physics-class-12-unit-01-chapter-03-gausss-lawin-electrostatics-l-3-4-k4rcz6kas8q

<h3 id="success-stylefont-size25px-gausss-lawin-electrostatics-l-3-success-1"><Success style="font-size:25px;"> Gausss-Lawin-Electrostatics L-3 </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:100%;font-size:30px;text-align:left;'>
<ul>
<li>Relates Electric fields & Charges</li>
<li>FLUX : Flow in Latin</li>
<li>Electric flux and charges</li>
</ul>
</div>
<div style='float: right; width:0%;'>
<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-03-gausss-lawin-electrostatics-l-3_4-k4rcz6kas8q-00001.jpg"></p>
</div>
</main>
<hr>
<footer style = "font-size: 18px">  $\rightarrow$ Gauss's Law in Electrostatics $\rightarrow$ <span style = "color:blue"> Gauss's Law </span> $\rightarrow$ Fluid Flowing with Uniform Velocity $\rightarrow$ Volume Rate of Flow </footer>

<h3 id="success-stylefont-size25px-gausss-lawin-electrostatics-l-3-success-2"><Success style="font-size:25px;"> Gausss-Lawin-Electrostatics L-3 </Success></h3>
<h3 id="primary-stylefont-size24pxfluid-flowing-with-uniform-velocityprimary"><primary style="font-size:24px;">Fluid Flowing with Uniform Velocity</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li><math xmlns="http://www.w3.org/1998/Math/MathML"> <mstyle displaystyle="true"> <mover> <mi>v</mi> <mo stretchy="false">→</mo> </mover> <mo>=</mo> <mi>v</mi> <mover> <mi>j</mi> <mo>^</mo> </mover> </mstyle> </math></li>
</ul>
</div>
<div style='float: right; width:50%; max-width:450px '>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/b413360f-0336-466a-61d1-1082671d3100/public"  width="100%" >

</div>
</main>
<hr>
<footer style = "font-size: 18px"> Gauss's Law in Electrostatics $\rightarrow$ Gauss's Law $\rightarrow$ <span style = "color:blue"> Fluid Flowing with Uniform Velocity </span> $\rightarrow$ Volume Rate of Flow $\rightarrow$ Flux </footer>

<h3 id="success-stylefont-size25px-gausss-lawin-electrostatics-l-3-success-3"><Success style="font-size:25px;"> Gausss-Lawin-Electrostatics L-3 </Success></h3>
<h3 id="primary-stylefont-size24pxvolume-rate-of-flowprimary"><primary style="font-size:24px;">Volume Rate of Flow</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>S: Surface area</p>
</li>
<li>
<p>Volume rate of flow: v.S</p>
</li>
<li>
<p>Flux: V.S</p>
</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:450px '>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/9f82ceea-3db7-4e00-69ca-560fd52d2400/public"  width="100%" >

</div>
</main>
<hr>
<footer style = "font-size: 18px"> Gauss's Law $\rightarrow$ Fluid Flowing with Uniform Velocity $\rightarrow$ <span style = "color:blue"> Volume Rate of Flow </span> $\rightarrow$ Flux $\rightarrow$ Vector Area </footer>

<h3 id="success-stylefont-size25px-gausss-lawin-electrostatics-l-3-success-4"><Success style="font-size:25px;"> Gausss-Lawin-Electrostatics L-3 </Success></h3>
<h3 id="primary-stylefont-size24pxfluxprimary"><primary style="font-size:24px;">Flux</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>volume : $vS \cos \theta$</p>
</li>
<li>
<p>flux: $v S \cos \theta=\vec{v} \cdot \hat{n}S $</p>
</li>
<li>
<p>$\hat{n}$: unit normal to $S$</p>
</li>
</ul>
</div>
<div style='float: right; width:50%;max-width:400px '>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/a1be1ba3-2359-4db7-3203-da1f9d127500/public"  width="100%" >

