Правка разделов «Solution», «Answer»

giorgiotinashvili правка от 18 мая 2025 г., 19:46

правка #14448 предыдущая #14446 ← раньше позже →

en/10.1.1.md +2 −2

			### Statement

			$10.1.1.$ 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:
		@@ -20,10 +20,10 @@Solution
			\[
			v= \sqrt{\frac{2qV}{m}} \approx 1.96 \times 10^6 \, \mathrm{m/s}
			\]
		−	\[r \approx 0.2\~~,\mathrm~~{m} \]
		+	\[r \approx 0.2\mathrm{m} \]

			#### Answer

			\[
		−	\boxed {\, r \approx 0.2m \,}
		+	\boxed { r \approx 0.2m }
			\]

	### Statement		### Statement

	$10.1.1.$ A proton accelerated by a voltage of 20 kV enters a uniform magnetic field		$10.1.1.$ 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		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.		circle along which the proton moves in the magnetic field.


	### Solution		### Solution
	Using:		Using:

	\[		\[
	\frac{1}{2}mv^2 = q, \hspace{0.5cm} r=\frac{mv}{qB}		\frac{1}{2}mv^2 = q, \hspace{0.5cm} r=\frac{mv}{qB}
	\]		\]


	With:		With:
	\[q=1.6 \times 10^{-19}C, \hspace{0.5cm} m=1.67 \times 10^{-27}kg, \hspace{0.5cm} V=20kV, \hspace{0.5cm} B=0.10T\]		\[q=1.6 \times 10^{-19}C, \hspace{0.5cm} m=1.67 \times 10^{-27}kg, \hspace{0.5cm} V=20kV, \hspace{0.5cm} B=0.10T\]

	We get:		We get:
	@@ -20,10 +20,10 @@Solution
	\[		\[
	v= \sqrt{\frac{2qV}{m}} \approx 1.96 \times 10^6 \, \mathrm{m/s}		v= \sqrt{\frac{2qV}{m}} \approx 1.96 \times 10^6 \, \mathrm{m/s}
	\]		\]
	\[r \approx 0.2\~~,\mathrm~~{m} \]		\[r \approx 0.2\mathrm{m} \]

	#### Answer		#### Answer

	\[		\[
	\boxed {\, r \approx 0.2m \,}		\boxed { r \approx 0.2m }
	\]		\]