physics-class-12-unit-02-chapter-09-super-position-principle-for-electrostatic-force-l-9-9-zrqxt6j4g-a

<h3 id="success-stylefont-size25pxsuperposition-principle-for-electrostatic-force-l-9-success"><Success style="font-size:25px;">Superposition Principle for Electrostatic Force L-9 </Success></h3>
<h3 id="primary-stylefont-size24pxsuperposition-principle-for-electrostatic-forceprimary"><primary style="font-size:24px;">Superposition Principle for Electrostatic Force</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;text-align:left;font-size:30px;'>
</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-09-super-position-principle-for-electrostatic-force-l-9_9-zrqxt6j4g_a-014-0027.6.jpg"></p>
</main>
<hr>
<footer style = "font-size: 18px">  $\rightarrow$  $\rightarrow$ <span style = "color:blue"> Superposition Principle for Electrostatic Force </span> $\rightarrow$ Properties of Charge $\rightarrow$ Conductors & Insulators </footer>

<h3 id="success-stylefont-size25pxsuperposition-principle-for-electrostatic-force-l-9-success-1"><Success style="font-size:25px;">Superposition Principle for Electrostatic Force L-9 </Success></h3>
<h3 id="primary-stylefont-size24pxproperties-of-chargeprimary"><primary style="font-size:24px;">Properties of Charge</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>Conservation of Charge</p>
</li>
<li>
<p>Quantization of Charge</p>
</li>
<li>
<p>$e \simeq 1.6 \times 10^{-19} \mathrm{C}$</p>
</li>
<li>
<p><strong>Additivity of Charge</strong></p>
</li>
<li>
<p>$ n_1 : + ve $</p>
</li>
<li>
<p>$ n_2 : - ve $</p>
</li>
<li>
<p>$ (n_1  - n_2)e $</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-09-super-position-principle-for-electrostatic-force-l-9_9-zrqxt6j4g_a-001.jpg"></p>
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<hr>
<footer style = "font-size: 18px">  $\rightarrow$ Superposition Principle for Electrostatic Force $\rightarrow$ <span style = "color:blue"> Properties of Charge </span> $\rightarrow$ Conductors & Insulators $\rightarrow$ Coulomb's Law </footer>

<h3 id="success-stylefont-size25pxsuperposition-principle-for-electrostatic-force-l-9-success-2"><Success style="font-size:25px;">Superposition Principle for Electrostatic Force L-9 </Success></h3>
<h3 id="primary-stylefont-size24pxconductors--insulatorsprimary"><primary style="font-size:24px;">Conductors & Insulators</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;text-align:left;font-size:30px;'>
<ul>
<li>Semiconductors</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-09-super-position-principle-for-electrostatic-force-l-9_9-zrqxt6j4g_a-002.jpg"></p>
</main>
<hr>
<footer style = "font-size: 18px"> Superposition Principle for Electrostatic Force $\rightarrow$ Properties of Charge $\rightarrow$ <span style = "color:blue">Conductors & Insulators </span> $\rightarrow$ Coulomb's Law $\rightarrow$ Coulomb's Law </footer>

<h3 id="success-stylefont-size25pxsuperposition-principle-for-electrostatic-force-l-9-success-3"><Success style="font-size:25px;">Superposition Principle for Electrostatic Force L-9 </Success></h3>
<h3 id="primary-stylefont-size24pxcoulombs-lawprimary"><primary style="font-size:24px;">Coulomb’s Law</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$\vec{r_{21}}=\vec{r_2}-\vec{r_1}$</p>
</li>
<li>
<p>$\vec{F_{21}}=\frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r_{21}^2} \hat{r}_{21}$</p>
</li>
<li>
<p>$\vec{F_{12}}=\frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r_{12}^2} \hat{r}_{12}$</p>
</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/7b6abcda-c637-4dca-3ee5-a6c1234fa900/public" width="70%">
</main>
<hr>
<footer style = "font-size: 18px"> Properties of Charge $\rightarrow$ Conductors & Insulators $\rightarrow$ <span style = "color:blue"> Coulomb's Law </span> $\rightarrow$ Coulomb's Law $\rightarrow$ Unit of Charge </footer>