</div>
</main>
<hr>
<footer style = "font-size: 18px"> Fluid Flowing with Uniform Velocity $\rightarrow$ Volume Rate of Flow $\rightarrow$ <span style = "color:blue"> Flux </span> $\rightarrow$ Vector Area $\rightarrow$ Vector Area </footer>

<h3 id="success-stylefont-size25px-gausss-lawin-electrostatics-l-3-success-5"><Success style="font-size:25px;"> Gausss-Lawin-Electrostatics L-3 </Success></h3>
<h3 id="primary-stylefont-size24pxvector-areaprimary"><primary style="font-size:24px;">Vector Area</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>Vecter Area: $\overrightarrow{S}=S \hat{n}$</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:450px '>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/dba280a5-6294-4ec6-d130-089b06b58700/public"  width="100%" >

</div>
</main>
<hr>
<footer style = "font-size: 18px"> Volume Rate of Flow $\rightarrow$ Flux $\rightarrow$ <span style = "color:blue"> Vector Area </span> $\rightarrow$ Vector Area $\rightarrow$ Electric Flux </footer>

<h3 id="success-stylefont-size25px-gausss-lawin-electrostatics-l-3-success-6"><Success style="font-size:25px;"> Gausss-Lawin-Electrostatics L-3 </Success></h3>
<h3 id="primary-stylefont-size24pxvector-areaprimary-1"><primary style="font-size:24px;">Vector Area</primary></h3>
<hr>
<main>
<div style='float: left; width:70%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>Vector Area:$\overrightarrow{S}=S \hat{\jmath}$</p>
</li>
<li>
<p>Vector Area: $\vec{S} = S \hat{i}$</p>
</li>
</ul>
</div>
<div style='float: right; width:30%; max-width:250px; '>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/5927f7df-a506-4300-fc2b-5c255a6d3900/public"  width="100%" >
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/9080a355-235a-4fcf-659f-14f4872d2600/public"  width="100%" >

</div>
</main>
<hr>
<footer style = "font-size: 18px"> Flux $\rightarrow$ Vector Area $\rightarrow$ <span style = "color:blue"> Vector Area </span> $\rightarrow$ Electric Flux $\rightarrow$ Electric Field </footer>

<h3 id="success-stylefont-size25px-gausss-lawin-electrostatics-l-3-success-7"><Success style="font-size:25px;"> Gausss-Lawin-Electrostatics L-3 </Success></h3>
<h3 id="primary-stylefont-size24pxelectric-fluxprimary"><primary style="font-size:24px;">Electric Flux</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>Uniform Electric Field</li>
<li>Electric flux: $\begin{aligned} \Phi & =E S \ & =\vec{E} \cdot \vec{S}\end{aligned}$</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:450px '>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/0de80002-945c-4124-b009-cc266f2d0200/public"  width="100%" >

</div>
</main>
<hr>
<footer style = "font-size: 18px"> Vector Area $\rightarrow$ Vector Area $\rightarrow$ <span style = "color:blue"> Electric Flux </span> $\rightarrow$ Electric Field $\rightarrow$ Electric Flux Calculation</footer>

<h3 id="success-stylefont-size25px-gausss-lawin-electrostatics-l-3-success-8"><Success style="font-size:25px;"> Gausss-Lawin-Electrostatics L-3 </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%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>Cube of side L</p>
</li>
<li>
<p>Uniform electric field $\vec{E} = E_0 \hat{j}$</p>
</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:450px '>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/54e280d4-b0d1-46c8-c56c-a3b47900f200/public"  width="100%" >

</div>
</main>
<hr>
<footer style = "font-size: 18px"> Vector Area $\rightarrow$ Electric Flux $\rightarrow$ <span style = "color:blue"> Electric Field </span> $\rightarrow$ Electric Flux Calculation $\rightarrow$ Electric Flux Calculation </footer>

