physics-class-12-unit-01-chapter-04-applications-of-gausss-law-l-4-4-js-lo4fq-5m

<h3 id="success-stylefont-size25px-applications-of-gausss-law-l-4-success-1"><Success style="font-size:25px;"> Applications-Of-Gausss-Law L-4 </Success></h3>
<h3 id="primary-stylefont-size24pxgausss-lawprimary"><primary style="font-size:24px;">Gauss’s Law</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$\begin{aligned}\Phi=\frac{q_1+q_2}{\epsilon_0}\end{aligned}$</p>
</li>
<li>
<p>$\Phi=\frac{\sum q_i}{\epsilon_0}$</p>
</li>
<li>
<p>Flux: $\vec{E} \cdot d \vec{s}$</p>
</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/ae0ce371-0c81-45fa-d2fe-4f61daf78300/public"  width="70%" >

</main>
<hr>
<footer style = "font-size: 18px">  $\rightarrow$ Electrostatics $\rightarrow$ <span style = "color:blue"> Gauss's Law </span> $\rightarrow$ Integral Form $\rightarrow$ Electric Field </footer>

<h3 id="success-stylefont-size25px-applications-of-gausss-law-l-4-success-2"><Success style="font-size:25px;"> Applications-Of-Gausss-Law L-4 </Success></h3>
<h3 id="primary-stylefont-size24px-integral-formprimary"><primary style="font-size:24px;"> Integral Form</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>$\bar{\Phi}=\oint \vec{E} \cdot d \vec{A}=\frac{Q_{\text {enc }}}{\epsilon_0}$</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:450px;'>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/c98a7558-8034-490b-0413-ebdaea389400/public"  width="70%" >

</main>
<hr>
<footer style = "font-size: 18px"> Electrostatics $\rightarrow$ Gauss's Law $\rightarrow$ <span style = "color:blue"> Integral Form </span> $\rightarrow$ Electric Field $\rightarrow$ Electric Field due to Sphere </footer>

<h3 id="success-stylefont-size25px-applications-of-gausss-law-l-4-success-3"><Success style="font-size:25px;"> Applications-Of-Gausss-Law L-4 </Success></h3>
<h3 id="primary-stylefont-size24pxelectric-fieldprimary"><primary style="font-size:24px;">Electric Field</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>Excess charge : Q</li>
<li>at the surface of the conductor</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:450px;'>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/99323627-04c9-4a84-b036-e3567ba3ab00/public"  width="100%" >

</main>
<hr>
<footer style = "font-size: 18px"> Gauss's Law $\rightarrow$ Integral Form $\rightarrow$ <span style = "color:blue"> Electric Field </span> $\rightarrow$ Electric Field due to Sphere $\rightarrow$ Electric Field due to Sphere </footer>

<h3 id="success-stylefont-size25px-applications-of-gausss-law-l-4-success-4"><Success style="font-size:25px;"> Applications-Of-Gausss-Law L-4 </Success></h3>
<h3 id="primary-stylefont-size24pxelectric-field-due-to-sphereprimary"><primary style="font-size:24px;">Electric Field due to Sphere</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>Field produce by a charged conducting sphere</li>
</ul>
<ul>
<li>$\sigma=\frac{Q}{4 \pi R^2}$</li>
</ul>
<ul>
<li>$|\vec{E}|$ depends only on r</li>
<li>$\vec{E}$ is along $\hat r$</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/afcb69d0-6e8b-41e2-4b11-fb01e2c0ba00/public"  width="70%" >

</main>
<hr>
<footer style = "font-size: 18px"> Integral Form $\rightarrow$ Electric Field $\rightarrow$ <span style = "color:blue"> Electric Field due to Sphere </span> $\rightarrow$ Electric Field due to Sphere $\rightarrow$ Electric Field due to Sphere </footer>

