physics-class-12-unit-02-chapter-05-electrostatic-potential-and-potential-energy-l-5-9-s0r7m46rqt4

<h3 id="success-stylefont-size25px-electrostatic-potential-and-potential-energy--l-5-success"><Success style="font-size:25px;"> Electrostatic Potential and Potential Energy  L-5 </Success></h3>
<h3 id="primary-stylefont-size24pxelectrostatic-potential-and-potential-energyprimary"><primary style="font-size:24px;">Electrostatic Potential and Potential Energy</primary></h3>
<hr>
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<div style='float: left; width:100%;text-align:left;font-size:30px;'>
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<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-05-electrostatic-potential-and-potential-energy-l-5_9-s0r7m46rqt4-014-0027.6.jpg"></p>
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<footer style = "font-size: 18px">  $\rightarrow$  $\rightarrow$ <span style = "color:blue"> Electrostatic Potential and Potential Energy </span> $\rightarrow$ Electrostatic Potential Energy $\rightarrow$ Electrostatic Potential Energy </footer>

<h3 id="success-stylefont-size25px-electrostatic-potential-and-potential-energy--l-5-success-1"><Success style="font-size:25px;"> Electrostatic Potential and Potential Energy  L-5 </Success></h3>
<h3 id="primary-stylefont-size24pxelectrostatic-potential-energyprimary"><primary style="font-size:24px;">Electrostatic Potential Energy</primary></h3>
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<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$ \vec{E}=-E_0 \hat{\imath} $</p>
</li>
<li>
<p>$ \vec{F}_{el}=-q E_0 \hat{c} $</p>
</li>
<li>
<p>$ \vec F_{ext} = -\vec F_{el} = q E_0 \hat{i} $</p>
</li>
<li>
<p>$ \vec l = (x_{f}-x_{i}) \hat i $</p>
</li>
</ul>
<ul>
<li>Work done by the external force on the charge $=\vec{F}_{ext } \cdot \vec{l}$</li>
</ul>
<ul>
<li>$ =q E_0\left(x_{f}-x_i\right)$ $ =q E_0 h$</li>
</ul>
</div>
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<footer style = "font-size: 18px">  $\rightarrow$ Electrostatic Potential and Potential Energy $\rightarrow$ <span style = "color:blue"> Electrostatic Potential Energy </span> $\rightarrow$ Electrostatic Potential Energy $\rightarrow$ Energy </footer>

<h3 id="success-stylefont-size25px-electrostatic-potential-and-potential-energy--l-5-success-2"><Success style="font-size:25px;"> Electrostatic Potential and Potential Energy  L-5 </Success></h3>
<h3 id="primary-stylefont-size24pxelectrostatic-potential-energyprimary-1"><primary style="font-size:24px;">Electrostatic Potential Energy</primary></h3>
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<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$ \vec{E}=-E_0 \hat{\imath} $</p>
</li>
<li>
<p>$ \vec{F}_{el}=-q E_0 \hat{c} $</p>
</li>
<li>
<p>$ \vec F_{ext} = -\vec F_{el} = q E_0 \hat{i} $</p>
</li>
<li>
<p>$ \vec l = (x_{f}-x_{i}) \hat i $</p>
</li>
</ul>
<ul>
<li>Work done by the external force on the charge $=\vec{F}_{ext } \cdot \vec{l}$</li>
</ul>
<ul>
<li>$ =q E_0\left(x_{f}-x_i\right)$ $ =q E_0 h$</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>
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<footer style = "font-size: 18px"> Electrostatic Potential and Potential Energy $\rightarrow$ Electrostatic Potential Energy $\rightarrow$ <span style = "color:blue"> Electrostatic Potential Energy </span> $\rightarrow$ Energy $\rightarrow$ Energy </footer>

<h3 id="success-stylefont-size25px-electrostatic-potential-and-potential-energy--l-5-success-3"><Success style="font-size:25px;"> Electrostatic Potential and Potential Energy  L-5 </Success></h3>
<h3 id="primary-stylefont-size24pxenergyprimary"><primary style="font-size:24px;">Energy</primary></h3>
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<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>W = q $E_0$ h > 0</li>
</ul>
<ul>
<li>
<p>Initial energy : $U_i$</p>
</li>
<li>
<p>Final energy : $U_f$</p>
</li>
</ul>
</div>
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<footer style = "font-size: 18px"> Electrostatic Potential Energy $\rightarrow$ Electrostatic Potential Energy $\rightarrow$ <span style = "color:blue"> Energy </span> $\rightarrow$ Energy $\rightarrow$ Work Done </footer>

