physics-class-12-unit-02-chapter-04-potential-due-to-different-charge-distributions-l-4-9-cy03rfcumn4

<h3 id="success-stylefont-size25px-potential-due-to-different-charge-distributions-l-4-success-1"><Success style="font-size:25px;"> Potential-Due-to-Different-Charge-Distributions L-4 </Success></h3>
<h3 id="primary-stylefont-size24pxelectrostatics-potential-energyprimary"><primary style="font-size:24px;">Electrostatics Potential Energy</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>Potential energy of a pair of point charges Q & q is $U=\frac{Qq}{4 \pi \epsilon_0 r}$</p>
</li>
<li>
<p>Potential energy of a system of charges</p>
</li>
<li>
<p>$U=\frac{q_1q_2}{4 \pi \epsilon_0 r_{12}}+\frac{q_1q_3}{4 \pi \epsilon_0 r_{13}}+\frac{q_2q_3}{4 \pi \epsilon_0 r_{23}}$</p>
</li>
</ul>
</div>
<div style='float: right; width:0%;'>
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<hr>
<footer style = "font-size: 18px">  $\rightarrow$ Potential due to Different Charge Distribution $\rightarrow$ <span style = "color:blue"> Electrostatics Potential Energy </span> $\rightarrow$ Electrostatics Potential $\rightarrow$ Work Done </footer>

<h3 id="success-stylefont-size25px-potential-due-to-different-charge-distributions-l-4-success-2"><Success style="font-size:25px;"> Potential-Due-to-Different-Charge-Distributions L-4 </Success></h3>
<h3 id="primary-stylefont-size24pxelectrostatics-potentialprimary"><primary style="font-size:24px;">Electrostatics Potential</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>Electrostatics potential for a point charge Q.</p>
</li>
<li>
<p>$V(r)=\frac{Q}{4 \pi \epsilon_0 r}$</p>
</li>
<li>
<p>V(r) is a scalar quantity.</p>
</li>
<li>
<p>$V\vec{(r)}$ and $\vec{E}\vec{(r)}$ are related.</p>
</li>
<li>
<p>Unit of potential 1 Volt = 1 J/C</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-04-potential-due-to-different-charge-distributions-l-4_9-cy03rfcumn4-002.jpg"></p>
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</main>
<hr>
<footer style = "font-size: 18px"> Potential due to Different Charge Distribution $\rightarrow$ Electrostatics Potential Energy $\rightarrow$ <span style = "color:blue"> Electrostatics Potential </span> $\rightarrow$ Work Done $\rightarrow$ Superposition Principle </footer>

<h3 id="success-stylefont-size25px-potential-due-to-different-charge-distributions-l-4-success-3"><Success style="font-size:25px;"> Potential-Due-to-Different-Charge-Distributions L-4 </Success></h3>
<h3 id="primary-stylefont-size24pxwork-doneprimary"><primary style="font-size:24px;">Work Done</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>Unit of energy : electron volt(eV)</p>
</li>
<li>
<p>$1eV=(1e)\times 1V=1.6 \times 10^{-19}J$</p>
</li>
<li>
<p>Work done by an external force in moving a unit charge from a point $r_i$ to $r_f$ is</p>
</li>
<li>
<p>$W=V(r_f)-V(r_i)$</p>
</li>
<li>
<p>For a point charge</p>
</li>
<li>
<p>$W=\frac{Q}{4 \pi \epsilon_0}(\frac{1}{r_f}-\frac{1}{r_i})$</p>
</li>
</ul>
</div>
<div style='float: right; width:0%;'>
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</div>
</main>
<hr>
<footer style = "font-size: 18px"> Electrostatics Potential Energy $\rightarrow$ Electrostatics Potential $\rightarrow$ <span style = "color:blue"> Work Done </span> $\rightarrow$ Superposition Principle $\rightarrow$ Potential Due to Conducting Sphere </footer>