<h3 id="success-stylefont-size25px-gausss-lawin-electrostatics-l-3-success-9"><Success style="font-size:25px;"> Gausss-Lawin-Electrostatics L-3 </Success></h3>
<h3 id="primary-stylefont-size24pxelectric-flux-calculationprimary"><primary style="font-size:24px;">Electric Flux Calculation</primary></h3>
<hr>
<main>
<div style='float: left; width:70%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>$\vec{E} = E_0 \hat{j}$</p>
</li>
<li>
<p>Electric field lines</p>
</li>
<li>
<p>Area: $S=L^2$</p>
</li>
</ul>
</div>
<div style='float: right; width:30%; max-width:250px '>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/d68d4a05-979b-4d65-0f73-ce820c4d4900/public"  width="100%" >
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/e0bffec5-5614-42b1-649b-ea8fe0b3af00/public"  width="100%" >

</div>
</main>
<hr>
<footer style = "font-size: 18px"> Electric Flux $\rightarrow$ Electric Field $\rightarrow$ <span style = "color:blue"> Electric Flux Calculation </span> $\rightarrow$ Electric Flux Calculation $\rightarrow$ Total Electric Flux </footer>

<h3 id="success-stylefont-size25px-gausss-lawin-electrostatics-l-3-success-10"><Success style="font-size:25px;"> Gausss-Lawin-Electrostatics L-3 </Success></h3>
<h3 id="primary-stylefont-size24pxelectric-flux-calculationprimary-1"><primary style="font-size:24px;">Electric Flux Calculation</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>$\vec{E}=E_0 \hat{j}$</p>
</li>
<li>
<p>Flux $ \Phi_1=\vec{E} \cdot \vec{S}  =E_0 \hat{j} \cdot S \hat{j}$</p>
</li>
<li>
<p>$ \text { (HCDI) }  =E_0 S$</p>
</li>
<li>
<p>$ \text { Flux } \Phi_2=\vec{E} \cdot \vec{S}  =E_0 \hat{j}[ S \hat{j}]$</p>
</li>
<li>
<p>$ \text { (AFGB) }  = -E_0 S$</p>
</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:450px '>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/8f44f826-175f-4261-e04b-50efd2c77100/public"  width="100%" >

</div>
</main>
<hr>
<footer style = "font-size: 18px"> Electric Field $\rightarrow$ Electric Flux Calculation $\rightarrow$ <span style = "color:blue"> Electric Flux Calculation </span> $\rightarrow$ Total Electric Flux $\rightarrow$ Electric Flux Calculation </footer>

<h3 id="success-stylefont-size25px-gausss-lawin-electrostatics-l-3-success-11"><Success style="font-size:25px;"> Gausss-Lawin-Electrostatics L-3 </Success></h3>
<h3 id="primary-stylefont-size24pxtotal-electric-fluxprimary"><primary style="font-size:24px;">Total Electric Flux</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;font-size:30px;text-align:left;'>
<ul>
<li>$  \text { Flux Through(BCHG) }=\Phi_3=\vec{E} \cdot \vec{S} $</li>
</ul>
<ul>
<li>$=E_0 \hat{j} \cdot S \hat{i}  =0$</li>
<li>$\text { Total Electric flux} = E_0 S -E_0 S = 0$</li>
</ul>
</div>
<div style='float: right; width:0%;'>

</div>
</main>
<hr>
<footer style = "font-size: 18px"> Electric Flux Calculation $\rightarrow$ Electric Flux Calculation $\rightarrow$ <span style = "color:blue"> Total Electric Flux </span> $\rightarrow$ Electric Flux Calculation $\rightarrow$ Vector Areas of Surfaces </footer>

<h3 id="success-stylefont-size25px-gausss-lawin-electrostatics-l-3-success-12"><Success style="font-size:25px;"> Gausss-Lawin-Electrostatics L-3 </Success></h3>
<h3 id="primary-stylefont-size24pxelectric-flux-calculationprimary-2"><primary style="font-size:24px;">Electric Flux Calculation</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>The cube is now rotated-</li>
<li>Face AFGB makes an angle $\theta$ with the $x $ - Axis</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:450px '>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/70787f83-058f-4fce-d500-a3c650877e00/public"  width="100%" >

