax supported through dollar sign wrappers $, ex.,$\alpha^2_0$produces $\alpha^2_0$. type this... to get...$\int_0^\infty$$\int_0^\infty$$\partial$$\partial$$\Rightarrow$$\Rightarrow$$\ddot{x},\dot{x}$$\ddot{x},\dot{x}$$\sqrt{z}$$\sqrt{z}$$\langle my \rangle$$\langle my \rangle$$\left( abacadabra \right)_{me}$$\left( abacadabra \right)_{me}$$\vec{E}$$\vec{E}$$\frac{a}{b}\$ $\frac{a}{b}$