<h3 id="success-stylefont-size25px-potential-due-to-different-charge-distributions-l-4-success-4"><Success style="font-size:25px;"> Potential-Due-to-Different-Charge-Distributions L-4 </Success></h3>
<h3 id="primary-stylefont-size24pxsuperposition-principleprimary"><primary style="font-size:24px;">Superposition Principle</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<p><strong>Superposition Principle</strong></p>
<ul>
<li>
<p>$V(r) = \frac{q_1}{4 \pi \epsilon_0 r_1}+\frac{q_2}{4 \pi \epsilon_0 r_2}+\frac{q_3}{4 \pi \epsilon_0 r_3}$</p>
</li>
<li>
<p>$= \sum\frac{q_i}{4 \pi \epsilon_0 r_i}$</p>
</li>
</ul>
<p><strong>Distribution of charges</strong></p>
<ul>
<li>$V(r)=\frac{1}{4 \pi \epsilon_0}\int\frac{dq}{r^1}$</li>
</ul>
</div>
<div style='float: right; width:50%;'>

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<hr>
<footer style = "font-size: 18px"> Electrostatics Potential $\rightarrow$ Work Done $\rightarrow$ <span style = "color:blue"> Superposition Principle </span> $\rightarrow$ Potential Due to Conducting Sphere $\rightarrow$ Potential Due to Conducting Sphere </footer>

<h3 id="success-stylefont-size25px-potential-due-to-different-charge-distributions-l-4-success-5"><Success style="font-size:25px;"> Potential-Due-to-Different-Charge-Distributions L-4 </Success></h3>
<h3 id="primary-stylefont-size24pxpotential-due-to-conducting-sphereprimary"><primary style="font-size:24px;">Potential Due to Conducting Sphere</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;font-size:30px;text-align:left;'>
<p><strong>Potential of a charged conducting sphere-</strong></p>
<ul>
<li>
<p>$\vec{E}=\frac{Q \hat{r}}{4 \pi \epsilon_0 r^2},r>R$ = 0, r<R</p>
</li>
<li>
<p>V(r) = $\int_\infty^r$ $\vec{F}_{enc}$ . $d\vec{r}$</p>
</li>
<li>
<p>$ = -\frac{Q}{4 \pi \epsilon_0}$</p>
</li>
<li>
<p>$\int_\infty^r \frac{dr}{r^2}$</p>
</li>
<li>
<p>$= \frac{Q}{4 \pi \epsilon_0 r}$ r>R</p>
</li>
<li>
<p>$V(R) = \frac{Q}{4 \pi \epsilon_0 R}$ at r=R</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-04-potential-due-to-different-charge-distributions-l-4_9-cy03rfcumn4-005.jpg"></p>
</main>
<hr>
<footer style = "font-size: 18px"> Work Done $\rightarrow$ Superposition Principle $\rightarrow$ <span style = "color:blue"> Potential Due to Conducting Sphere </span> $\rightarrow$ Potential Due to Conducting Sphere $\rightarrow$ Example </footer>

<h3 id="success-stylefont-size25px-potential-due-to-different-charge-distributions-l-4-success-6"><Success style="font-size:25px;"> Potential-Due-to-Different-Charge-Distributions L-4 </Success></h3>
<h3 id="primary-stylefont-size24pxpotential-due-to-conducting-sphereprimary-1"><primary style="font-size:24px;">Potential Due to Conducting Sphere</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;'>

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<hr>
<footer style = "font-size: 18px"> Superposition Principle $\rightarrow$ Potential Due to Conducting Sphere $\rightarrow$ <span style = "color:blue"> Potential Due to Conducting Sphere </span> $\rightarrow$ Example $\rightarrow$ Example </footer>

<h3 id="success-stylefont-size25px-potential-due-to-different-charge-distributions-l-4-success-7"><Success style="font-size:25px;"> Potential-Due-to-Different-Charge-Distributions L-4 </Success></h3>
<h3 id="primary-stylefont-size24pxexampleprimary"><primary style="font-size:24px;">Example</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<p><strong>Conducting sphere of radius R = 10cm = 0.1m</strong></p>
<ul>
<li>
<p>$Q = 1nC=10^{-9}C$</p>
</li>
<li>
<p>$V=\frac{Q}{4 \pi \epsilon_0 R}=\frac{10^{-9}\times9\times10^9}{0.1}=90V$</p>
</li>
<li>
<p>$E=\frac{Q}{4 \pi \epsilon_0 R^2}=\frac{V}{R}=\frac{90}{0.1}=900V/m$</p>
</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:450px;'>