</div>
</main>
<hr>
<footer style = "font-size: 18px"> Electric Flux Calculation $\rightarrow$ Total Electric Flux $\rightarrow$ <span style = "color:blue"> Electric Flux Calculation </span> $\rightarrow$ Vector Areas of Surfaces $\rightarrow$ Electric Flux </footer>

<h3 id="success-stylefont-size25px-gausss-lawin-electrostatics-l-3-success-13"><Success style="font-size:25px;"> Gausss-Lawin-Electrostatics L-3 </Success></h3>
<h3 id="primary-stylefont-size24pxvector-areas-of-surfacesprimary"><primary style="font-size:24px;">Vector Areas of Surfaces</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
</div>
<div style='float: right; width:100%; max-width:450px '>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/b380551f-dad8-4715-6b40-abad40f2a800/public"  width="70%" >

</div>
</main>
<hr>
<footer style = "font-size: 18px"> Total Electric Flux $\rightarrow$ Electric Flux Calculation $\rightarrow$ <span style = "color:blue"> Vector Areas of Surfaces </span> $\rightarrow$ Electric Flux $\rightarrow$ Flux </footer>

<h3 id="success-stylefont-size25px-gausss-lawin-electrostatics-l-3-success-14"><Success style="font-size:25px;"> Gausss-Lawin-Electrostatics L-3 </Success></h3>
<h3 id="primary-stylefont-size24pxelectric-fluxprimary-1"><primary style="font-size:24px;">Electric Flux</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>Electric flux $B C H G$</p>
</li>
<li>
<p>$ \Phi_1  =\vec{E} \cdot \vec{S}  =E_0 \hat{j} \cdot S(\hat{i} \cos \theta+\hat{j} \sin \theta)  =E_0 S \sin \theta $</p>
</li>
<li>
<p>$ \text { Flux through(ADIF) }$</p>
</li>
<li>
<p>$ {\Phi}_2  =\vec{E} \cdot \overrightarrow{S} $</p>
</li>
<li>
<p>= $ E_0 \hat{j} \cdot S(-\hat{i} \cos {\theta} -\hat{j} \sin {\theta})$</p>
</li>
<li>
<p>$=-S E_0\sin \theta$</p>
</li>
</ul>
</div>
<div style='float: right; width:0%;'>

</div>
</main>
<hr>
<footer style = "font-size: 18px"> Electric Flux Calculation $\rightarrow$ Vector Areas of Surface $\rightarrow$ <span style = "color:blue"> Electric Flux </span> $\rightarrow$ Flux $\rightarrow$ Total Flux </footer>

<h3 id="success-stylefont-size25px-gausss-lawin-electrostatics-l-3-success-15"><Success style="font-size:25px;"> Gausss-Lawin-Electrostatics L-3 </Success></h3>
<h3 id="primary-stylefont-size24pxfluxprimary-1"><primary style="font-size:24px;">Flux</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;font-size:30px;text-align:left;'>
<ul>
<li>$
\Phi_3  =\vec{E} \vec{S} =E_0 \hat{j} \cdot S(-\hat{i} \sin \theta+\hat{j} \cos \theta) =E_0 S \cos \theta $</li>
</ul>
<ul>
<li>Flux</li>
</ul>
<ul>
<li>$
\Phi_4 =\vec{E} \cdot \overrightarrow{S}  =E_0 \hat{j} \cdot S(\hat{i} \sin \theta-\hat{j} \cos \theta) = -E_0 S \cos \theta $</li>
</ul>
<ul>
<li>Flux through top and bottom surfaces $= 0 $</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-03-gausss-lawin-electrostatics-l-3_4-k4rcz6kas8q-000015.jpg"></p>
</div>
</main>
<hr>
<footer style = "font-size: 18px"> Vector Areas of Surface $\rightarrow$ Electric Flux $\rightarrow$ <span style = "color:blue"> Flux </span> $\rightarrow$ Total Flux $\rightarrow$ Electric Flux through sphere </footer>