<h3 id="success-stylefont-size25px-electrostatic-potential-and-potential-energy--l-5-success-4"><Success style="font-size:25px;"> Electrostatic Potential and Potential Energy  L-5 </Success></h3>
<h3 id="primary-stylefont-size24pxenergyprimary-1"><primary style="font-size:24px;">Energy</primary></h3>
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<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>W = q $E_0$ h < 0</li>
</ul>
<ul>
<li>
<p>Initial energy : $U_i$</p>
</li>
<li>
<p>Final energy : $U_f$</p>
</li>
</ul>
<ul>
<li>$U_f$ < $U_i$, $U_f$ > $U_i$</li>
</ul>
<ul>
<li>Similar figure for $\vec E $ pointing upwards.</li>
</ul>
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<footer style = "font-size: 18px"> Electrostatic Potential Energy $\rightarrow$ Energy $\rightarrow$ <span style = "color:blue"> Energy </span> $\rightarrow$ Work Done $\rightarrow$ Work Done </footer>

<h3 id="success-stylefont-size25px-electrostatic-potential-and-potential-energy--l-5-success-5"><Success style="font-size:25px;"> Electrostatic Potential and Potential Energy  L-5 </Success></h3>
<h3 id="primary-stylefont-size24pxwork-doneprimary"><primary style="font-size:24px;">Work Done</primary></h3>
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<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>Path 1</p>
</li>
<li>
<p>$A \rightarrow  c$</p>
</li>
<li>
<p>$ \vec{E}=-E_0 \hat{i} $</p>
</li>
<li>
<p>$\overrightarrow{\mathrm{l}} =\left(z_f-z_2\right) \hat{k}$</p>
</li>
</ul>
</div>
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<footer style = "font-size: 18px"> Energy $\rightarrow$ Energy $\rightarrow$ <span style = "color:blue"> Work Done </span> $\rightarrow$ Work Done $\rightarrow$ Total Work Done </footer>

<h3 id="success-stylefont-size25px-electrostatic-potential-and-potential-energy--l-5-success-6"><Success style="font-size:25px;"> Electrostatic Potential and Potential Energy  L-5 </Success></h3>
<h3 id="primary-stylefont-size24pxwork-doneprimary-1"><primary style="font-size:24px;">Work Done</primary></h3>
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<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>Work done in moving the charge from A to C</li>
</ul>
<ul>
<li>
<p>= $\vec F_{ext} \vec{l}$ = -$F_{el} \cdot \vec {l} $</p>
</li>
<li>
<p>= +q $E_0 \hat{\imath} \cdot \left(z_f-z_i\right) \hat{k}$</p>
</li>
<li>
<p>= 0 $c+B \quad$ Work done $ = q E_0\left(x_f-x_i\right)$</p>
</li>
</ul>
</div>
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<footer style = "font-size: 18px"> Energy $\rightarrow$ Work Done $\rightarrow$ <span style = "color:blue"> Work Done </span> $\rightarrow$ Total Work Done $\rightarrow$ Topic </footer>

<h3 id="success-stylefont-size25px-electrostatic-potential-and-potential-energy--l-5-success-7"><Success style="font-size:25px;"> Electrostatic Potential and Potential Energy  L-5 </Success></h3>
<h3 id="primary-stylefont-size24pxtotal-work-doneprimary"><primary style="font-size:24px;">Total Work Done</primary></h3>
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<main>
<div style='float: left; width:100%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>Total work done = q $E_0 (x_f - x_i)$</p>
</li>
<li>
<p>Path 2 - A $\rightarrow $ D     work done q $E_0 (x_f - x_i)$</p>
</li>
<li>
<p>D $\rightarrow $ B work done = 0</p>
</li>
</ul>
<ul>
<li>Total work done by the external force in moving from A to B via D = q $E_0 (x_f - x_i)$</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-05-electrostatic-potential-and-potential-energy-l-5_9-s0r7m46rqt4-005.jpg">
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<footer style = "font-size: 18px"> Work Done $\rightarrow$ Work Done $\rightarrow$ <span style = "color:blue"> Total Work Done </span> $\rightarrow$ Topic $\rightarrow$ Example </footer>