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<footer style = "font-size: 18px"> Potential Due to Conducting Sphere $\rightarrow$ Potential Due to Conducting Sphere $\rightarrow$ <span style = "color:blue"> Example </span> $\rightarrow$ Example $\rightarrow$ Potential Due to a Dipole </footer>

<h3 id="success-stylefont-size25px-potential-due-to-different-charge-distributions-l-4-success-8"><Success style="font-size:25px;"> Potential-Due-to-Different-Charge-Distributions L-4 </Success></h3>
<h3 id="primary-stylefont-size24pxexampleprimary-1"><primary style="font-size:24px;">Example</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>$E_{max}=3\times10^6V/m$ in out</p>
</li>
<li>
<p>R = 0.1m</p>
</li>
</ul>
<p><strong>Maximum Potential</strong></p>
<ul>
<li>
<p>$V_{max} = E_{max} R$ $=3\times10^6\times0.1=3\times10^5V$ = 300 kV</p>
</li>
<li>
<p>R = 1cm = 0.01m</p>
</li>
<li>
<p>$V_{max}=300kV$</p>
</li>
</ul>
</div>
<div style='float: right; width:0%;'>
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<hr>
<footer style = "font-size: 18px"> Potential Due to Conducting Sphere $\rightarrow$ Example $\rightarrow$ <span style = "color:blue"> Example </span> $\rightarrow$ Potential Due to a Dipole $\rightarrow$ Potential Due to a Dipole </footer>

<h3 id="success-stylefont-size25px-potential-due-to-different-charge-distributions-l-4-success-9"><Success style="font-size:25px;"> Potential-Due-to-Different-Charge-Distributions L-4 </Success></h3>
<h3 id="primary-stylefont-size24pxpotential-due-to-a-dipoleprimary"><primary style="font-size:24px;">Potential Due to a Dipole</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>$V(P)=\frac{q}{4 \pi \epsilon_0 r_1}-\frac{q}{4 \pi \epsilon_0 r_2}$</p>
</li>
<li>
<p>$=\frac{q}{4 \pi \epsilon_0}(\frac{1}{r_1}-\frac{1}{r_2})$</p>
</li>
<li>
<p>$r_1^2 = r^2+a^2-2ar\cos\theta$</p>
</li>
<li>
<p>$2_2^2=r^2+a^2+2ar\cos\theta$</p>
</li>
</ul>
</div>
<div style='float: right; width:50%;'>

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<hr>
<footer style = "font-size: 18px"> Example $\rightarrow$ Example $\rightarrow$ <span style = "color:blue"> Potential Due to a Dipole </span> $\rightarrow$ Potential Due to a Dipole $\rightarrow$ Potential Due to a Dipole </footer>

<h3 id="success-stylefont-size25px-potential-due-to-different-charge-distributions-l-4-success-10"><Success style="font-size:25px;"> Potential-Due-to-Different-Charge-Distributions L-4 </Success></h3>
<h3 id="primary-stylefont-size24pxpotential-due-to-a-dipoleprimary-1"><primary style="font-size:24px;">Potential Due to a Dipole</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>$r_1^2=r^2+a^2-2ar\cos\theta$ $=r^2(1+\frac{a^2}{r^2}-\frac{2a}{r}\cos\theta)$</p>
</li>
<li>
<p>$r_1=r(1+\frac{a^2}{r^2}-\frac{2a}{r}\cos\theta)^{1/2}$</p>
</li>
<li>
<p>$\frac{1}{r_1}=\frac{1}{r}(1+\frac{a^2}{r^2}-\frac{2a}{r}\cos\theta)^{-1/2}$</p>
</li>
<li>
<p>r » a</p>
</li>
<li>
<p>$\frac{1}{r_1}\simeq\frac{1}{r}(1+\frac{a}{r}\cos\theta)$</p>
</li>
<li>
<p>Negative terms of order $\frac{a^2}{r^2}$ and greater.</p>
</li>
</ul>
</div>
<div style='float: right; width:0%;'>
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<hr>
<footer style = "font-size: 18px"> Example $\rightarrow$ Potential Due to a Dipole $\rightarrow$ <span style = "color:blue"> Potential Due to a Dipole </span> $\rightarrow$ Potential Due to a Dipole $\rightarrow$ Potential Due to a Dipole </footer>