<h3 id="success-stylefont-size25px-applications-of-gausss-law-l-4-success-5"><Success style="font-size:25px;"> Applications-Of-Gausss-Law L-4 </Success></h3>
<h3 id="primary-stylefont-size24pxelectric-field-due-to-sphereprimary-1"><primary style="font-size:24px;">Electric Field due to Sphere</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$\oint \vec{E} \cdot d \vec{A}=\frac{Q_{\text {enc }}}{\epsilon_0}$</p>
</li>
<li>
<p>$\oint {E} \ d {A}=\frac{Q_{\text {enc }}}{\epsilon_0}$</p>
</li>
<li>
<p>${E} \oint  \ d {A}=\frac{Q_{\text {enc }}}{\epsilon_0}$</p>
</li>
<li>
<p>E. $4 \pi r^2=\frac{Q_\text { enc }}{\epsilon_0} = \frac{Q}{\epsilon_0}$</p>
</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/b542d6ec-b4f1-4e0f-5e60-c86a1901bd00/public"  width="70%" >

</main>
<hr>
<footer style = "font-size: 18px"> Electric Field $\rightarrow$ Electric Field due to Sphere $\rightarrow$ <span style = "color:blue"> Electric Field due to Sphere </span> $\rightarrow$ Electric Field due to Sphere
 $\rightarrow$ Field due to a Line Charge </footer>

<h3 id="success-stylefont-size25px-applications-of-gausss-law-l-4-success-6"><Success style="font-size:25px;"> Applications-Of-Gausss-Law L-4 </Success></h3>
<h3 id="primary-stylefont-size24pxelectric-field-due-to-sphereprimary-2"><primary style="font-size:24px;">Electric Field due to Sphere</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$ E=\frac{Q}{4 \pi \epsilon_0 r^2}$</p>
</li>
<li>
<p>$\vec{E}=\frac{Q}{4 \pi \epsilon_0 r^2} \hat{r}$</p>
</li>
<li>
<p>$\sigma=\frac{Q}{4 \pi R^2}$</p>
</li>
<li>
<p>r=R</p>
</li>
<li>
<p>$\vec{E}=\frac{Q}{4 \pi \epsilon_0 R^2} \hat{r}  =\frac{\sigma}{\epsilon_0} \hat{r}$</p>
</li>
<li>
<p>$=\frac{\sigma}{\epsilon_0} \hat{n}$</p>
</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/4b308325-71b2-4038-ada1-5cc8b3168700/public"  width="70%" >

</main>
<hr>
<footer style = "font-size: 18px"> Electric Field due to Sphere $\rightarrow$ Electric Field due to Sphere $\rightarrow$ <span style = "color:blue"> Electric Field due to Sphere </span> $\rightarrow$ Field due to a Line Charge $\rightarrow$ Field due to a Line Charge </footer>

<h3 id="success-stylefont-size25px-applications-of-gausss-law-l-4-success-7"><Success style="font-size:25px;"> Applications-Of-Gausss-Law L-4 </Success></h3>
<h3 id="primary-stylefont-size24pxfield-due-to-a-line-chargeprimary"><primary style="font-size:24px;">Field due to a Line Charge</primary></h3>
<hr>
<main> 
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>Field due to a line charge density(infinitely long)</li>
<li>Charge per unit length:</li>
</ul>
<ul>
<li>
<p>$ d E=\frac{\lambda d z}{4 \pi \epsilon_0 s^2} \cos \theta$</p>
</li>
<li>
<p>$s^2=r^2+z^2$</p>
</li>
<li>
<p>dE= $\frac{\lambda d z}{4 \pi \epsilon_0\left(r^2+z^2\right)} \frac{r}{\sqrt{r^2+z^2}}$</p>
</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/cfe8f008-023f-40b2-6987-f22264fd6e00/public"  width="70%" >

</main>
<hr>
<footer style = "font-size: 18px"> Electric Field due to Sphere $\rightarrow$ Electric Field due to Sphere $\rightarrow$ <span style = "color:blue"> Field due to a Line Charge </span> $\rightarrow$ Field due to a Line Charge $\rightarrow$ Field due to a Line Charge </footer>

