Translated 9.1.1-9.1.5

astrosander edited Oct 14, 2024, 5:45 PM

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		+	<span><img src="../../img/book.png"></span><span>Savchenko Solutions</span>
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		+	<h3 id="back-link"><a href="../../#9.1">$\leftarrow$Back</a></h3>
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		+	<h3> Statement </h3>
		+	<p>
		+	$9.1.2.$ A charge of $1$ C moving at a speed of $1 \text{ m/s}$ in a magnetic field is acted upon by a force of $10$ N. The charge moves at an angle of $30^{\circ}$ to the direction of the magnetic field induction. What is the induction of this field?
		+	</p>
		+
		+	<h3>Solution</h3>
		+	<p>
		+	Lorentz force acting on a moving particle in a magnetic field
		+	$$ \vec{F} = q(\vec{v}\times \vec{B}) $$
		+	rewriting in scalar form we get
		+	$$ F = qvB\sin\alpha $$
		+	where $\alpha$ is the angle between $\vec{B}$ and $\vec{v}$ </p><p>
		+	Substituting the values from the condition, we get
		+	$$ \boxed{{B} = \frac{F}{qv \sin\alpha} = 20 \text{ T}} $$
		+	</p>
		+
		+	<h4>Answer</h4>
		+	<p>
		+	$${B} = \frac{F}{qv \sin\alpha} = 20 \text{ T}$$
		+	</p>
		+	<p style="text-align: right; font-style: italic; font-size: 14;">
		+	Andrei Yersh<br>
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			<meta name="author" content="Aliaksandr Melnichenka">
			<meta name="date" content="2023-10" scheme="YYYY-MM">
			<meta property="og:title" content="A charge of 1 C moving at a speed of 1 \text{ m/s} in a magnetic field is acted upon by a force of 10 N. The charge moves at an angle of 30^{\circ} to the direction of the magnetic field induction. What is the induction of this field?">
			<meta property="og:image" content="img/logo.png">
			<meta property="og:description" content="A charge of 1 C moving at a speed of 1 \text{ m/s} in a magnetic field is acted upon by a force of 10 N. The charge moves at an angle of 30^{\circ} to the direction of the magnetic field induction. What is the induction of this field?">
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			<title>A charge of 1 C moving at a speed of 1 \text{ m/s} in a magnetic field is acted upon by a force of 10 N. The charge moves at an angle of 30^{\circ} to the direction of the magnetic field induction. What is the induction of this field?</title>
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			<span><img src="../../img/book.png"></span><span>Savchenko Solutions</span>
			</div>
			</a>
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			Solutions of Savchenko Problems in Physics <br>
			<i><b>knowledge must be free</b></i>
			</p>
			</header>

			<h3 id="back-link"><a href="../../#9.1">$\leftarrow$Back</a></h3>

			<h3> Statement </h3>
			<p>
			$9.1.2.$ A charge of $1$ C moving at a speed of $1 \text{ m/s}$ in a magnetic field is acted upon by a force of $10$ N. The charge moves at an angle of $30^{\circ}$ to the direction of the magnetic field induction. What is the induction of this field?
			</p>

			<h3>Solution</h3>
			<p>
			Lorentz force acting on a moving particle in a magnetic field
			$$ \vec{F} = q(\vec{v}\times \vec{B}) $$
			rewriting in scalar form we get
			$$ F = qvB\sin\alpha $$
			where $\alpha$ is the angle between $\vec{B}$ and $\vec{v}$ </p><p>
			Substituting the values from the condition, we get
			$$ \boxed{{B} = \frac{F}{qv \sin\alpha} = 20 \text{ T}} $$
			</p>

			<h4>Answer</h4>
			<p>
			$${B} = \frac{F}{qv \sin\alpha} = 20 \text{ T}$$
			</p>
			<p style="text-align: right; font-style: italic; font-size: 14;">
			Andrei Yersh<br>
			</p>


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