<h3 id="success-stylefont-size25px-potential-due-to-different-charge-distributions-l-4-success-11"><Success style="font-size:25px;"> Potential-Due-to-Different-Charge-Distributions L-4 </Success></h3>
<h3 id="primary-stylefont-size24pxpotential-due-to-a-dipoleprimary-2"><primary style="font-size:24px;">Potential Due to a Dipole</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>$r_2^2=r^2+a^2+2ar\cos\theta$</p>
</li>
<li>
<p>$\frac{1}{r_2}\simeq\frac{1}{r}(1-\frac{a}{r}\cos\theta)$</p>
</li>
<li>
<p>$\frac{1}{r_1}-\frac{1}{r_2}\simeq\frac{2a}{r^2}\cos\theta$</p>
</li>
<li>
<p>$V(P)=\frac{q}{4 \pi \epsilon_0}.\frac{2a}{r^2}\cos\theta$</p>
</li>
<li>
<p>$\vec{|p|}=q.2q$</p>
</li>
<li>
<p>$V(P)=\frac{\vec{|p|}\cos\theta}{4 \pi \epsilon_0 r^2}=\frac{\vec{p}.\hat{g}}{4 \pi \epsilon_0 r^2}$</p>
</li>
</ul>
</div>
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<footer style = "font-size: 18px"> Potential Due to a Dipole $\rightarrow$ Potential Due to a Dipole $\rightarrow$ <span style = "color:blue"> Potential Due to a Dipole </span> $\rightarrow$ Potential Due to a Dipole $\rightarrow$ Potential of an Infinite Linear Charge Density </footer>

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<h3 id="primary-stylefont-size24pxpotential-due-to-a-dipoleprimary-3"><primary style="font-size:24px;">Potential Due to a Dipole</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>$V(r)=\frac{\vec{p}.\hat{r}}{4 \pi \epsilon_0 r^2}$r»a</p>
</li>
<li>
<p>$V(r)=\frac{P\cos\theta}{4 \pi \epsilon_0 r^2}$</p>
</li>
<li>
<p>$\theta=0;V(r)=\frac{p}{4 \pi \epsilon_0 r^2}$</p>
</li>
<li>
<p>$\theta=\pi;V(r)=-\frac{p}{4 \pi \epsilon_0 r^2}$</p>
</li>
<li>
<p>$\theta=\frac{\pi}{2};V(r)=0$</p>
</li>
</ul>
</div>
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<footer style = "font-size: 18px"> Potential Due to a Dipole $\rightarrow$ Potential Due to a Dipole $\rightarrow$ <span style = "color:blue"> Potential Due to a Dipole </span> $\rightarrow$ Potential of an Infinite Linear Charge Density $\rightarrow$ Potential of an Infinite Linear Charge Density </footer>

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<h3 id="primary-stylefont-size24pxpotential-of-an-infinite-linear-charge-densityprimary"><primary style="font-size:24px;">Potential of an Infinite Linear Charge Density</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>$2 \pi r.l.E=\frac{\lambda l}{\epsilon_0}$</p>
</li>
<li>
<p>$\vec{E}=\frac{\lambda}{2\pi\epsilon_0r}.\hat{r}$</p>
</li>
<li>
<p>$W=-int_{r_a}^{r_b}\frac{\lambda \hat{r}}{2 \pi \epsilon_0 r}.\hat{r}dr$</p>
</li>
<li>
<p>$=-\frac{\lambda}{2 \pi \epsilon_0}\int_{r_a}^{r_b}\frac{dr}{r}=\frac{\lambda}{2 \pi \epsilon_0}ln(\frac{r_a}{r_b})$</p>
</li>
</ul>
</div>
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<hr>
<footer style = "font-size: 18px"> Potential Due to a Dipole $\rightarrow$ Potential Due to a Dipole $\rightarrow$ <span style = "color:blue"> Potential of an Infinite Linear Charge Density </span> $\rightarrow$ Potential of an Infinite Linear Charge Density $\rightarrow$ Equipotential Surfaces </footer>

