physics-class-12-unit-02-chapter-06-field-due-to-dipole-and-continuous-charge-distributions-l-6-9-69fd7tbs0fq

<h3 id="success-stylefont-size25pxfield-due-to-dipole-and-continous-charge-distributions--l-6-success-1"><Success style="font-size:25px;">Field due to Dipole and Continous Charge Distributions  L-6 </Success></h3>
<h3 id="primary-stylefont-size24pxelectric-dipoleprimary"><primary style="font-size:24px;">Electric Dipole</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>$\vec{E}=\frac{\vec{p}}{2 \pi \epsilon_0 x^3}$   x»2a</p>
</li>
<li>
<p>$\vec{p}=q.2a\hat{i}$</p>
</li>
<li>
<p><strong>Dipole moment</strong></p>
</li>
</ul>
</div>
<div style='float: right; width:50%;'>

<p><img alt="alt text" src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/a8508813-9ede-4e00-2f00-cf2cc4772600/public"></p>
</div>
</main>
<hr>
<footer style = "font-size: 18px">  $\rightarrow$ Field due to Dipole and Continous Charge Distributions $\rightarrow$ <span style = "color:blue"> Electric Dipole </span> $\rightarrow$ Electric Dipole at an Angle $\rightarrow$ Resultant Electric Dipole </footer>

<h3 id="success-stylefont-size25pxfield-due-to-dipole-and-continous-charge-distributions--l-6-success-2"><Success style="font-size:25px;">Field due to Dipole and Continous Charge Distributions  L-6 </Success></h3>
<h3 id="primary-stylefont-size24pxelectric-dipole-at-an-angleprimary"><primary style="font-size:24px;">Electric Dipole at an Angle</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>$\vec{E}_{+q}=\frac{1}{4 \pi \epsilon_0}\frac{q}{r^2}(-\cos\theta\hat{i}+\sin\theta\hat{j})$</p>
</li>
<li>
<p>$\vec{E}_{-q}=\frac{1}{4 \pi \epsilon_0}\frac{q}{r^2}(-\cos\theta\hat{i}-\sin\theta\hat{j})$</p>
</li>
</ul>
</div>
<div style='float: right; width:50%;'>

<p><img alt="alt text" src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/f4147c40-3a38-4899-f6ed-5f311775f900/public"></p>
</div>
</main>
<hr>
<footer style = "font-size: 18px"> Field due to Dipole and Continous Charge Distributions $\rightarrow$ Electric Dipole $\rightarrow$ <span style = "color:blue"> Electric Dipole at an Angle </span> $\rightarrow$ Resultant Electric Dipole $\rightarrow$ Electric Dipole and Different Point </footer>

<h3 id="success-stylefont-size25pxfield-due-to-dipole-and-continous-charge-distributions--l-6-success-3"><Success style="font-size:25px;">Field due to Dipole and Continous Charge Distributions  L-6 </Success></h3>
<h3 id="primary-stylefont-size24pxresultant-electric-dipoleprimary"><primary style="font-size:24px;">Resultant Electric Dipole</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>$\vec{E}$ = $\vec{E}$<sub>+q</sub>    + $\vec{E}_{-q}$  $=\frac{1}{4 \pi \epsilon_0}\frac{q}{r^2}(-2\cos\theta\hat{i})$</p>
</li>
<li>
<p>$\vec{E}=\frac{1}{4 \pi\epsilon_0}\frac{q}{r^2}(-2\cos\theta\hat{i})$$=-\frac{q(2a)\hat{i}}{4 \pi \epsilon_0 r^3}=-\frac{\vec{p}}{4 \pi \epsilon_0 r^3}$</p>
</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-02-chapter-06-field-due-to-dipole-and-continuous-charge-distributions-l-6_9-69fd7tbs0fq-003.jpg"></p>
<div>
</main>
<hr>
<footer style = "font-size: 18px"> Electric Dipole $\rightarrow$ Electric Dipole at an Angle $\rightarrow$ <span style = "color:blue"> Resultant Electric Dipole </span> $\rightarrow$ Electric Dipole and Different Point $\rightarrow$ Atom as a Dipole </footer>