<h3 id="success-stylefont-size25pxsuperposition-principle-for-electrostatic-force-l-9-success-4"><Success style="font-size:25px;">Superposition Principle for Electrostatic Force L-9 </Success></h3>
<h3 id="primary-stylefont-size24pxcoulombs-lawprimary-1"><primary style="font-size:24px;">Coulomb’s Law</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$\vec{r}_{12}=\vec{r_1}-\vec{r_2}$</p>
</li>
<li>
<p>$= - (\vec{r_2}-\vec{r_1}) = - \vec{r}_{21}$</p>
</li>
<li>
<p>$\vec{F_{12}}=\frac{-1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r_{12}^2} \hat{r}_{12}$</p>
</li>
<li>
<p>$\left|\stackrel{\rightharpoonup}{r_{12}}\right|=\left|\vec{r}_{21}\right|$</p>
</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/7c7244d8-4e04-489c-fc37-92980d7c3600/public" width="70%">
</main>
<hr>
<footer style = "font-size: 18px"> Conductors & Insulators $\rightarrow$ Coulomb's Law $\rightarrow$ <span style = "color:blue"> Coulomb's Law </span> $\rightarrow$ Unit of Charge $\rightarrow$ Unit of Charge </footer>

<h3 id="success-stylefont-size25pxsuperposition-principle-for-electrostatic-force-l-9-success-5"><Success style="font-size:25px;">Superposition Principle for Electrostatic Force L-9 </Success></h3>
<h3 id="primary-stylefont-size24pxunit-of-chargeprimary"><primary style="font-size:24px;">Unit of Charge</primary></h3>
<hr>
<main> 
<div style='float: left; width:99%;text-align:left;font-size:20px;'>
<table>
<thead>
<tr>
<th>Unit of Charge</th>
<th>Coulomb</th>
</tr>
</thead>
<tbody>
<tr>
<td>Electron Charge</td>
<td>$1.6\times^{-19}C$</td>
</tr>
</tbody>
</table>
<ul>
<li>
<p>In 1 C, Number of Electron</p>
</li>
<li>
<p>$\frac{1}{1.6\times {10}^{-19}}\simeq 6\times{10}^{18}$</p>
</li>
<li>
<p>1 $\mu$ = $\text{1 micro Coulomb} = 10^{-6}C$</p>
</li>
<li>
<p>1 nc = $\text{1 nano Coulomb} = 10^{-9}C$</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-09-super-position-principle-for-electrostatic-force-l-9_9-zrqxt6j4g_a-005.jpg"></p>
</main>
<hr>
<footer style = "font-size: 18px"> Coulomb's Law $\rightarrow$ Coulomb's Law $\rightarrow$ <span style = "color:blue"> Unit of Charge </span> $\rightarrow$ Unit of Charge $\rightarrow$ Unit of Charge </footer>

<h3 id="success-stylefont-size25pxsuperposition-principle-for-electrostatic-force-l-9-success-6"><Success style="font-size:25px;">Superposition Principle for Electrostatic Force L-9 </Success></h3>
<h3 id="primary-stylefont-size24pxunit-of-chargeprimary-1"><primary style="font-size:24px;">Unit of Charge</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>Milli $(\mathrm{m}) \rightarrow 10^{-3}$</p>
</li>
<li>
<p>Micro $({\mu}) \rightarrow 10^{-6}$</p>
</li>
<li>
<p>Nano $(n) \rightarrow 10^{-9}$</p>
</li>
<li>
<p>Pico $(p) \rightarrow 10^{-12}$</p>
</li>
<li>
<p>Femto $(f) \rightarrow 10^{-15}$</p>
</li>
<li>
<p>Atto $(a) \rightarrow 10^{-18}$</p>
</li>
<li>
<p>Zepto $(z) \rightarrow 10^{-21}$</p>
</li>
<li>
<p>Yocto $(y) \rightarrow 10^{-24}$</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-09-super-position-principle-for-electrostatic-force-l-9_9-zrqxt6j4g_a-006.jpg"></p>
</main>
<hr>
<footer style = "font-size: 18px"> Coulomb's Law $\rightarrow$ Unit of Charge $\rightarrow$ <span style = "color:blue"> Unit of Charge </span> $\rightarrow$ Unit of Charge $\rightarrow$ Principle of Superposition </footer>

