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$$
\begin{array}{l}{\text { A particle with charge } 6.40 \times 10^{-19} \mathrm{C} \text { travels in a }} \\ {\text { circular orbit with radius } 4.68 \mathrm{mm} \text { due to the force exerted on it by }} \\ {\text { a magnetic field with magnitude } 1.65 \mathrm{T} \text { and perpendicular to the }} \\ {\text { orbit. (a) What is the magnitude of the linear momentum } \vec{p} \text { of the }} \\ {\text { particle? ( b) What is the magnitude of the angular momentum } \vec{L} \text { of }} \\ {\text { the particle? }}\end{array}
$$

$$
P=m v
$$$$
, \quad L=R p
$$

$$
|q| V B=m \frac{V^{2}}{R} \leftarrow
$$

(a) $$
P=m v=m\left(\frac{R q B}{m}\right)
$$$$
=R q B=
$$$$
\left(4.68 * 10^{-3}\right) *
$$$$
\left(6.4 * 10^{-14}\right)(1.65)
$$

\(∴ P=4.94 * 10^{-21} \mathrm{kg} \cdot \mathrm{m} / \mathrm{s} \)

(b) $$
L=R_{p}
$$$$
=R^{2} q B=\left(4.68 * 16^{-3}\right)^{2}\left(64*10^{-19}\right)(1.65)
$$

\(∴ L=2.31 * 10^{-23} \mathrm{kg} \cdot \mathrm{m}^ 2 / \mathrm{s} \)

OR

$$
L=\left(4.68*10^{-3}\right)\left(4.94 * 10^{-21}\right)=2.31*10^{-23} \mathrm{kg} \cdot \mathrm{m}^{2} / s
$$

$$
\begin{array}{l}{\text { A physicist wishes to produce electromagnetic waves of }} \\ {\text { frequency } 3.0 \text { THz }\left(1 \mathrm{THz}=1 \text { terahertz }=10^{12} \mathrm{Hz} \text { using a }\right.} \\ {\text { magnetron (see Example } 27.3 ) \text { . (a) What magnetic field would be }} \\ {\text { required? Compare this field with the strongest constant magnetic }} \\ {\text { fields yet produced on earth, about } 45 \mathrm{T} \text { . (b) Would there be any }} \\ {\text { advantage to using protons instead of electrons in the magnetron? }} \\ {\text { Why or why not? }}\end{array}
$$

$$
B=\frac{m 2 \pi f}{| q|}
$$

$$
q=-e \quad \longrightarrow \quad m=9 \cdot 11 \quad * 10^{-31} \mathrm{kg}
$$

$$
q=+e \rightarrow \quad m=1.67*10^{-27} \mathrm{kg}
$$

(a) $$
B=\frac{m 2 \pi f}{| q |}=
$$$$
\frac{9.11 * 10^{-31}*2 \pi * 3*10^{12}}{1.6 * 10^{-19}}
$$

\(∴ \quad B=107 \mathrm{T} \)

$$
\frac{107}{45}=2.4
$$

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