<h3 id="success-stylefont-size25pxfield-due-to-dipole-and-continous-charge-distributions--l-6-success-4"><Success style="font-size:25px;">Field due to Dipole and Continous Charge Distributions  L-6 </Success></h3>
<h3 id="primary-stylefont-size24pxelectric-dipole-and-different-pointprimary"><primary style="font-size:24px;">Electric Dipole and Different Point</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>$r^3=a^2+y^2$</p>
</li>
<li>
<p>$\vec{E}=-\frac{\vec{p}}{4 \pi \epsilon_0 r^3(a^2+y^2)^{3/2}}$</p>
</li>
<li>
<p>y » a</p>
</li>
<li>
<p>$\vec{E}=-\frac{\vec{p}}{4 \pi \epsilon_0y^3}$</p>
</li>
</ul>
<ul>
<li>
<p>$a\rightarrow0$</p>
</li>
<li>
<p>$q\rightarrow\infty$ q.2a = P  Point dipole</p>
</li>
</ul>
</div>
<div style='float: right; width:50%;'>

<p><img alt="alt text" src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/9046e17e-322e-40b1-67fb-b953d40a5000/public"></p>
</div>
</main>
<hr>
<footer style = "font-size: 18px"> Electric Dipole at an Angle $\rightarrow$ Resultant Electric Dipole $\rightarrow$ <span style = "color:blue"> Electric Dipole and Different Point </span> $\rightarrow$ Atom as a Dipole $\rightarrow$ Water Molecule </footer>

<h3 id="success-stylefont-size25pxfield-due-to-dipole-and-continous-charge-distributions--l-6-success-5"><Success style="font-size:25px;">Field due to Dipole and Continous Charge Distributions  L-6 </Success></h3>
<h3 id="primary-stylefont-size24pxatom-as-a-dipoleprimary"><primary style="font-size:24px;">Atom as a Dipole</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>Atom in absence of any external electric field</p>
</li>
<li>
<p>Centers of positive and negative charges coincide</p>
</li>
<li>
<p>Atom in presence of external electric field</p>
</li>
<li>
<p>Centers of positive and negative charges do not coincide</p>
</li>
<li>
<p>Forms a dipole</p>
</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>

<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/dc52087b-e487-46ba-2b6c-20a0af407c00/public" width="100%">
</div>
</main>
<hr>
<footer style = "font-size: 18px"> Resultant Electric Dipole $\rightarrow$ Electric Dipole and Different Point $\rightarrow$ <span style = "color:blue"> Atom as a Dipole </span> $\rightarrow$ Water Molecule $\rightarrow$ Dipole in Nature </footer>

<h3 id="success-stylefont-size25pxfield-due-to-dipole-and-continous-charge-distributions--l-6-success-6"><Success style="font-size:25px;">Field due to Dipole and Continous Charge Distributions  L-6 </Success></h3>
<h3 id="primary-stylefont-size24pxwater-moleculeprimary"><primary style="font-size:24px;">Water Molecule</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>Water molecule $({H}_2O)$ is a dipole</p>
</li>
<li>
<p>Consequences are profound:</p>
</li>
<li>
<p>Excellent solvent for ionic substances like salt</p>
</li>
<li>
<p>If water molecule was not a dipole, it would be a poor solvent</p>
</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>

<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/8b9ef306-1ffe-47af-03ad-e6a504f7e600/public" width="100%">
</div>
</main>
<hr>
<footer style = "font-size: 18px"> Electric Dipole and Different Point $\rightarrow$ Atom as a Dipole $\rightarrow$ <span style = "color:blue"> Water Molecule </span> $\rightarrow$ Dipole in Nature $\rightarrow$ Net Force </footer>

<h3 id="success-stylefont-size25pxfield-due-to-dipole-and-continous-charge-distributions--l-6-success-8"><Success style="font-size:25px;">Field due to Dipole and Continous Charge Distributions  L-6 </Success></h3>
<h3 id="primary-stylefont-size24pxnet-forceprimary"><primary style="font-size:24px;">Net Force</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>Net force = 0</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>

<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/0f54a71c-b229-4d9d-de0a-308b5de34200/public" width="100%">
</div>
</main>
<hr>
<footer style = "font-size: 18px"> Water Molecule $\rightarrow$ Dipole in Nature $\rightarrow$ <span style = "color:blue"> Net Force </span> $\rightarrow$ Torque $\rightarrow$ Non-Uniform Electric Field </footer>