<h3 id="success-stylefont-size25pxsuperposition-principle-for-electrostatic-force-l-9-success-7"><Success style="font-size:25px;">Superposition Principle for Electrostatic Force L-9 </Success></h3>
<h3 id="primary-stylefont-size24pxunit-of-chargeprimary-2"><primary style="font-size:24px;">Unit of Charge</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;text-align:left;font-size:30px;'>
<ul>
<li>Kilo $(k) \rightarrow 10^{3}$</li>
<li>Mega $(M) \rightarrow 10^{6}$</li>
<li>Giga $(G) \rightarrow 10^{9}$</li>
<li>Tera $(T) \rightarrow 10^{12}$</li>
<li>Pata $(P) \rightarrow 10^{15}$</li>
<li>Exa $(E) \rightarrow 10^{18}$</li>
<li>Zetta $(Z) \rightarrow 10^{21}$</li>
<li>Yotta $(Y) \rightarrow 10^{24}$</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-09-super-position-principle-for-electrostatic-force-l-9_9-zrqxt6j4g_a-007.jpg"></p>
</main>
<hr>
<footer style = "font-size: 18px"> Unit of Charge $\rightarrow$ Unit of Charge $\rightarrow$ <span style = "color:blue"> Unit of Charge </span> $\rightarrow$ Principle of Superposition $\rightarrow$ Force Due to Charges </footer>

<h3 id="success-stylefont-size25pxsuperposition-principle-for-electrostatic-force-l-9-success-8"><Success style="font-size:25px;">Superposition Principle for Electrostatic Force L-9 </Success></h3>
<h3 id="primary-stylefont-size24pxprinciple-of-superpositionprimary"><primary style="font-size:24px;">Principle of Superposition</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$\vec{F}_{12}$</p>
</li>
<li>
<p>$\vec{F}_{13}$</p>
</li>
<li>
<p>$\vec{F_1}=\vec{F_{12}}+\vec{F_{13}}$</p>
</li>
<li>
<p><strong>Very Significant Result</strong></p>
</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/ca1b7aea-58e3-464c-2c1d-71e7aa756500/public" width="70%">
</main>
<hr>
<footer style = "font-size: 18px"> Unit of Charge $\rightarrow$ Unit of Charge $\rightarrow$ <span style = "color:blue"> Principle of Superposition </span> $\rightarrow$ Force Due to Charges $\rightarrow$ Force Due to Charges </footer>

<h3 id="success-stylefont-size25pxsuperposition-principle-for-electrostatic-force-l-9-success-9"><Success style="font-size:25px;">Superposition Principle for Electrostatic Force L-9 </Success></h3>
<h3 id="primary-stylefont-size24pxforce-due-to-chargesprimary"><primary style="font-size:24px;">Force Due to Charges</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$\vec{F_1}=\frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r_{12}^2} \hat{r}_{12}$</p>
</li>
<li>
<p>$+ \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_3}{r_{13}^2} \hat{r}_{13}$</p>
</li>
<li>
<p>$\vec{F_{12}} = \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r_{12}^2} \hat{r}_{12}$</p>
</li>
<li>
<p>$\vec{F_{13}} =\frac{1}{4 \pi \epsilon_0} \frac{q_1 q_3}{r_{13}^2} \hat{r}_{13}$</p>
</li>
<li>
<ul>
<li>Large number of point charges: N charge</li>
</ul>
</li>
<li>
<p>$\vec{F_1}=\sum_{j=2}^N \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_j}{r_{1 j}^2} \hat{r}_{1 j}$</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-09-super-position-principle-for-electrostatic-force-l-9_9-zrqxt6j4g_a-009.jpg"></p>
</main>
<hr>
<footer style = "font-size: 18px"> Unit of Charge $\rightarrow$ Principle of Superposition $\rightarrow$ <span style = "color:blue"> Force Due to Charges </span> $\rightarrow$ Force Due to Charges $\rightarrow$ Example-1(Case-1) </footer>

<h3 id="success-stylefont-size25pxsuperposition-principle-for-electrostatic-force-l-9-success-10"><Success style="font-size:25px;">Superposition Principle for Electrostatic Force L-9 </Success></h3>
<h3 id="primary-stylefont-size24pxforce-due-to-chargesprimary-1"><primary style="font-size:24px;">Force Due to Charges</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;text-align:left;font-size:30px;'>
<ul>
<li>$\vec{F_2}=\sum_{j=1} \frac{1}{4 \pi \epsilon_0} \frac{q_2 q_j}{r_{2 j}^2} \hat{r}_{2 j}$, & j = 3 to N</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-09-super-position-principle-for-electrostatic-force-l-9_9-zrqxt6j4g_a-0010.jpg"></p>
</main>
<hr>
<footer style = "font-size: 18px"> Principle of Superposition $\rightarrow$ Force Due to Charges $\rightarrow$ <span style = "color:blue"> Force Due to Charges </span> $\rightarrow$ Example-1(Case-1) $\rightarrow$ Example-1(Case-1) </footer>

