Edits to “Statement”, “Solution”, “Answer”
en/10.1.1.md
+19 −3
| @@ -1,13 +1,29 @@ | |||
| ### Statement | |||
| − | $10.1.1.$ | ||
| + | $10.1.1.$ A proton accelerated by a voltage of 20 kV enters a uniform magnetic field | ||
| + | with an induction of 0.1 T perpendicular to the field. Find the radius of the | ||
| + | circle along which the proton moves in the magnetic field. | ||
| + | |||
| ### Solution | |||
| + | Using: | ||
| − |  | ||
| + | \[ | ||
| + | \frac{1}{2}mv^2 = q, \hspace{0.5cm} r=\frac{mv}{qB} | ||
| + | \] | ||
| + | With: | ||
| + | \[q=1.6 \times 10^{-19}C, \hspace{0.5cm} m=1.67 \times 10^{-27}kg, \hspace{0.5cm} V=20kV, \hspace{0.5cm} B=0.10T\] | ||
| + | We get: | ||
| + | \[ | ||
| + | v= \sqrt{\frac{2qV}{m}} \approx 1.96 \times 10^6 \, \mathrm{m/s} | ||
| + | \] | ||
| + | \[r \approx 0.2\,\mathrm{m} \] | ||
| + | |||
| #### Answer | |||
| − | [Insert a concise answer or boxed result] | ||
| + | \[ | ||
| + | \boxed {\, r \approx 0.2m \,} | ||
| + | \] | ||
| @@ -1,13 +1,29 @@ | |||
| ### Statement | ### Statement | ||
| $10.1.1.$ |
$10.1.1.$ A proton accelerated by a voltage of 20 kV enters a uniform magnetic field | ||
| with an induction of 0.1 T perpendicular to the field. Find the radius of the | |||
| circle along which the proton moves in the magnetic field. | |||
| ### Solution | ### Solution | ||
| Using: | |||
|  | \[ | ||
| \frac{1}{2}mv^2 = q, \hspace{0.5cm} r=\frac{mv}{qB} | |||
| \] | |||
| With: | |||
| \[q=1.6 \times 10^{-19}C, \hspace{0.5cm} m=1.67 \times 10^{-27}kg, \hspace{0.5cm} V=20kV, \hspace{0.5cm} B=0.10T\] | |||
| We get: | |||
| \[ | |||
| v= \sqrt{\frac{2qV}{m}} \approx 1.96 \times 10^6 \, \mathrm{m/s} | |||
| \] | |||
| \[r \approx 0.2\,\mathrm{m} \] | |||
| #### Answer | #### Answer | ||
| [Insert a concise answer or boxed result] | \[ | ||
| \boxed {\, r \approx 0.2m \,} | |||
| \] | |||