<h3 id="success-stylefont-size25pxfield-due-to-dipole-and-continous-charge-distributions--l-6-success-9"><Success style="font-size:25px;">Field due to Dipole and Continous Charge Distributions  L-6 </Success></h3>
<h3 id="primary-stylefont-size24pxtorqueprimary"><primary style="font-size:24px;">Torque</primary></h3>
<hr>
<main>
<div style='float: left; width:60%;font-size:30px;text-align:left;'>
<ul>
<li>Net torque(magnitude) = $qE.2a\sin\theta$</li>
</ul>
<ul>
<li>
<p>$=pE\sin\theta$</p>
</li>
<li>
<p>$|\vec{p}\times\vec{E}|=pE\sin\theta$</p>
</li>
<li>
<p>Torque $\vec{\tau}=\vec{p}\times\vec{E}$</p>
</li>
</ul>
</div>
<div style='float: right; width:40%; max-width:400px;'>

<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/ea4f8201-1a3f-46dc-bb45-c178aa9f3800/public" width="100%">
</div>
</main>
<hr>
<footer style = "font-size: 18px"> Dipole in Nature $\rightarrow$ Net Force $\rightarrow$ <span style = "color:blue"> Torque </span> $\rightarrow$ Non-Uniform Electric Field $\rightarrow$ Electric Fields in Biological Systems </footer>

<h3 id="success-stylefont-size25pxfield-due-to-dipole-and-continous-charge-distributions--l-6-success-10"><Success style="font-size:25px;">Field due to Dipole and Continous Charge Distributions  L-6 </Success></h3>
<h3 id="primary-stylefont-size24pxnon-uniform-electric-fieldprimary"><primary style="font-size:24px;">Non-Uniform Electric Field</primary></h3>
<hr>
<main>
<div style='float: left; width:60%;font-size:30px;text-align:left;'>
<ul>
<li>Net force along x distance = q (E(+q) - E(-q))</li>
</ul>
<ul>
<li>E(-q) > E(+q)</li>
</ul>
</div>
<div style='float: right; width:40%; max-width:400px;'>

<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/6de1e8da-84ae-43e1-26d6-800c0be65c00/public" width="100%">
</div>
</main>
<hr>
<footer style = "font-size: 18px"> Net Force $\rightarrow$ Torque $\rightarrow$ <span style = "color:blue"> Non-Uniform Electric Field </span> $\rightarrow$ Electric Fields in Biological Systems $\rightarrow$ Electrostatic Field and Spiders </footer>

<h3 id="success-stylefont-size25pxfield-due-to-dipole-and-continous-charge-distributions--l-6-success-11"><Success style="font-size:25px;">Field due to Dipole and Continous Charge Distributions  L-6 </Success></h3>
<h3 id="primary-stylefont-size24pxelectric-fields-in-biological-systemsprimary"><primary style="font-size:24px;">Electric Fields in Biological Systems</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>Flowers use electric fields to attract bees</p>
</li>
<li>
<p>Have a slight negative charge</p>
</li>
<li>
<p>Bumble bees have a positive charge due to friction of the air when they fly</p>
</li>
<li>
<p>When the bee lands on the flower negatively charged pollen grains sticksto the bee and thus help in pollination</p>
</li>
<li>
<p>Distortion of the bee’s own field by the floral electric fields enable the bees to differentiate between flowers and also to learn which ones are the best for food</p>
</li>
<li>
<p>The distortions deflect the hairs covering the body of the bee which triggers the nerve cells at their base to send signals to the brain</p>
</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-02-chapter-06-field-due-to-dipole-and-continuous-charge-distributions-l-6_9-69fd7tbs0fq-0011.jpg"></p>
</div>
</main>
<hr>
<footer style = "font-size: 18px"> Torque $\rightarrow$ Non-Uniform Electric Field $\rightarrow$ <span style = "color:blue"> Electric Fields in Biological Systems </span> $\rightarrow$ Electrostatic Field and Spiders $\rightarrow$ Application of Electrical Fields </footer>

<h3 id="success-stylefont-size25pxfield-due-to-dipole-and-continous-charge-distributions--l-6-success-12"><Success style="font-size:25px;">Field due to Dipole and Continous Charge Distributions  L-6 </Success></h3>
<h3 id="primary-stylefont-size24pxelectrostatic-field-and-spidersprimary"><primary style="font-size:24px;">Electrostatic Field and Spiders</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>Spider webs covered by electrically conductive glue reach out to grab different charged particles from pollen to insects whether they are positively or negatively charged</p>
</li>
<li>
<p>The webs also distort the electric field of the earth over a very small distance which can be sensed by many insects such as bees</p>
</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-02-chapter-06-field-due-to-dipole-and-continuous-charge-distributions-l-6_9-69fd7tbs0fq-0012.jpg"></p>
</div>
</main>
<hr>
<footer style = "font-size: 18px"> Non-Uniform Electric Field $\rightarrow$ Electric Fields in Biological Systems $\rightarrow$ <span style = "color:blue"> Electrostatic Field and Spiders </span> $\rightarrow$ Application of Electrical Fields $\rightarrow$ Application of Electrical Fields </footer>