<h3 id="success-stylefont-size25px-electrostatic-potential-and-potential-energy--l-5-success-8"><Success style="font-size:25px;"> Electrostatic Potential and Potential Energy  L-5 </Success></h3>
<h3 id="primary-stylefont-size24pxtopicprimary"><primary style="font-size:24px;">Topic</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>Path 3 -$ \vec{l}=\left(x_f-x_i\right) \hat{\imath}+\left(z_f-z_i\right) \hat{k}$</p>
</li>
<li>
<p>$ \vec F_{ext}$ = $-\vec F_{e l} = q E_0 \hat{i} $ (Conservative Force)</p>
</li>
<li>
<p>Work done = $\overrightarrow{F_{ext}} \cdot \vec{l} $</p>
</li>
<li>
<p>$ =q E_0 \hat{\imath} \cdot\left[\left(x_f-x_i\right) \hat{\imath}+\left(z_f-z_i\right) \hat{k}\right] $ $=q E_0\left(x_f-x_i\right)$</p>
</li>
</ul>
<ul>
<li>Work done is independent of pair followed</li>
</ul>
<p><span style="color:green"></span></p>
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<hr>
<footer style = "font-size: 18px"> Work Done $\rightarrow$ Total Work Done $\rightarrow$ <span style = "color:blue"> Topic </span> $\rightarrow$ Example $\rightarrow$ Work Done by External Force </footer>

<h3 id="success-stylefont-size25px-electrostatic-potential-and-potential-energy--l-5-success-9"><Success style="font-size:25px;"> Electrostatic Potential and Potential Energy  L-5 </Success></h3>
<h3 id="primary-stylefont-size24pxexampleprimary"><primary style="font-size:24px;">Example</primary></h3>
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<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>Point charge Q</p>
</li>
<li>
<p>$\vec{F}_{\text {el}} = q \vec{E}$ $ =-\frac{q Q}{4 \pi E_0 r^2} \hat{r} $</p>
</li>
<li>
<p>$\vec f_{ext} =  \vec f_{el}$ $ =-\frac{q Q}{4 \pi E_0 r^2} \hat{r} $</p>
</li>
<li>
<p>Work done = $\int^{r_f}_{r_i} \vec F .\vec {dl}$</p>
</li>
<li>
<p>$\vec {dl} = d \vec{r}$ = $\hat r .d r $</p>
</li>
</ul>
</div>
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<footer style = "font-size: 18px"> Total Work Done $\rightarrow$ Topic $\rightarrow$ <span style = "color:blue"> Example </span> $\rightarrow$ Work Done by External Force $\rightarrow$ Work Done </footer>

<h3 id="success-stylefont-size25px-electrostatic-potential-and-potential-energy--l-5-success-10"><Success style="font-size:25px;"> Electrostatic Potential and Potential Energy  L-5 </Success></h3>
<h3 id="primary-stylefont-size24pxwork-done-by-external-forceprimary"><primary style="font-size:24px;">Work Done by External Force</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>Work done by external force $=\int_{r_i}^{r_f} F_{ext} \cdot \overrightarrow{dl} $</p>
</li>
<li>
<p>$ =\int_{r_i}^{r_f}\left(-\frac{q Q}{4 \pi E_0 r^2} \hat{r}\right) \cdot d r \hat{r} $</p>
</li>
<li>
<p>$ =-\frac{q Q}{4 \pi E_0} \int_{r_i}^{r_f} \frac{d r}{r^2} $</p>
</li>
<li>
<p>$ =-\left.\frac{q Q}{4 \pi E_0}\left(-\frac{1}{r}\right)\right|_{r_i} ^{r_f} $</p>
</li>
<li>
<p>$ =\frac{q Q}{4 \pi E_0}\left(\frac{1}{r_f}-\frac{1}{r_i}\right) $</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-05-electrostatic-potential-and-potential-energy-l-5_9-s0r7m46rqt4-008.jpg"></p>
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<hr>
<footer style = "font-size: 18px"> Topic $\rightarrow$ Example $\rightarrow$ <span style = "color:blue"> Work Done by External Force </span> $\rightarrow$ Work Done $\rightarrow$ Work Done </footer>