<h3 id="success-stylefont-size25px-applications-of-gausss-law-l-4-success-8"><Success style="font-size:25px;"> Applications-Of-Gausss-Law L-4 </Success></h3>
<h3 id="primary-stylefont-size24pxfield-due-to-a--line-chargeprimary"><primary style="font-size:24px;">Field due to a  Line Charge</primary></h3>
<hr>
<main> 
<div style='float: left; width:100%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$ d E=\frac{\lambda dzr}{4 \pi \epsilon_0\left(r^2+z^2\right)^{3 / 2}}$</p>
</li>
<li>
<p>$E=\frac{\lambda r}{4 \pi \epsilon_0} \int_{-\infty}^{+\infty} \frac{d z}{\left(r^2+z^2\right)^{3 / 2}}$</p>
</li>
<li>
<p>$z=r \tan \phi$</p>
</li>
<li>
<p>$d z=r \sec ^2 \phi d \phi$</p>
</li>
<li>
<p>$r^2+z^2=r^2+r^2 \tan ^2 \phi=r^2 \operatorname{sec}^2 \phi$</p>
</li>
</ul>
</div>
<div style='float: right; width:0%; max-width:400px;'>
<p><img alt="image" src="https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/physics-class-12-unit-01-chapter-04-applications-of-gausss-law-l-4_4-js_lo4fq-5m-00009.jpg"></p>
</main>
<hr>
<footer style = "font-size: 18px"> Electric Field due to Sphere $\rightarrow$ Field due to a Line Charge $\rightarrow$ <span style = "color:blue"> Field due to a Line Charge </span> $\rightarrow$ Field due to a Line Charge $\rightarrow$ Field due to a Line Charge </footer>

<h3 id="success-stylefont-size25px-applications-of-gausss-law-l-4-success-9"><Success style="font-size:25px;"> Applications-Of-Gausss-Law L-4 </Success></h3>
<h3 id="primary-stylefont-size24pxfield-due-to-a-line-chargeprimary-1"><primary style="font-size:24px;">Field due to a Line Charge</primary></h3>
<hr>
<main> 
<div style='float: left; width:100%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$ E =\frac{\lambda r}{4 \pi \epsilon_0} \int_{-\pi / 2}^{+\pi / 2} \frac{r \sec ^2 \phi d \phi}{r^3 \sec ^3 \phi}$</p>
</li>
<li>
<p>$=\frac{\lambda}{4 \pi \epsilon_0 r} \int_{-\pi / 2}^{\pi / 2} \cos \phi d \phi$</p>
</li>
<li>
<p>$=\frac{\lambda}{4 \pi \epsilon_0 r} \sin |_{-\pi / 2}^{\pi / 2}$</p>
</li>
<li>
<p>$E  =\frac{\lambda}{2 \pi \epsilon_0 r}$</p>
</li>
</ul>
</div>
<div style='float: right; width:0%; max-width:400px;'>
<p><img alt="image" src="https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/physics-class-12-unit-01-chapter-04-applications-of-gausss-law-l-4_4-js_lo4fq-5m-012.jpg"></p>
</main>
<hr>
<footer style = "font-size: 18px"> Field due to a Line Charge $\rightarrow$ Field due to a Line Charge $\rightarrow$ <span style = "color:blue"> Field due to a Line Charge </span> $\rightarrow$ Field due to a Line Charge $\rightarrow$ Gaussian Surface </footer>

<h3 id="success-stylefont-size25px-applications-of-gausss-law-l-4-success-10"><Success style="font-size:25px;"> Applications-Of-Gausss-Law L-4 </Success></h3>
<h3 id="primary-stylefont-size24pxfield-due-to-a-line-chargeprimary-2"><primary style="font-size:24px;">Field due to a Line Charge</primary></h3>
<hr>
<main> 
<div style='float: left; width:50%;text-align:left;font-size:30px;'>