<h3 id="success-stylefont-size25pxfield-due-to-dipole-and-continous-charge-distributions--l-6-success-13"><Success style="font-size:25px;">Field due to Dipole and Continous Charge Distributions  L-6 </Success></h3>
<h3 id="primary-stylefont-size24pxapplication-of-electrical-fieldsprimary"><primary style="font-size:24px;">Application of Electrical Fields</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>Some fishes have evolved organs capable of generating electricity</p>
</li>
<li>
<p><strong>Electric eel:</strong></p>
</li>
<li>
<p>Low voltage pulses to sense their environment</p>
</li>
<li>
<p>Extremely high voltages ( $600 \mathrm{~V}$ ) to stun or kill prey</p>
</li>
<li>
<p>produce three different kinds of electrical discharges:</p>
</li>
<li>
<p>low-voltage pulses for sensing their environment;</p>
</li>
<li>
<p>short sequences of two or three millisecond, high-voltage pulses given off while hunting;</p>
</li>
<li>
<p>volleys of high-voltage, high-frequency pulses when the eel is capturing prey or defending itself</p>
</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-02-chapter-06-field-due-to-dipole-and-continuous-charge-distributions-l-6_9-69fd7tbs0fq-0013.jpg"></p>
</div>
</main>
<hr>
<footer style = "font-size: 18px"> Electric Fields in Biological Systems $\rightarrow$ Electrostatic Field and Spiders $\rightarrow$ <span style = "color:blue"> Application of Electrical Fields </span> $\rightarrow$ Application of Electrical Fields $\rightarrow$ Application of Electrical Fields </footer>

<h3 id="success-stylefont-size25pxfield-due-to-dipole-and-continous-charge-distributions--l-6-success-14"><Success style="font-size:25px;">Field due to Dipole and Continous Charge Distributions  L-6 </Success></h3>
<h3 id="primary-stylefont-size24pxapplication-of-electrical-fieldsprimary-1"><primary style="font-size:24px;">Application of Electrical Fields</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;font-size:30px;text-align:left;'>
<ul>
<li>
<p><strong>Elephantnose fish</strong></p>
</li>
<li>
<p>Due to poor eyesight uses electric fields to navigate</p>
</li>
<li>
<p>Can tell difference between living and dead bugs buried upto $2 \mathrm{cm}$ in the sea floor</p>
</li>
<li>
<p><strong>Platypus</strong></p>
</li>
<li>
<p>Use electrical impulses to catch prey in murky water</p>
</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-02-chapter-06-field-due-to-dipole-and-continuous-charge-distributions-l-6_9-69fd7tbs0fq-0014.jpg"></p>
</div>
</main>
<hr>
<footer style = "font-size: 18px"> Electrostatic Field and Spiders $\rightarrow$ Application of Electrical Fields $\rightarrow$ <span style = "color:blue"> Application of Electrical Fields </span> $\rightarrow$ Application of Electrical Fields $\rightarrow$ Continuous Charge Distributions </footer>

<h3 id="success-stylefont-size25pxfield-due-to-dipole-and-continous-charge-distributions--l-6-success-15"><Success style="font-size:25px;">Field due to Dipole and Continous Charge Distributions  L-6 </Success></h3>
<h3 id="primary-stylefont-size24pxapplication-of-electrical-fieldsprimary-2"><primary style="font-size:24px;">Application of Electrical Fields</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;font-size:30px;text-align:left;'>
<ul>
<li>
<p><strong>Sharks</strong></p>
</li>
<li>
<p>Extremely sensitive: can detect voltage gradients of one billionth of a volt</p>
</li>
<li>
<p><strong>Electric rays</strong></p>
</li>
<li>
<p>Generate voltages ranging from 10 V to 220 V</p>
</li>
</ul>
</div>
</main>
<hr>
<footer style = "font-size: 18px"> Application of Electrical Fields $\rightarrow$ Application of Electrical Fields $\rightarrow$ <span style = "color:blue"> Application of Electrical Fields </span> $\rightarrow$ Continuous Charge Distributions $\rightarrow$ Symbols </footer>