<h3 id="success-stylefont-size25px-gausss-lawin-electrostatics-l-3-success-16"><Success style="font-size:25px;"> Gausss-Lawin-Electrostatics L-3 </Success></h3>
<h3 id="primary-stylefont-size24pxtotal-fluxprimary"><primary style="font-size:24px;">Total Flux</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;font-size:30px;text-align:left;'>
<ul>
<li>$ \text { Total flux } =E_0 S \sin \theta - E_0 S \sin \theta  + E_0 S \cos \theta -  E_0 S \cos \theta = 0 $</li>
</ul>
</div>
<div style='float: right; width:0%;'>

</div>
</main>
<hr>
<footer style = "font-size: 18px"> Electric Flux $\rightarrow$ Flux $\rightarrow$ <span style = "color:blue"> Total Flux </span> $\rightarrow$ Electric Flux through Sphere $\rightarrow$ Electric Flux through Arbitrary Surface </footer>

<h3 id="success-stylefont-size25px-gausss-lawin-electrostatics-l-3-success-17"><Success style="font-size:25px;"> Gausss-Lawin-Electrostatics L-3 </Success></h3>
<h3 id="primary-stylefont-size24pxelectric-flux-through-sphereprimary"><primary style="font-size:24px;">Electric Flux through Sphere</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>Sphere of radius $R$</p>
</li>
<li>
<p>$ \vec{E}=\frac{1}{4 \pi \epsilon_0} \frac{q}{r^2} \hat{r} $</p>
</li>
<li>
<p>$ d \vec{s} $</p>
</li>
<li>
<p>$d \phi=\vec{E} \cdot d \vec{s} $</p>
</li>
<li>
<p>$ E=\frac{1}{4 \pi \epsilon_0} \frac{q}{R^2} $</p>
</li>
<li>
<p>$ \Phi  =E \cdot 4 \pi R^2 $</p>
</li>
<li>
<p>Total flux $=q / \epsilon_0 $</p>
</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:450px '>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/b0f82196-9156-49c5-bd71-c72601dddb00/public"  width="100%" >

</div>
</main>
<hr>
<footer style = "font-size: 18px"> Flux $\rightarrow$ Total Flux $\rightarrow$ <span style = "color:blue"> Electric Flux through Sphere </span> $\rightarrow$ Electric Flux through Arbitrary Surface $\rightarrow$ Flux </footer>

<h4 id="success-stylefont-size25px-gausss-lawin-electrostatics-l-3-success-18"><Success style="font-size:25px;"> Gausss-Lawin-Electrostatics L-3 </Success></h4>
<h3 id="primary-stylefont-size24pxelectric-flux-through-arbitrary-surfaceprimary"><primary style="font-size:24px;">Electric Flux through Arbitrary Surface</primary></h3>
<hr>
<main>
<div style='float: left; width:70%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>Electric flux passing through the spherical surface $S_1$ and the arbitrary closed surface $S_2$ are the same.</p>
</li>
<li>
<p>Gauss’s Law :</p>
</li>
<li>
<p>$ \oint \vec{E} \cdot d \vec{A}=\frac{Q_{\text {enc }}}{\epsilon_0} $</p>
</li>
</ul>
</div>
<div style='float: right; width:30%; max-width:250px '>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/681bdb58-9642-4d65-fd5b-fc987fb92900/public"  width="50%" >
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/27aa9fc5-d83e-48d3-3eb6-260924e3a000/public"  width="50%" >


</div>
</main>
<hr>
<footer style = "font-size: 18px"> Total Flux $\rightarrow$ Electric Flux through Sphere $\rightarrow$ <span style = "color:blue"> Electric Flux through Arbitrary Surface </span> $\rightarrow$ Flux $\rightarrow$ Flux </footer>

