Правка раздела «Answer»
en/10.1.2.md
+1 −1
| ### Statement | |||
| $10.1.2.$ [Insert the problem statement] | |||
| ### Solution | |||
| Inside the magnetic field, the electron moves following a circular trajectory with constant speed. | |||
| From Newton Second Law: | |||
| $\frac{m_e v^2}{R} = e |\vec{v} \times \vec{B}|$ | |||
| but $\vec{v}$ is perpendicular to $\vec{B}$, so | |||
| $\frac{m_e v^2}{R} = e v B$ | |||
| $R = \frac{m_e v}{eB}$ (1) | |||
| Applying Energy Conservation Law: | |||
| $\frac{m_e v^2}{2} = e U$ | |||
| $v = \sqrt{\frac{2eU}{m_e}}$ (2) | |||
| Substituting (2) into (1) | |||
| $R = \frac{1}{B}\sqrt{\frac{2m_e U}{e}} = 0.68 \rm{m}$ | |||
| @@ -27,4 +27,4 @@Solution | |||
| #### Answer | |||
| − | [Insert a concise answer or boxed result] | ||
| + | $R = \frac{1}{B}\sqrt{\frac{2m_e U}{e}} = 0.68 \rm{m}$ | ||
| ### Statement | ### Statement | ||
| $10.1.2.$ [Insert the problem statement] | $10.1.2.$ [Insert the problem statement] | ||
| ### Solution | ### Solution | ||
| Inside the magnetic field, the electron moves following a circular trajectory with constant speed. | Inside the magnetic field, the electron moves following a circular trajectory with constant speed. | ||
| From Newton Second Law: | From Newton Second Law: | ||
| $\frac{m_e v^2}{R} = e |\vec{v} \times \vec{B}|$ | $\frac{m_e v^2}{R} = e |\vec{v} \times \vec{B}|$ | ||
| but $\vec{v}$ is perpendicular to $\vec{B}$, so | but $\vec{v}$ is perpendicular to $\vec{B}$, so | ||
| $\frac{m_e v^2}{R} = e v B$ | $\frac{m_e v^2}{R} = e v B$ | ||
| $R = \frac{m_e v}{eB}$ (1) | $R = \frac{m_e v}{eB}$ (1) | ||
| Applying Energy Conservation Law: | Applying Energy Conservation Law: | ||
| $\frac{m_e v^2}{2} = e U$ | $\frac{m_e v^2}{2} = e U$ | ||
| $v = \sqrt{\frac{2eU}{m_e}}$ (2) | $v = \sqrt{\frac{2eU}{m_e}}$ (2) | ||
| Substituting (2) into (1) | Substituting (2) into (1) | ||
| $R = \frac{1}{B}\sqrt{\frac{2m_e U}{e}} = 0.68 \rm{m}$ | $R = \frac{1}{B}\sqrt{\frac{2m_e U}{e}} = 0.68 \rm{m}$ | ||
| @@ -27,4 +27,4 @@Solution | |||
| #### Answer | #### Answer | ||
| [Insert a concise answer or boxed result] | $R = \frac{1}{B}\sqrt{\frac{2m_e U}{e}} = 0.68 \rm{m}$ | ||