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<title>Two infinite plates of thickness h are charged uniformly in volume and stacked together. The bulk charge density of the first plate is \rho, and the second plate -\rho. Find the maximum electric field intensity.</title>
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<title>Two infinite plates of thickness h are charged uniformly in volume and stacked together. The bulk charge density of the first plate is \rho , and the second plate -\rho . Find the maximum electric field intensity.</title>
$6.2.11.$ Two infinite plates of thickness h are charged uniformly in volume and stacked together. The bulk charge density of the first plate is $\rho$, and the second plate -$\rho$. Find the maximum electric field intensity.
</p>
<center>
<figure>
<img src="statement.png"
loading="lazy" width="350" />
<figcaption>
For problem $6.2.11$
</figcaption>
</figure>
</center>
<h3>Solution</h3>
<p>
The absolute value of the total charge of each plate is $\rho S h$, where $S$ is the surface of the plate's biggest faces. So, applying Gauss Law, the absolute value of electric field intensity generated by this plate is:
</p>
<p>
$$E = \frac{\rho h}{\varepsilon_0}$$
</p>
<p>
Then, the field generated by one of these biggest faces of the plate is half of $E$. Let's consider now a point inside of one of these infinite plates (for example, in the upper one). The resultant field over this point is the vectorial sum of the fields generated by a lower negative plate, a plate with thickness $x$ (where $x$ is the distance from the boundary between plates and the point), and a upper plate with thickness $h-x$:
<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">
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<meta name="description" content="Two infinite plates of thickness h are charged uniformly in volume and stacked together. The bulk charge density of the first plate is \rho, and the second plate -\rho. Find the maximum electric field intensity.">
<meta name="description" content="Two infinite plates of thickness h are charged uniformly in volume and stacked together. The bulk charge density of the first plate is \rho, and the second plate -\rho. Find the maximum electric field intensity.">
<meta property="og:title" content="Two infinite plates of thickness h are charged uniformly in volume and stacked together. The bulk charge density of the first plate is \rho, and the second plate -\rho. Find the maximum electric field intensity.">
<meta property="og:title" content="Two infinite plates of thickness h are charged uniformly in volume and stacked together. The bulk charge density of the first plate is \rho, and the second plate -\rho. Find the maximum electric field intensity.">
<meta property="og:image" content="img/logo.png">
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<meta property="og:description" content="Two infinite plates of thickness h are charged uniformly in volume and stacked together. The bulk charge density of the first plate is \rho, and the second plate -\rho. Find the maximum electric field intensity.">
<meta property="og:description" content="Two infinite plates of thickness h are charged uniformly in volume and stacked together. The bulk charge density of the first plate is \rho, and the second plate -\rho. Find the maximum electric field intensity.">
<title>Two infinite plates of thickness h are charged uniformly in volume and stacked together. The bulk charge density of the first plate is \rho, and the second plate -\rho. Find the maximum electric field intensity.</title>
<title>Two infinite plates of thickness h are charged uniformly in volume and stacked together. The bulk charge density of the first plate is \rho , and the second plate -\rho . Find the maximum electric field intensity.</title>
$6.2.11.$ Two infinite plates of thickness h are charged uniformly in volume and stacked together. The bulk charge density of the first plate is $\rho$, and the second plate -$\rho$. Find the maximum electric field intensity.
$6.2.11.$ Two infinite plates of thickness h are charged uniformly in volume and stacked together. The bulk charge density of the first plate is $\rho$, and the second plate -$\rho$. Find the maximum electric field intensity.
</p>
</p>
<center>
<center>
<figure>
<figure>
<img src="statement.png"
<img src="statement.png"
loading="lazy" width="350" />
loading="lazy" width="350" />
<figcaption>
<figcaption>
For problem $6.2.11$
For problem $6.2.11$
</figcaption>
</figcaption>
</figure>
</figure>
</center>
</center>
<h3>Solution</h3>
<h3>Solution</h3>
<p>
<p>
The absolute value of the total charge of each plate is $\rho S h$, where $S$ is the surface of the plate's biggest faces. So, applying Gauss Law, the absolute value of electric field intensity generated by this plate is:
The absolute value of the total charge of each plate is $\rho S h$, where $S$ is the surface of the plate's biggest faces. So, applying Gauss Law, the absolute value of electric field intensity generated by this plate is:
</p>
</p>
<p>
<p>
$$E = \frac{\rho h}{\varepsilon_0}$$
$$E = \frac{\rho h}{\varepsilon_0}$$
</p>
</p>
<p>
<p>
Then, the field generated by one of these biggest faces of the plate is half of $E$. Let's consider now a point inside of one of these infinite plates (for example, in the upper one). The resultant field over this point is the vectorial sum of the fields generated by a lower negative plate, a plate with thickness $x$ (where $x$ is the distance from the boundary between plates and the point), and a upper plate with thickness $h-x$:
Then, the field generated by one of these biggest faces of the plate is half of $E$. Let's consider now a point inside of one of these infinite plates (for example, in the upper one). The resultant field over this point is the vectorial sum of the fields generated by a lower negative plate, a plate with thickness $x$ (where $x$ is the distance from the boundary between plates and the point), and a upper plate with thickness $h-x$:
<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>