<h3 id="success-stylefont-size25pxfield-due-to-dipole-and-continous-charge-distributions--l-6-success-16"><Success style="font-size:25px;">Field due to Dipole and Continous Charge Distributions  L-6 </Success></h3>
<h3 id="primary-stylefont-size24pxcontinuous-charge-distributionsprimary"><primary style="font-size:24px;">Continuous Charge Distributions</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>Volume charges density ${(\rho)}c/m^2$</p>
</li>
<li>
<p>Surface charges density ${(\sigma)}c/m^2$</p>
</li>
<li>
<p>Line charges density ${(\lambda)} c/m^2$</p>
</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-02-chapter-06-field-due-to-dipole-and-continuous-charge-distributions-l-6_9-69fd7tbs0fq-0015.jpg"></p>
</div>
</main>
<hr>
<footer style = "font-size: 18px"> Application of Electrical Fields $\rightarrow$ Application of Electrical Fields $\rightarrow$ <span style = "color:blue"> Continuous Charge Distributions </span> $\rightarrow$ Symbols $\rightarrow$ Volume Charge Density </footer>

<h3 id="success-stylefont-size25pxfield-due-to-dipole-and-continous-charge-distributions--l-6-success-17"><Success style="font-size:25px;">Field due to Dipole and Continous Charge Distributions  L-6 </Success></h3>
<h3 id="primary-stylefont-size24pxsymbolsprimary"><primary style="font-size:24px;">Symbols</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>$\alpha\quad\beta\quad\gamma\quad\delta $</p>
</li>
<li>
<p>$\epsilon\quad\zeta\quad\eta\quad\theta $</p>
</li>
<li>
<p>$i\quad\kappa\quad\lambda\quad\mu $</p>
</li>
<li>
<p>$\nu\quad\xi\quad o\quad\pi $</p>
</li>
<li>
<p>$\rho \quad \sigma \quad \tau \quad u $</p>
</li>
<li>
<p>$\phi\quad\chi\quad\psi\quad\omega$</p>
</li>
</ul>
</div>
<div style='float: right; width:50%;'>

</div>
</main>
<hr>
<footer style = "font-size: 18px"> Application of Electrical Fields $\rightarrow$ Continuous Charge Distributions $\rightarrow$ <span style = "color:blue"> Symbols </span> $\rightarrow$ Volume Charge Density $\rightarrow$ Surface Charge Density </footer>

<h3 id="success-stylefont-size25pxfield-due-to-dipole-and-continous-charge-distributions--l-6-success-18"><Success style="font-size:25px;">Field due to Dipole and Continous Charge Distributions  L-6 </Success></h3>
<h3 id="primary-stylefont-size24pxvolume-charge-densityprimary"><primary style="font-size:24px;">Volume Charge Density</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>Charge per unit volume</p>
</li>
<li>
<p>$\rho$ = charge/unit volume</p>
</li>
<li>
<p>$c/m^3$</p>
</li>
<li>
<p>$\Delta v \quad \Delta Q$</p>
</li>
<li>
<p>$\rho=\frac{\Delta Q}{\Delta v}$</p>
</li>
</ul>
</div>
<div style='float: right; width:50%;'>

<p><img alt="alt text" src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/21ac88e3-20a6-4966-d1d6-bdac30fbfc00/public"></p>
</div>
</main>
<hr>
<footer style = "font-size: 18px"> Continuous Charge Distributions $\rightarrow$ Symbols $\rightarrow$ <span style = "color:blue"> Volume Charge Density </span> $\rightarrow$ Surface Charge Density $\rightarrow$ Line Charge Density </footer>

<h3 id="success-stylefont-size25pxfield-due-to-dipole-and-continous-charge-distributions--l-6-success-19"><Success style="font-size:25px;">Field due to Dipole and Continous Charge Distributions  L-6 </Success></h3>
<h3 id="primary-stylefont-size24pxsurface-charge-densityprimary"><primary style="font-size:24px;">Surface Charge Density</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>$Q=A.d.\rho$ $\quad \rho d \rightarrow \sigma$</p>
</li>
<li>
<p>$=A(\rho.d)$ $=A\sigma$</p>
</li>
<li>
<p>$\sigma=\frac{Q}{A}$ Charge/unit area</p>
</li>
</ul>
</div>
<div style='float: right; width:50%;'>