<h3 id="success-stylefont-size25px-gausss-lawin-electrostatics-l-3-success-19"><Success style="font-size:25px;"> Gausss-Lawin-Electrostatics L-3 </Success></h3>
<h3 id="primary-stylefont-size24pxfluxprimary-2"><primary style="font-size:24px;">Flux</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>$ \Phi=\frac{q}{\epsilon_0}  $
-$ \text { Gauss’s law } \Phi=\frac{q}{\epsilon_0} $</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px '>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/7c3b3362-9bd7-4fc0-870c-6a3eee7e8700/public"  width="50%" >

</div>
</main>
<hr>
<footer style = "font-size: 18px"> Electric Flux through Sphere $\rightarrow$ Electric Flux through Arbitrary Surface $\rightarrow$ <span style = "color:blue"> Flux </span> $\rightarrow$ Flux $\rightarrow$ Total Electric Flux </footer>

<h3 id="success-stylefont-size25px-gausss-lawin-electrostatics-l-3-success-20"><Success style="font-size:25px;"> Gausss-Lawin-Electrostatics L-3 </Success></h3>
<h3 id="primary-stylefont-size24pxfluxprimary-3"><primary style="font-size:24px;">Flux</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>$ \Phi=\frac{q}{\epsilon_0} $</li>
<li>Total Electric flux</li>
</ul>
<ul>
<li>
<p>$ \Phi  =\frac{q_1}{\epsilon_0}+\frac{q_2}{\epsilon_0} $</p>
</li>
<li>
<p>$=\frac {\Sigma q_1}{\epsilon_0} =\frac{Q}{\epsilon_0} $</p>
</li>
<li>
<p>Total charges enclosed by the surfaces</p>
</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:450px '>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/dfca7da0-f776-40e4-b977-85126a9ee100/public"  width="100%" >

</div>
</main>
<hr>
<footer style = "font-size: 18px"> Electric Flux through Arbitrary Surface $\rightarrow$ Flux $\rightarrow$ <span style = "color:blue"> Flux </span> $\rightarrow$ Total Electric Flux $\rightarrow$ Total Flux </footer>

<h3 id="success-stylefont-size25px-gausss-lawin-electrostatics-l-3-success-21"><Success style="font-size:25px;"> Gausss-Lawin-Electrostatics L-3 </Success></h3>
<h3 id="primary-stylefont-size24pxtotal-electric-fluxprimary-1"><primary style="font-size:24px;">Total Electric Flux</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>$ \bar{\Phi}  =\frac{q_1 + q_2+ q_3}{\epsilon_0} $</p>
</li>
<li>
<p>$=\frac{\sum_i q_i}{\epsilon_0} $</p>
</li>
<li>
<p>$\sum q_L:$ Charger enclosed by an surface</p>
</li>
<li>
<p>$ \text { Total flux}=\frac{\left(q_1+q_2\right)}{\epsilon_0} $</p>
</li>
<li>
<p>$\Phi=\frac{\text { charg enclosed }}{\epsilon_0}$</p>
</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:450px '>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/56b8b0af-85a6-4d22-ee88-97fa77e81c00/public"  width="100%" >


</div>
</main>
<hr>
<footer style = "font-size: 18px"> Flux $\rightarrow$ Flux $\rightarrow$ <span style = "color:blue"> Total Electric Flux </span> $\rightarrow$ Total Flux $\rightarrow$ Conductor </footer>

<h3 id="success-stylefont-size25px-gausss-lawin-electrostatics-l-3-success-22"><Success style="font-size:25px;"> Gausss-Lawin-Electrostatics L-3 </Success></h3>
<h3 id="primary-stylefont-size24pxtotal-fluxprimary-1"><primary style="font-size:24px;">Total Flux</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>$ \text { Total flux}=\frac{\left(q_1+q_2\right)}{\epsilon_0} $</p>
</li>
<li>
<p>$ \Phi=\frac{\text { charg enclosed }}{\epsilon_0}$</p>
</li>
</ul>
</div>
<div style='float: right; width:50%;  max-width:450px '>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/466c9f81-1a98-44fd-bc48-bc98bf9c1100/public"  width="100%" >

