<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
<meta name="description" content="Particles with mass m and charge q enter in a capacitor of length l under an angle lpha respect to plate's plane and exit forming an angle eta. Find the initial kinetic energy of particles, if the field intensity inside the capacitor is E.">
<meta property="og:title" content="Particles with mass m and charge q enter in a capacitor of length l under an angle lpha respect to plate's plane and exit forming an angle eta. Find the initial kinetic energy of particles, if the field intensity inside the capacitor is E.">
<meta property="og:image" content="img/logo.png">
@@ -14,9 +14,9 @@
<meta property="og:description" content="Particles with mass m and charge q enter in a capacitor of length l under an angle lpha respect to plate's plane and exit forming an angle eta. Find the initial kinetic energy of particles, if the field intensity inside the capacitor is E.">
<title>Particles with mass m and charge q enter in a capacitor of length l under an angle lpha respect to plate's plane and exit forming an angle eta. Find the initial kinetic energy of particles, if the field intensity inside the capacitor is E.</title>
Particles with mass $m$ and charge $q$ enter in a capacitor of length $l$ under an angle $\alpha$ respect to plate's plane and exit forming an angle $\beta$. Find the initial kinetic energy of particles, if the field intensity inside the capacitor is $E$.
</p>
<center>
<figure>
<img src="statement.png"
loading="lazy" alt="7.1.6" width="300" />
<figcaption>
For problem 7.1.6
</figcaption>
</figure>
</center>
<h3>Solution</h3>
<p>
Initial kinetic energy is defined as
$$K_0 = \frac{mv_0^2}{2} \;(1)$$
If we apply Newton's Second Law, acceleration can be defined,
$$a_y = \frac{qE}{m} \;(2)$$
As there are no forces in horizontal direction, the component of velocity in that direction is unaffected
$$v_0\cos{\alpha}=v_1\cos{\beta} \;(3)$$
For the horizontal path until exit's point
$$l = v_0\cos{\alpha}~t_v \;(4)$$
The time expended by particles during the path through the capacitor can be found from acceleration definition
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
<meta name="description" content="Particles with mass m and charge q enter in a capacitor of length l under an angle lpha respect to plate's plane and exit forming an angle eta. Find the initial kinetic energy of particles, if the field intensity inside the capacitor is E.">
<meta name="description" content="Particles with mass m and charge q enter in a capacitor of length l under an angle lpha respect to plate's plane and exit forming an angle eta. Find the initial kinetic energy of particles, if the field intensity inside the capacitor is E.">
<meta property="og:title" content="Particles with mass m and charge q enter in a capacitor of length l under an angle lpha respect to plate's plane and exit forming an angle eta. Find the initial kinetic energy of particles, if the field intensity inside the capacitor is E.">
<meta property="og:title" content="Particles with mass m and charge q enter in a capacitor of length l under an angle lpha respect to plate's plane and exit forming an angle eta. Find the initial kinetic energy of particles, if the field intensity inside the capacitor is E.">
<meta property="og:image" content="img/logo.png">
<meta property="og:image" content="img/logo.png">
@@ -14,9 +14,9 @@
<meta property="og:description" content="Particles with mass m and charge q enter in a capacitor of length l under an angle lpha respect to plate's plane and exit forming an angle eta. Find the initial kinetic energy of particles, if the field intensity inside the capacitor is E.">
<meta property="og:description" content="Particles with mass m and charge q enter in a capacitor of length l under an angle lpha respect to plate's plane and exit forming an angle eta. Find the initial kinetic energy of particles, if the field intensity inside the capacitor is E.">
<title>Particles with mass m and charge q enter in a capacitor of length l under an angle lpha respect to plate's plane and exit forming an angle eta. Find the initial kinetic energy of particles, if the field intensity inside the capacitor is E.</title>
<title>Particles with mass m and charge q enter in a capacitor of length l under an angle lpha respect to plate's plane and exit forming an angle eta. Find the initial kinetic energy of particles, if the field intensity inside the capacitor is E.</title>
Particles with mass $m$ and charge $q$ enter in a capacitor of length $l$ under an angle $\alpha$ respect to plate's plane and exit forming an angle $\beta$. Find the initial kinetic energy of particles, if the field intensity inside the capacitor is $E$.
Particles with mass $m$ and charge $q$ enter in a capacitor of length $l$ under an angle $\alpha$ respect to plate's plane and exit forming an angle $\beta$. Find the initial kinetic energy of particles, if the field intensity inside the capacitor is $E$.
</p>
</p>
<center>
<center>
<figure>
<figure>
<img src="statement.png"
<img src="statement.png"
loading="lazy" alt="7.1.6" width="300" />
loading="lazy" alt="7.1.6" width="300" />
<figcaption>
<figcaption>
For problem 7.1.6
For problem 7.1.6
</figcaption>
</figcaption>
</figure>
</figure>
</center>
</center>
<h3>Solution</h3>
<h3>Solution</h3>
<p>
<p>
Initial kinetic energy is defined as
Initial kinetic energy is defined as
$$K_0 = \frac{mv_0^2}{2} \;(1)$$
$$K_0 = \frac{mv_0^2}{2} \;(1)$$
If we apply Newton's Second Law, acceleration can be defined,
If we apply Newton's Second Law, acceleration can be defined,
$$a_y = \frac{qE}{m} \;(2)$$
$$a_y = \frac{qE}{m} \;(2)$$
As there are no forces in horizontal direction, the component of velocity in that direction is unaffected
As there are no forces in horizontal direction, the component of velocity in that direction is unaffected
$$v_0\cos{\alpha}=v_1\cos{\beta} \;(3)$$
$$v_0\cos{\alpha}=v_1\cos{\beta} \;(3)$$
For the horizontal path until exit's point
For the horizontal path until exit's point
$$l = v_0\cos{\alpha}~t_v \;(4)$$
$$l = v_0\cos{\alpha}~t_v \;(4)$$
The time expended by particles during the path through the capacitor can be found from acceleration definition
The time expended by particles during the path through the capacitor can be found from acceleration definition
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
