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<h2>Solutions of Savchenko Physics Textbook</h2>
<p class="author">
Aliaksandr Melnichenka <br/>
October 2023
</p>
</header>
− <main>
− <article>
− <h3 id="back-link"><a href="../">$\leftarrow$Back</a></h3>
−
− <h4>Statement</h4>
− <p>
− $10.2.8$
− A plane capacitor is placed in a homogeneous magnetic field od induction $B$ parallel to the plates. From point A, electrons enter perpendicularly to magnetic field direction. The tension (voltage) applied to the plates is $V$. What is the condition for which electrons pass through the capacitor?
− </p>
− <center>
− <figure>
− <img src="statement.png"
− loading="lazy" alt="10.2.8" width="300" />
− <figcaption>
− For problem 10.2.8
− </figcaption>
− </figure>
− </center>
− <h4>Solution</h4>
− <p class="TxtSolutions">
− Electrons pass through capacitor if they don't collide with plates. So, supposing a capacitor of infinite length, electron's velocity must be parallel to the plates (or its horizontal range over a plate greater than its enter's height). This is possible if electric and magnetic forces are in equilibrium (equal absolute values and opposed directions).
− </p>
− <center>
− $evB = eE$
− </center>
− <center>
− $v = \frac{E}{B}$
− </center>
− <p calss="TxtSolutions">
− As $E=\frac{V}{h}$,
− </p>
− <center>
− $\boxed{v = \frac{V}{Bh}}$
− </center>
− <p class="TxtSolutions">
− This device is known as speed's selector.
− </p>
− <p class="TxtSolutions" style="text-align: right; font-style: italic; font-size: 14;">
− BSc. Luis Daniel Fernández Quintana<br>
− Physics Department (FCNE)<br>
− Universidad de Oriente, Cuba<br>
+ <h3 id="back-link"><a href="../">$\leftarrow$Back</a></h3>
+
+ <h3> Statement </h3>
+ <p>
+ $10.2.8$
+ A plane capacitor is placed in a homogeneous magnetic field od induction $B$ parallel to the plates. From point A, electrons enter perpendicularly to magnetic field direction. The tension (voltage) applied to the plates is $V$. What is the condition for which electrons pass through the capacitor?
</p>
− </article>
− </main>
+ <center>
+ <figure>
+ <img src="statement.png"
+ loading="lazy" alt="10.2.8" width="300" />
+ <figcaption>
+ For problem 10.2.8
+ </figcaption>
+ </figure>
+ </center>
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+ <h3>Solution</h3>
+ <p>
+ Electrons pass through capacitor if they don't collide with plates. So, supposing a capacitor of infinite length, electron's velocity must be parallel to the plates (or its horizontal range over a plate greater than its enter's height). This is possible if electric and magnetic forces are in equilibrium (equal absolute values and opposed directions).
+ $$evB = eE$$
+ $$v = \frac{E}{B}$$
+ As $E=\frac{V}{h}$,
+ $$\boxed{v = \frac{V}{Bh}}$$
+ This device is known as speed's selector.
+ </p>
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+ <p style="text-align: right; font-style: italic; font-size: 14;">
+ BSc. Luis Daniel Fernández Quintana<br>
+ Physics Department (FCNE)<br>
+ Universidad de Oriente, Cuba<br>
+ </p>
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