<h3 id="success-stylefont-size25px-electrostatic-potential-and-potential-energy--l-5-success-11"><Success style="font-size:25px;"> Electrostatic Potential and Potential Energy  L-5 </Success></h3>
<h3 id="primary-stylefont-size24pxwork-doneprimary-2"><primary style="font-size:24px;">Work Done</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$U_B < U_A$</p>
</li>
<li>
<p>Work done $=\frac{q Q}{4 \pi E_0}\left(\frac{1}{r_f}-\frac{1}{r_i}\right)$</p>
</li>
<li>
<p>q & Q both +ve</p>
</li>
<li>
<p>$(r_f > r_i)$</p>
</li>
<li>
<p>Work done $<0$</p>
</li>
<li>
<p>Work done = $ \frac{(-q) Q}{4 \pi E_0}\left(\frac{1}{r_f}-\frac{1}{r_i}\right) $</p>
</li>
<li>
<p>$ U_B > U_A $</p>
</li>
</ul>
</div>
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<hr>
<footer style = "font-size: 18px"> Example $\rightarrow$ Work Done by External Force $\rightarrow$ <span style = "color:blue"> Work Done </span> $\rightarrow$ Work Done $\rightarrow$ Work Done </footer>

<h3 id="success-stylefont-size25px-electrostatic-potential-and-potential-energy--l-5-success-12"><Success style="font-size:25px;"> Electrostatic Potential and Potential Energy  L-5 </Success></h3>
<h3 id="primary-stylefont-size24pxwork-doneprimary-3"><primary style="font-size:24px;">Work Done</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$\frac{q Q}{4 \pi E_0}\left(\frac{1}{r_f}-\frac{1}{r_i}\right)$</p>
</li>
<li>
<p>Path independence</p>
</li>
</ul>
</div>
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<hr>
<footer style = "font-size: 18px"> Work Done by External Force $\rightarrow$ Work Done $\rightarrow$ <span style = "color:blue"> Work Done </span> $\rightarrow$ Work Done $\rightarrow$ Work Done </footer>

<h3 id="success-stylefont-size25px-electrostatic-potential-and-potential-energy--l-5-success-13"><Success style="font-size:25px;"> Electrostatic Potential and Potential Energy  L-5 </Success></h3>
<h3 id="primary-stylefont-size24pxwork-doneprimary-4"><primary style="font-size:24px;">Work Done</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$\int \vec{F}_{ext} \cdot \overrightarrow{d l}$</p>
</li>
<li>
<p>=$\int_{A_{C_1}}^{B} \vec{F}_{ext} \cdot \overrightarrow{d l}$</p>
</li>
<li>
<p>$+\int_{B_{c_2}}^{A} \vec{F}_{ext} \cdot \overrightarrow{d l}$</p>
</li>
<li>
<p>$\int_{A_{C_1}}^{B} \vec{F}_{ext} \cdot \overrightarrow{d l}$</p>
</li>
<li>
<p>=$\int_{A_{C_2}}^{B} \vec{F}_{ext} \cdot \overrightarrow{d l}$</p>
</li>
<li>
<p>=$-\int_{B_{c_2}}^{A} \vec{F}_{ext} \cdot \overrightarrow{d l}$</p>
</li>
</ul>
</div>
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<hr>
<footer style = "font-size: 18px"> Work Done $\rightarrow$ Work Done $\rightarrow$ <span style = "color:blue"> Work Done </span> $\rightarrow$ Work Done $\rightarrow$ Electrostatic Potential Energy </footer>

<h3 id="success-stylefont-size25px-electrostatic-potential-and-potential-energy--l-5-success-14"><Success style="font-size:25px;"> Electrostatic Potential and Potential Energy  L-5 </Success></h3>
<h3 id="primary-stylefont-size24pxwork-doneprimary-5"><primary style="font-size:24px;">Work Done</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;text-align:left;font-size:30px;'>
<ul>
<li>$\oint \vec{F}_{ext} \cdot \overrightarrow{d l}$</li>
</ul>
<ul>
<li>Not work done in a closed path = 0</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-05-electrostatic-potential-and-potential-energy-l-5_9-s0r7m46rqt4-0012.jpg"></p>
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<hr>
<footer style = "font-size: 18px"> Work Done $\rightarrow$ Work Done $\rightarrow$ <span style = "color:blue"> Work Done </span> $\rightarrow$ Electrostatic Potential Energy
 $\rightarrow$ Potential Energy </footer>