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<h3 id="primary-stylefont-size24pxpotential-of-an-infinite-linear-charge-densityprimary-1"><primary style="font-size:24px;">Potential of an Infinite Linear Charge Density</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>Zero of potential at same r value</p>
</li>
<li>
<p>Let V=0 at $r=r_a=R$ and let $r_b=r$</p>
</li>
<li>
<p>$V(r)=\frac{\lambda}{2 \pi \epsilon_0}ln(\frac{R}{r})$</p>
</li>
</ul>
</div>
<div style='float: right; width:0%;'>
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<hr>
<footer style = "font-size: 18px"> Potential Due to a Dipole $\rightarrow$ Potential of an Infinite Linear Charge Density $\rightarrow$ <span style = "color:blue"> Potential of an Infinite Linear Charge Density </span> $\rightarrow$ Equipotential Surfaces $\rightarrow$ Uniform Electric Field </footer>

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<h3 id="primary-stylefont-size24pxequipotential-surfacesprimary"><primary style="font-size:24px;">Equipotential Surfaces</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>$V=\frac{Q}{4 \pi \epsilon_0 r}$</p>
</li>
<li>
<p>$r=r_1 ; V=V_1=\frac{Q}{4 \pi \epsilon_0 r_1}$</p>
</li>
<li>
<p>$r=r_2;v=v_2=\frac{Q}{4 \pi \epsilon_0 r_2}$</p>
</li>
<li>
<p>$r_2>r_1$</p>
</li>
<li>
<p>What about if</p>
</li>
<li>
<p>$v_2>v_1$ and $v_1>v_2?$</p>
</li>
</ul>
</div>
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<hr>
<footer style = "font-size: 18px"> Potential of an Infinite Linear Charge Density $\rightarrow$ Potential of an Infinite Linear Charge Density $\rightarrow$ <span style = "color:blue"> Equipotential Surfaces </span> $\rightarrow$ Uniform Electric Field $\rightarrow$ Equipotentials of Point Charge </footer>

<h3 id="success-stylefont-size25px-potential-due-to-different-charge-distributions-l-4-success-16"><Success style="font-size:25px;"> Potential-Due-to-Different-Charge-Distributions L-4 </Success></h3>
<h3 id="primary-stylefont-size24pxuniform-electric-fieldprimary"><primary style="font-size:24px;">Uniform Electric Field</primary></h3>
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<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>$\vec{E}=E_0\hat{k}$</li>
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<footer style = "font-size: 18px"> Potential of an Infinite Linear Charge Density $\rightarrow$ Equipotential Surfaces $\rightarrow$ <span style = "color:blue"> Uniform Electric Field </span> $\rightarrow$ Equipotentials of Point Charge $\rightarrow$ Equipotentials of a Dipole </footer>

<h3 id="success-stylefont-size25px-potential-due-to-different-charge-distributions-l-4-success-17"><Success style="font-size:25px;"> Potential-Due-to-Different-Charge-Distributions L-4 </Success></h3>
<h3 id="primary-stylefont-size24pxequipotentials-of-point-chargeprimary"><primary style="font-size:24px;">Equipotentials of Point Charge</primary></h3>
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<footer style = "font-size: 18px"> Equipotential Surfaces $\rightarrow$ Uniform Electric Field $\rightarrow$ <span style = "color:blue"> Equipotentials of Point Charge </span> $\rightarrow$ Equipotentials of a Dipole $\rightarrow$ Electric Field and Potential </footer>