<p><img alt="alt text" src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/415f15d2-d572-4580-587f-c7e08acb3e00/public"></p>
</div>
</main>
<hr>
<footer style = "font-size: 18px"> Symbols $\rightarrow$ Volume Charge Density $\rightarrow$ <span style = "color:blue"> Surface Charge Density </span> $\rightarrow$ Line Charge Density $\rightarrow$ Gauss's Law </footer>

<h3 id="success-stylefont-size25pxfield-due-to-dipole-and-continous-charge-distributions--l-6-success-20"><Success style="font-size:25px;">Field due to Dipole and Continous Charge Distributions  L-6 </Success></h3>
<h3 id="primary-stylefont-size24pxline-charge-densityprimary"><primary style="font-size:24px;">Line Charge Density</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>Volume = Al</p>
</li>
<li>
<p><strong>Total charge</strong></p>
</li>
<li>
<p>$Q=\rho . A . l$ $=(\rho A)l$</p>
</li>
<li>
<p>$A \rightarrow 0, \rho \rightarrow \infty, \rho A = \lambda$</p>
</li>
</ul>
</div>
<div style='float: right; width:50%;'>

<p><img alt="alt text" src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/747875e1-c41b-4381-fbca-8a74dc6f0e00/public"></p>
</div>
</main>
<hr>
<footer style = "font-size: 18px"> Volume Charge Density $\rightarrow$ Surface Charge Density $\rightarrow$ <span style = "color:blue"> Line Charge Density </span> $\rightarrow$ Gauss's Law $\rightarrow$ Angle(Radian) </footer>

<h3 id="success-stylefont-size25pxfield-due-to-dipole-and-continous-charge-distributions--l-6-success-21"><Success style="font-size:25px;">Field due to Dipole and Continous Charge Distributions  L-6 </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>
<p>CARL FRIEDRICH GAUSS (1777-1855)</p>
</li>
<li>
<p>Gauss’s law for electricity states that the electric flux $\phi$ across any closed surface is proportional to the net electric charge q enclosed by the surface; that is, $\phi = \frac{q}{\epsilon_0}$, where $\epsilon_0$ is the electric permittivity of free space and has a value of $8.854 \times 10^{–12}$ square coulombs per newton per square metre.</p>
</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-02-chapter-06-field-due-to-dipole-and-continuous-charge-distributions-l-6_9-69fd7tbs0fq-0022.jpg"></p>
</div>
</main>
<hr>
<footer style = "font-size: 18px"> Surface Charge Density $\rightarrow$ Line Charge Density $\rightarrow$ <span style = "color:blue"> Gauss's Law </span> $\rightarrow$ Angle(Radian) $\rightarrow$ Solid Angle </footer>

<h3 id="success-stylefont-size25pxfield-due-to-dipole-and-continous-charge-distributions--l-6-success-22"><Success style="font-size:25px;">Field due to Dipole and Continous Charge Distributions  L-6 </Success></h3>
<h3 id="primary-stylefont-size24pxangleradianprimary"><primary style="font-size:24px;">Angle(Radian)</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>$\theta (radious) = \frac{l}{R}$</li>
</ul>
<ul>
<li>$l=2 \pi R$ $\quad \theta=2\pi$ radians</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px'>

<p><img alt="alt text" src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/2a37477f-be1d-4209-dde5-b4ae39550d00/public"></p>
</div>
</main>
<hr>
<footer style = "font-size: 18px"> Line Charge Density $\rightarrow$ Gauss's Law $\rightarrow$ <span style = "color:blue"> Angle(Radian) </span> $\rightarrow$ Solid Angle $\rightarrow$ Solid Angle </footer>

<h3 id="success-stylefont-size25pxfield-due-to-dipole-and-continous-charge-distributions--l-6-success-23"><Success style="font-size:25px;">Field due to Dipole and Continous Charge Distributions  L-6 </Success></h3>
<h3 id="primary-stylefont-size24pxsolid-angleprimary"><primary style="font-size:24px;">Solid Angle</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>Solid angle = $\frac{S}{R^2}$</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>