<h3 id="success-stylefont-size25px-electrostatic-potential-and-potential-energy--l-5-success-15"><Success style="font-size:25px;"> Electrostatic Potential and Potential Energy  L-5 </Success></h3>
<h3 id="primary-stylefont-size24pxelectrostatic-potential-energyprimary-2"><primary style="font-size:24px;">Electrostatic Potential Energy</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>Work done by external force = $\frac{q Q}{4 \pi E_0}\left(\frac{1}{r_f}-\frac{1}{r_i}\right)$</p>
</li>
<li>
<p>Reference point r = $\infty$</p>
</li>
</ul>
<ul>
<li>Zero of potential energy</li>
</ul>
<ul>
<li>
<p>$r_i = \infty$</p>
</li>
<li>
<p>$r_f$ = r</p>
</li>
<li>
<p>U (r) = $\frac {Q q} {4 \pi E_0 r}$</p>
</li>
</ul>
</div>
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<hr>
<footer style = "font-size: 18px"> Work Done $\rightarrow$ Work Done $\rightarrow$ <span style = "color:blue"> Electrostatic Potential Energy </span> $\rightarrow$ Potential Energy $\rightarrow$ Potential Energy </footer>

<h3 id="success-stylefont-size25px-electrostatic-potential-and-potential-energy--l-5-success-16"><Success style="font-size:25px;"> Electrostatic Potential and Potential Energy  L-5 </Success></h3>
<h3 id="primary-stylefont-size24pxpotential-energyprimary"><primary style="font-size:24px;">Potential Energy</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$U_{12} = \frac {Q q} {4 \pi E_0 r}$</p>
</li>
<li>
<p>W = $\int_{\infty}^{C} \vec{F}_{ext} \cdot \overrightarrow{d l}$</p>
</li>
<li>
<p>= - $\int_{\infty}^{C} \vec{F}_{el} \cdot \overrightarrow{d l}$</p>
</li>
<li>
<p>= $\vec F_{el} = q_3 \vec E_1 + q_3 \vec E_2 $</p>
</li>
</ul>
</div>
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<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/3aab1d79-fd7d-43a8-3119-eacf88017b00/public"  width="50%" >

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<hr>
<footer style = "font-size: 18px"> Electrostatic Potential Energy $\rightarrow$ Potential Energy $\rightarrow$ <span style = "color:blue"> Potential Energy </span> $\rightarrow$ Total Potential Energy $\rightarrow$ Electrostatics Potential </footer>

<h3 id="success-stylefont-size25px-electrostatic-potential-and-potential-energy--l-5-success-17"><Success style="font-size:25px;"> Electrostatic Potential and Potential Energy  L-5 </Success></h3>
<h3 id="primary-stylefont-size24pxtotal-potential-energyprimary"><primary style="font-size:24px;">Total Potential Energy</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>W =$-q_ 3\int_ {\infty}^{C} \vec{E}_ {1} \cdot \overrightarrow{d l}$ -$q_ 3\int_ {\infty}^{C} \vec{E}_ {2} \cdot \overrightarrow{d l}$</p>
</li>
<li>
<p>= $\frac {q_1 q_3} {4 \pi E_{0} r_{13}} + \frac {q_2 q_3} {4 \pi E_{0} r_{23}}$</p>
</li>
<li>
<p>Total potential energy, U =  $\frac {q_1 q_2} {4 \pi E_{0} r_{12}} + \frac {q_1 q_3} {4 \pi E_{0} r_{13}} + \frac {q_2 q_3} {4 \pi E_{0} r_{23}}$</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-05-electrostatic-potential-and-potential-energy-l-5_9-s0r7m46rqt4-0016.jpg"></p>
</div>
</main>
<hr>
<footer style = "font-size: 18px"> Electrostatic Potential Energy $\rightarrow$ Potential Energy $\rightarrow$ <span style = "color:blue"> Total Potential Energy </span> $\rightarrow$  Electrostatic Potential $\rightarrow$ Point Charge </footer>

