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<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?
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<img src="statement.png"
loading="lazy" alt="10.2.8" width="300" />
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For problem 10.2.8
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<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).
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$evB = eE$
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$v = \frac{E}{B}$
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As $E=\frac{V}{h}$,
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$\boxed{v = \frac{V}{Bh}}$
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<p class="TxtSolutions">
This device is known as speed's selector.
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<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>
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