<p><img alt="alt text" src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/9a9818fa-dfa2-4fdf-0f47-c4da0177ff00/public"></p>
</div>
</main>
<hr>
<footer style = "font-size: 18px"> Gauss's Law $\rightarrow$ Angle(Radian) $\rightarrow$ <span style = "color:blue"> Solid Angle </span> $\rightarrow$ Solid Angle $\rightarrow$ Problem </footer>

<h3 id="success-stylefont-size25pxfield-due-to-dipole-and-continous-charge-distributions--l-6-success-24"><Success style="font-size:25px;">Field due to Dipole and Continous Charge Distributions  L-6 </Success></h3>
<h3 id="primary-stylefont-size24pxsolid-angleprimary-1"><primary style="font-size:24px;">Solid Angle</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>Solid angle subtended by sun on Earth $=\sim 6.8\times10^{-5}$</p>
</li>
<li>
<p>Solid angle subtended by moon on earth $= \sim 6.7 \times 10^{-5}$ steradian</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-02-chapter-06-field-due-to-dipole-and-continuous-charge-distributions-l-6_9-69fd7tbs0fq-0025.jpg"></p>
</div>
</main>
<hr>
<footer style = "font-size: 18px"> Angle(Radian) $\rightarrow$ Solid Angle $\rightarrow$ <span style = "color:blue"> Solid Angle </span> $\rightarrow$ Problem $\rightarrow$ Solid Angle </footer>

<h3 id="success-stylefont-size25pxfield-due-to-dipole-and-continous-charge-distributions--l-6-success-25"><Success style="font-size:25px;">Field due to Dipole and Continous Charge Distributions  L-6 </Success></h3>
<h3 id="primary-stylefont-size24pxproblemprimary"><primary style="font-size:24px;">Problem</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;font-size:30px;text-align:left;'>
<ul>
<li>To hold a small circular sheet of paper at a distance of 25 cm from my eyes. What is the radius of the circular piece of paper required to just block the moon</li>
</ul>
</div>
<div style='float: right; width:0%; max-width:400px;'>

</div>
</main>
<hr>
<footer style = "font-size: 18px"> Solid Angle $\rightarrow$ Solid Angle $\rightarrow$ <span style = "color:blue"> Problem </span> $\rightarrow$ Solid Angle $\rightarrow$ Solid Angle </footer>

<h3 id="success-stylefont-size25pxfield-due-to-dipole-and-continous-charge-distributions--l-6-success-26"><Success style="font-size:25px;">Field due to Dipole and Continous Charge Distributions  L-6 </Success></h3>
<h3 id="primary-stylefont-size24pxsolid-angleprimary-2"><primary style="font-size:24px;">Solid Angle</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>$d\Omega = \frac{\sqrt{1}}{R_1^2}=\frac{\sqrt{2}}{R_2^2}$</p>
</li>
<li>
<p>$\omega$ = Small omega</p>
</li>
<li>
<p>$\Omega$ = Capital omega</p>
</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>

<p><img alt="alt text" src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/11b177f0-36a2-4465-b1b7-3227a0a47f00/public"></p>
</div>
</main>
<hr>
<footer style = "font-size: 18px"> Solid Angle $\rightarrow$ Problem $\rightarrow$ <span style = "color:blue"> Solid Angle </span> $\rightarrow$ Solid Angle $\rightarrow$ Thank You </footer>

<h3 id="success-stylefont-size25pxfield-due-to-dipole-and-continous-charge-distributions--l-6-success-27"><Success style="font-size:25px;">Field due to Dipole and Continous Charge Distributions  L-6 </Success></h3>
<h3 id="primary-stylefont-size24pxsolid-angleprimary-3"><primary style="font-size:24px;">Solid Angle</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>$d\Omega=\frac{\sqrt{1}}{R_1^2}=\frac{\sqrt{2}}{R_2^2}$</p>
</li>
<li>
<p>$\sqrt{1}=R_1^2 d \Omega$</p>
</li>
<li>
<p>$\sqrt{2}=R_2^2 d \Omega$</p>
</li>
<li>
<p>$R_1$</p>
</li>
<li>
<p>$R_2$</p>
</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>

<p><img alt="alt text" src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/1955180d-1dad-469c-fbc1-ebb886139600/public"></p>
</div>
</main>
<hr>
<footer style = "font-size: 18px"> Problem $\rightarrow$ Solid Angle $\rightarrow$ <span style = "color:blue"> Solid Angle </span> $\rightarrow$ Thank You $\rightarrow$  </footer>