<h3 id="success-stylefont-size25px-electrostatic-potential-and-potential-energy--l-5-success-18"><Success style="font-size:25px;"> Electrostatic Potential and Potential Energy  L-5 </Success></h3>
<h3 id="primary-stylefont-size24pxelectrostatic-potentialprimary"><primary style="font-size:24px;">Electrostatic Potential</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>Work done by an external force in bringing a unit potential charge from uniformily to the point in the electrostatic potential at that point.</p>
</li>
<li>
<p>U = $\frac{q Q}{4 \pi E_0}\left(\frac{1}{r_f}-\frac{1}{r_i}\right)$= $\frac {Q q} {4 \pi E_0 r}$</p>
</li>
<li>
<p>$r_i = \infty$</p>
</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/a47d89dd-b975-4d51-dd63-3fbfb0beb700/public"  width="70%" >

</div>
</main>
<hr>
<footer style = "font-size: 18px"> Potential Energy $\rightarrow$ Total Potential Energy $\rightarrow$ <span style = "color:blue"> Electrostatic Potential </span> $\rightarrow$  Point Charge $\rightarrow$ Work Done </footer>

<h3 id="success-stylefont-size25px-electrostatic-potential-and-potential-energy--l-5-success-19"><Success style="font-size:25px;"> Electrostatic Potential and Potential Energy  L-5 </Success></h3>
<h3 id="primary-stylefont-size24pxpoint-chargeprimary"><primary style="font-size:24px;">Point Charge</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;font-size:30px;text-align:left;'>
<ul>
<li>V (r)= $\frac {Q} {4 \pi E_0 r}$  <strong>Point charge</strong></li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/6926b847-362c-490f-8a8b-0b513a4fe100/public"  width="60%" >

</div>
</main>
<hr>
<footer style = "font-size: 18px"> Total Potential Energy $\rightarrow$ Electrostatic Potential $\rightarrow$ <span style = "color:blue"> Point Charge </span> $\rightarrow$ Work Done $\rightarrow$ Unit Potential </footer>

<h3 id="success-stylefont-size25px-electrostatic-potential-and-potential-energy--l-5-success-20"><Success style="font-size:25px;"> Electrostatic Potential and Potential Energy  L-5 </Success></h3>
<h3 id="primary-stylefont-size24pxwork-doneprimary-6"><primary style="font-size:24px;">Work Done</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>Work done by the external force to a unit +ve charge from $r_i$ to $r_f$ = $V(r_f) - V(r_i)$</li>
</ul>
</div>
<div style='float: right; width:50%;'>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/135b5c86-1f0c-4432-cceb-fd5e9a487e00/public"  width="60%" >

<div>
</main>
<hr>
<footer style = "font-size: 18px">  Electrostatic Potential $\rightarrow$ Point Charge $\rightarrow$ <span style = "color:blue"> Work Done </span> $\rightarrow$ Unit Potential $\rightarrow$ Unit Potential </footer>

<h3 id="success-stylefont-size25px-electrostatic-potential-and-potential-energy--l-5-success-21"><Success style="font-size:25px;"> Electrostatic Potential and Potential Energy  L-5 </Success></h3>
<h3 id="primary-stylefont-size24pxunit-potentialprimary"><primary style="font-size:24px;">Unit Potential</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;text-align:left;font-size:30px;'>
<ul>
<li>Unit potential : Volt</li>
</ul>
<ul>
<li>(Alessandro Volta 1745-1827)</li>
</ul>
<ul>
<li>Electric field : $\frac {V}{m}$ {volt per meter}</li>
</ul>
</div>
<div style='float: right; width:0%;'>

</div>
</main>
<hr>
<footer style = "font-size: 18px"> Point Charge $\rightarrow$ Work Done $\rightarrow$ <span style = "color:blue"> Unit Potential </span> $\rightarrow$ Unit Potential $\rightarrow$ Unit Potential </footer>

<h3 id="success-stylefont-size25px-electrostatic-potential-and-potential-energy--l-5-success-22"><Success style="font-size:25px;"> Electrostatic Potential and Potential Energy  L-5 </Success></h3>
<h3 id="primary-stylefont-size24pxunit-potentialprimary-1"><primary style="font-size:24px;">Unit Potential</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>Unit potential : Volt</li>
</ul>
<ul>
<li>(Alessandro Volta 1745-1827)</li>
</ul>
<ul>
<li>Electric field : $\frac {V}{m}$ {volt per meter}</li>
</ul>
<ul>
<li>
<p><strong>Example :</strong></p>
</li>
<li>
<p><strong>Potential:</strong> V(A) = $\frac {q_1}{4\pi E_0 r} + \frac{q_2}{4\pi E_0 r} = 0$</p>
</li>
<li>
<p>$q_2 = - q_1$</p>
</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/e7aac2ca-cc3a-4acf-4cfb-8d70f3757600/public"  width="70%" >