<h3 id="success-stylefont-size25px-potential-due-to-different-charge-distributions-l-4-success-18"><Success style="font-size:25px;"> Potential-Due-to-Different-Charge-Distributions L-4 </Success></h3>
<h3 id="primary-stylefont-size24pxequipotentials-of-a-dipoleprimary"><primary style="font-size:24px;">Equipotentials of a Dipole</primary></h3>
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<footer style = "font-size: 18px"> Uniform Electric Field $\rightarrow$ Equipotentials of Point Charge $\rightarrow$ <span style = "color:blue"> Equipotentials of a Dipole </span> $\rightarrow$ Electric Field and Potential $\rightarrow$ Electric Field and Potential </footer>

<h3 id="success-stylefont-size25px-potential-due-to-different-charge-distributions-l-4-success-19"><Success style="font-size:25px;"> Potential-Due-to-Different-Charge-Distributions L-4 </Success></h3>
<h3 id="primary-stylefont-size24pxelectric-field-and-potentialprimary"><primary style="font-size:24px;">Electric Field and Potential</primary></h3>
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<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>Consider two adjacent equipotentials surfaces</p>
</li>
<li>
<p>Work done by the external force in moving a unit charge from point A to point B</p>
</li>
<li>
<p>$dW=(v_0+dv)-v_0$ = dv</p>
</li>
<li>
<p>Work done in also given by $-\vec{E}.\vec{dl}$ $=-Edl\cos \theta$</p>
</li>
</ul>
</div>
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<hr>
<footer style = "font-size: 18px"> Equipotentials of Point Charge $\rightarrow$ Equipotentials of a Dipole $\rightarrow$ <span style = "color:blue"> Electric Field and Potential </span> $\rightarrow$ Electric Field and Potential $\rightarrow$ Potential of a Pair Charge </footer>

<h3 id="success-stylefont-size25px-potential-due-to-different-charge-distributions-l-4-success-21"><Success style="font-size:25px;"> Potential-Due-to-Different-Charge-Distributions L-4 </Success></h3>
<h3 id="primary-stylefont-size24pxpotential-of-a-pair-chargeprimary"><primary style="font-size:24px;">Potential of a Pair Charge</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>$V(r)=\frac{Q}{4 \pi \epsilon_0 r}$</p>
</li>
<li>
<p>$=\frac{Q}{4 \pi \epsilon_0(x^2+y^2+z^2)^{1/2}}$</p>
</li>
<li>
<p>$E_x=-\frac{dv}{dx}=-\frac{Q(-1/2).2x}{4 \pi \epsilon_0 (x^2+y^2+z^2)^{3/2}}$</p>
</li>
<li>
<p>$=\frac{Q}{4 \pi \epsilon_0 (x^2+y^2+z^2)}\frac{x}{\sqrt{x^2+y^2+z^2}}$</p>
</li>
<li>
<p>$=\frac{Q}{4 \pi \epsilon_0r^2}(\frac{x}{r})$</p>
</li>
</ul>
</div>
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<footer style = "font-size: 18px"> Electric Field and Potential $\rightarrow$ Electric Field and Potential $\rightarrow$ <span style = "color:blue"> Potential of a Pair Charge </span> $\rightarrow$ Problem $\rightarrow$ Thankyou </footer>

<h3 id="success-stylefont-size25px-potential-due-to-different-charge-distributions-l-4-success-22"><Success style="font-size:25px;"> Potential-Due-to-Different-Charge-Distributions L-4 </Success></h3>
<h3 id="primary-stylefont-size24pxproblemprimary"><primary style="font-size:24px;">Problem</primary></h3>
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<main>
<div style='float: left; width:100%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>An electric dipole of moment $\vec{p}=10\hat{k}nC.m$ is located at the origin in force sphere. Calculate the potential or a point P with coordinates.</p>
</li>
<li>
<p>$x_P=0.5m$</p>
</li>
<li>
<p>$y_p=0$</p>
</li>
<li>
<p>$z_P=0.87m$</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-04-potential-due-to-different-charge-distributions-l-4_9-cy03rfcumn4-0023.jpg"></p>
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<hr>
<footer style = "font-size: 18px"> Electric Field and Potential $\rightarrow$ Potential of a Pair Charge $\rightarrow$ <span style = "color:blue"> Problem </span> $\rightarrow$ Thankyou $\rightarrow$ </footer>