</div>
</main>
<hr>
<footer style = "font-size: 18px"> Flux $\rightarrow$ Total Electric Flux $\rightarrow$ <span style = "color:blue"> Total Flux </span> $\rightarrow$ Conductor $\rightarrow$ Flux </footer>

<h3 id="success-stylefont-size25px-gausss-lawin-electrostatics-l-3-success-23"><Success style="font-size:25px;"> Gausss-Lawin-Electrostatics L-3 </Success></h3>
<h3 id="primary-stylefont-size24pxconductorprimary"><primary style="font-size:24px;">Conductor</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>Net flux $=0$</p>
</li>
<li>
<p>$=\frac{\text {charges enclosed }}{\epsilon_0}$</p>
</li>
<li>
<p>Gaussian Surface</p>
</li>
<li>
<p>Excess charges: Surface</p>
</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:450px '>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/da895b3d-23f1-49ba-2246-2328c0fed300/public"  width="70%" >

</div>
</main>
<hr>
<footer style = "font-size: 18px"> Total Electric Flux $\rightarrow$ Total Flux $\rightarrow$ <span style = "color:blue"> Conductor </span> $\rightarrow$ Flux $\rightarrow$ Conducting Sphere with Charge +Q </footer>

<h3 id="success-stylefont-size25px-gausss-lawin-electrostatics-l-3-success-24"><Success style="font-size:25px;"> Gausss-Lawin-Electrostatics L-3 </Success></h3>
<h3 id="primary-stylefont-size24pxfluxprimary-4"><primary style="font-size:24px;">Flux</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>Flux=$\frac{q}{\epsilon_0}$</p>
</li>
<li>
<p>Flux=$-\frac{q}{\epsilon_0}$</p>
</li>
<li>
<p>Flux = 0</p>
</li>
</ul>
</div>
<div style='float: right; width:50%; '>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/e0d5b591-1ccb-417e-901c-d09aeba42d00/public"  width="100%" >

</div>
</main>
<hr>
<footer style = "font-size: 18px"> Total Flux $\rightarrow$ Conductor $\rightarrow$ <span style = "color:blue"> Flux </span> $\rightarrow$ Conducting Sphere with Charge +Q $\rightarrow$ Problem </footer>

<h3 id="success-stylefont-size25px-gausss-lawin-electrostatics-l-3-success-25"><Success style="font-size:25px;"> Gausss-Lawin-Electrostatics L-3 </Success></h3>
<h3 id="primary-stylefont-size24pxconducting-sphere-with-charge-qprimary"><primary style="font-size:24px;">Conducting Sphere with Charge +Q</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>Surface charge density $ \sigma=\frac{Q}{4 \pi R^2} $</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:450px '>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/ccbba93f-4df7-4adc-4c6c-c39a2f5a8b00/public"  width="100%" >

</div>
</main>
<hr>
<footer style = "font-size: 18px"> Conductor $\rightarrow$ Flux $\rightarrow$ <span style = "color:blue"> Conducting Sphere with Charge +Q </span> $\rightarrow$ Problem $\rightarrow$ Thankyou </footer>

<h3 id="success-stylefont-size25px-gausss-lawin-electrostatics-l-3-success-26"><Success style="font-size:25px;"> Gausss-Lawin-Electrostatics L-3 </Success></h3>
<h3 id="primary-stylefont-size24pxproblemprimary"><primary style="font-size:24px;">Problem</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>
<p><strong>Question.</strong> Calculate the electric flux through $ S_1 \times \sqrt{2} $</p>
</li>
<li>
<p><strong>Question.</strong> Draw a closed surface through which flux is</p>
</li>
<li>
<p>a) maximum & Negative</p>
</li>
<li>
<p>b) positve and maximum</p>
</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:450px '>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/70a0bd94-3d32-4292-352c-e5d144c48500/public"  width="80%" >

</div>
</main>
<hr>
<footer style = "font-size: 18px"> Flux $\rightarrow$ Conducting Sphere with Charge +Q $\rightarrow$ <span style = "color:blue"> Problem </span> $\rightarrow$ Thankyou $\rightarrow$ </footer>