<ul>
<li>$\vec{E}=\frac{\lambda \hat{r}}{2 \pi \epsilon_r}$</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:300px;'>

<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/d82c0e80-5351-467c-9856-57012c8cc200/public"  width="70%" >

</main>
<hr>
<footer style = "font-size: 18px"> Field due to a Line Charge $\rightarrow$ Field due to a Line Charge $\rightarrow$ <span style = "color:blue"> Field due to a Line Charge </span> $\rightarrow$ Gaussian Surface $\rightarrow$ Gaussian Surface </footer>

<h3 id="success-stylefont-size25px-applications-of-gausss-law-l-4-success-11"><Success style="font-size:25px;"> Applications-Of-Gausss-Law L-4 </Success></h3>
<h3 id="primary-stylefont-size24pxgaussian-surfaceprimary"><primary style="font-size:24px;">Gaussian Surface</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>E $ \cdot 2 \pi r \cdot l=\frac{Q_\text{enc}}{\epsilon_0}=\frac{\lambda l}{\epsilon_0}$</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:450px;'>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/9401f141-f95d-442c-e4dc-b3bdf118b200/public"  width="100%" >

</main>
<hr>
<footer style = "font-size: 18px"> Field due to a Line Charge $\rightarrow$ Field due to a Line Charge $\rightarrow$ <span style = "color:blue"> Gaussian Surface </span> $\rightarrow$ Gaussian Surface $\rightarrow$ Field due to a Infinite Sheet </footer>

<h3 id="success-stylefont-size25px-applications-of-gausss-law-l-4-success-12"><Success style="font-size:25px;"> Applications-Of-Gausss-Law L-4 </Success></h3>
<h3 id="primary-stylefont-size24pxgaussian-surfaceprimary-1"><primary style="font-size:24px;">Gaussian Surface</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>$\vec{E}=\frac{\lambda}{2 \pi \epsilon_0 r} \hat{r}$</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/df63097f-c487-464c-659e-72eb61f6f600/public"  width="70%" >

</main>
<hr>
<footer style = "font-size: 18px"> Field due to a Line Charge $\rightarrow$ Gaussian Surface $\rightarrow$ <span style = "color:blue"> Gaussian Surface </span> $\rightarrow$ Field due to a Infinite Sheet $\rightarrow$ Gaussian Surface </footer>

<h3 id="success-stylefont-size25px-applications-of-gausss-law-l-4-success-13"><Success style="font-size:25px;"> Applications-Of-Gausss-Law L-4 </Success></h3>
<h3 id="primary-stylefont-size24pxfield-due-to-a-infinite-sheetprimary"><primary style="font-size:24px;">Field due to a Infinite Sheet</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>Field due to an infinite sheet of surfaces charge $\sigma$</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:450px;'>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/ffc0e4d7-1c87-4a95-e582-f57dd928e300/public"  width="100%" >

</main>
<hr>
<footer style = "font-size: 18px"> Gaussian Surface $\rightarrow$ Gaussian Surface $\rightarrow$ <span style = "color:blue"> Field due to a Infinite Sheet </span> $\rightarrow$ Gaussian Surface $\rightarrow$ Gaussian Surface </footer>

<h3 id="success-stylefont-size25px-applications-of-gausss-law-l-4-success-14"><Success style="font-size:25px;"> Applications-Of-Gausss-Law L-4 </Success></h3>
<h3 id="primary-stylefont-size24pxgaussian-surfaceprimary-2"><primary style="font-size:24px;">Gaussian Surface</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>Total electric flux = E.2A</li>
<li>Total charge enclosed = $\sigma$ .A</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:450px;'>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/093520e6-d7f8-40b8-6eff-f2819ef5a200/public"  width="100%" >