</div>
</main>
<hr>
<footer style = "font-size: 18px"> Work Done $\rightarrow$ Unit Potential $\rightarrow$ <span style = "color:blue"> Unit Potential </span> $\rightarrow$ Unit Potential $\rightarrow$ Unit Potential </footer>

<h3 id="success-stylefont-size25px-electrostatic-potential-and-potential-energy--l-5-success-23"><Success style="font-size:25px;"> Electrostatic Potential and Potential Energy  L-5 </Success></h3>
<h3 id="primary-stylefont-size24pxunit-potentialprimary-2"><primary style="font-size:24px;">Unit Potential</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>
<p><strong>Potential:</strong> V(A) = $\frac {q_1}{4\pi E_0 r} + \frac{q_2}{4\pi E_0 r} = 0$</p>
</li>
<li>
<p>$q_2 = - q_1$</p>
</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/f7b44845-4ac8-44a6-7262-e014f1ed0400/public"  width="70%" >

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

<h3 id="success-stylefont-size25px-electrostatic-potential-and-potential-energy--l-5-success-24"><Success style="font-size:25px;"> Electrostatic Potential and Potential Energy  L-5 </Success></h3>
<h3 id="primary-stylefont-size24pxunit-potentialprimary-3"><primary style="font-size:24px;">Unit Potential</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>
<p><strong>Potential:</strong> V(A) = $\frac {q_1}{4\pi E_0 r} + \frac{q_2}{4\pi E_0 r} = 0$</p>
</li>
<li>
<p>V(B) = $\frac {q_1}{4\pi E_0 r_1} - \frac{q_2}{4\pi E_0 r_2}$</p>
</li>
<li>
<p>$q_2 = - q_1$</p>
</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/cde5ad92-898f-4c8b-38c2-b014d7c3ce00/public"  width="70%" >

</div>
</main>
<hr>
<footer style = "font-size: 18px"> Unit Potential $\rightarrow$ Unit Potential $\rightarrow$ <span style = "color:blue"> Unit Potential </span> $\rightarrow$ Problem $\rightarrow$ Potential of a Charges </footer>

<h3 id="success-stylefont-size25px-electrostatic-potential-and-potential-energy--l-5-success-25"><Success style="font-size:25px;"> Electrostatic Potential and Potential Energy  L-5 </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>
<p>$V(B)  =\frac{10 \times 10^{-9} \times 9 \times 10^9}{4 \times 10^{-2}}-\frac{10 \times 10^{-9} \times 9 \times 10^9}{10 \times 10^{-2}}$</p>
</li>
<li>
<p>$ =2.25 \times 10^3-9 \times 10^2  =1.35 \times 10^3 \mathrm{~V} $</p>
</li>
<li>
<p>V(C) $ =-1.25 \times 10^3 \mathrm{V}$</p>
</li>
<li>
<p><strong>Problem:</strong> Calculate the work done in moving a charge of 5 nc from A to B and from A to C</p>
</li>
</ul>
</div>
<div style='float: right; width:0%;'>

</div>
</main>
<hr>
<footer style = "font-size: 18px"> Unit Potential $\rightarrow$ Unit Potential $\rightarrow$ <span style = "color:blue"> Problem </span> $\rightarrow$ Potential of a Charges $\rightarrow$ Thankyou </footer>

<h3 id="success-stylefont-size25px-electrostatic-potential-and-potential-energy--l-5-success-26"><Success style="font-size:25px;"> Electrostatic Potential and Potential Energy  L-5 </Success></h3>
<h3 id="primary-stylefont-size24pxpotential-of-a-chargesprimary"><primary style="font-size:24px;">Potential of a Charges</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>Potential of a charges conducting sphere.</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/1faf6e24-aaf0-4a77-8ae2-089e76ea9200/public"  width="50%" >

</div>
</main>
<hr>
<footer style = "font-size: 18px"> Unit Potential $\rightarrow$ Problem $\rightarrow$ <span style = "color:blue"> Potential of a Charges  </span> $\rightarrow$ Thankyou $\rightarrow$ </footer>