</main>
<hr>
<footer style = "font-size: 18px"> Gaussian Surface $\rightarrow$ Field due to a Infinite Sheet $\rightarrow$ <span style = "color:blue"> Gaussian Surface </span> $\rightarrow$ Gaussian Surface $\rightarrow$ Thin Conducting Plate </footer>

<h3 id="success-stylefont-size25px-applications-of-gausss-law-l-4-success-15"><Success style="font-size:25px;"> Applications-Of-Gausss-Law L-4 </Success></h3>
<h3 id="primary-stylefont-size24pxgaussian-surfaceprimary-3"><primary style="font-size:24px;">Gaussian Surface</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$E \cdot 2 A=\frac{\sigma A}{\epsilon_0}$</p>
</li>
<li>
<p>$\vec{E}=\frac{\sigma}{2 \epsilon_0} \hat{n}$</p>
</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:450px;'>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/d175bc92-496b-43a9-a49f-5c20df8aa700/public"  width="100%" >

</main>
<hr>
<footer style = "font-size: 18px"> Field due to a Infinite Sheet $\rightarrow$ Gaussian Surface $\rightarrow$ <span style = "color:blue"> Gaussian Surface </span> $\rightarrow$ Thin Conducting Plate $\rightarrow$ Gaussian Law </footer>

<h3 id="success-stylefont-size25px-applications-of-gausss-law-l-4-success-16"><Success style="font-size:25px;"> Applications-Of-Gausss-Law L-4 </Success></h3>
<h3 id="primary-stylefont-size24pxthin-conducting-plateprimary"><primary style="font-size:24px;">Thin Conducting Plate</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
</div>
<div style='float: left; width:50%; max-width:450px;'>
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</div>
<div style='float: right; width:50%;'>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/5ba3e549-fc4e-476d-7021-af315f27fc00/public"  width="100%" >
</div>


</main>
<hr>
<footer style = "font-size: 18px"> Gaussian Surface $\rightarrow$ Gaussian Surface $\rightarrow$ <span style = "color:blue"> Thin Conducting Plate </span> $\rightarrow$ Gaussian Law $\rightarrow$ Problem </footer>

<h3 id="success-stylefont-size25px-applications-of-gausss-law-l-4-success-17"><Success style="font-size:25px;"> Applications-Of-Gausss-Law L-4 </Success></h3>
<h3 id="primary-stylefont-size24pxgaussian-lawprimary"><primary style="font-size:24px;">Gaussian Law</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>$\oint \vec{E} \cdot d \vec{A}=\frac{Q_{\text {enc }}}{\epsilon_0}$</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:450px;'>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/e20515d8-120d-49fb-90b4-199c04c58600/public"  width="70%" >

</main>
<hr>
<footer style = "font-size: 18px"> Gaussian Surfac $\rightarrow$ Thin Conducting Plate $\rightarrow$ <span style = "color:blue"> Gaussian Law </span> $\rightarrow$ Problem $\rightarrow$ Thankyou </footer>

<h3 id="success-stylefont-size25px-applications-of-gausss-law-l-4-success-18"><Success style="font-size:25px;"> Applications-Of-Gausss-Law L-4 </Success></h3>
<h3 id="primary-stylefont-size24pxproblemprimary"><primary style="font-size:24px;">Problem</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;text-align:left;font-size:30px;'>
<ul>
<li>Positive charge Q is distributed uniformly throughout the volume of an insulating sphere of radius R. Using Gauss’s law obtain the electric field inside and outside the sphere.</li>
</ul>
</div>
<div style='float: right; width:0%; max-width:450px;'>
<p><img alt="image" src="https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/physics-class-12-unit-01-chapter-04-applications-of-gausss-law-l-4_4-js_lo4fq-5m-0025.jpg"></p>
</main>
<hr>
<footer style = "font-size: 18px"> Thin Conducting Plate $\rightarrow$ Gaussian Law $\rightarrow$ <span style = "color:blue"> Problem </span> $\rightarrow$ Thankyou $\rightarrow$ </footer>