<h3 id="success-stylefont-size25pxsuperposition-principle-for-electrostatic-force-l-9-success-11"><Success style="font-size:25px;">Superposition Principle for Electrostatic Force L-9 </Success></h3>
<h3 id="primary-stylefont-size24pxexample-1case-1primary"><primary style="font-size:24px;">Example-1(Case-1)</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$\left(-20 \times 10^{-9} \mathrm{C}\right)$  $\quad\left(5 \times 10^{-9} \mathrm{C}\right)$ $\quad\left(8 \times 10^{-9} \mathrm{c}\right)$</p>
</li>
<li>
<p>What is the Electrostatic force on $q_3?$</p>
</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>

<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/a2f5eea0-add7-4859-116a-39e4ac88fc00/public" width="70%">
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<hr>
<footer style = "font-size: 18px"> Force Due to Charges $\rightarrow$ Force Due to Charges $\rightarrow$ <span style = "color:blue"> Example-1(Case-1) </span> $\rightarrow$ Example-1(Case-1) $\rightarrow$ Example-1(Case-1) </footer>

<h3 id="success-stylefont-size25pxsuperposition-principle-for-electrostatic-force-l-9-success-12"><Success style="font-size:25px;">Superposition Principle for Electrostatic Force L-9 </Success></h3>
<h3 id="primary-stylefont-size24pxexample-1case-1primary-1"><primary style="font-size:24px;">Example-1(Case-1)</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$\vec{F_3}=\vec{F_{31}}+\vec{F_{32}}$</p>
</li>
<li>
<p>$\vec{F_{31}}=\frac{1}{4 \pi \epsilon_0} \frac{q_1 q_3}{r_{31}^2} \hat{r}_{31}$</p>
</li>
<li>
<p>$\left|\vec{r_{31}}\right|=1.5 \mathrm{~m} ; \quad \hat{r}_{31}=\hat{x}$</p>
</li>
<li>
<p>$\vec{r_{31}}=1.5\hat{x}$</p>
</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>

<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/f66d3930-6b27-461c-00b3-202b2e7ad600/public" width="70%">

</main>
<hr>
<footer style = "font-size: 18px"> Force Due to Charges $\rightarrow$ Example-1(Case-1) $\rightarrow$ <span style = "color:blue"> Example-1(Case-1) </span> $\rightarrow$ Example-1(Case-1) $\rightarrow$ Example-1(Case-1) </footer>

<h3 id="success-stylefont-size25pxsuperposition-principle-for-electrostatic-force-l-9-success-13"><Success style="font-size:25px;">Superposition Principle for Electrostatic Force L-9 </Success></h3>
<h3 id="primary-stylefont-size24pxexample-1case-1primary-2"><primary style="font-size:24px;">Example-1(Case-1)</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$\vec{F_{32}}=\frac{1}{4\pi\epsilon_0}\frac{q_2 q_3}{r_{32}^2}\hat{r}_{32}$</p>
</li>
<li>
<p>$\vec{r_{32}}=\vec{r_3}-\vec{r_2}=0.5\hat{x}$</p>
</li>
<li>
<p>$\left|\vec{r}_{32}\right|=0.5 m$</p>
</li>
<li>
<p>$\vec{F_{31}}=9 \times 10^9 \times \frac{\left(-20 \times 10^{-9}\right)\left(8 \times 10^{-9}\right)}{2.25} \hat{r}_{31}$</p>
</li>
<li>
<p>$ = - 6.4\times 10^{-7}\hat{x} (N) $</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-09-super-position-principle-for-electrostatic-force-l-9_9-zrqxt6j4g_a-00001.jpg">
<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-09-super-position-principle-for-electrostatic-force-l-9_9-zrqxt6j4g_a-00002.jpg"></p>
</main>
<hr>
<footer style = "font-size: 18px"> Example-1(Case-1) $\rightarrow$ Example-1(Case-1) $\rightarrow$ <span style = "color:blue"> Example-1(Case-1) </span> $\rightarrow$ Example-1(Case-1) $\rightarrow$ Example-1(Case-2) </footer>

<h3 id="success-stylefont-size25pxsuperposition-principle-for-electrostatic-force-l-9-success-14"><Success style="font-size:25px;">Superposition Principle for Electrostatic Force L-9 </Success></h3>
<h3 id="primary-stylefont-size24pxexample-1case-1primary-3"><primary style="font-size:24px;">Example-1(Case-1)</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$\vec{F_{32}}=\frac{1}{4 \pi \epsilon_0} \frac{q_2 q_3}{r_{32}^2} \hat{r}_{32}$</p>
</li>
<li>
<p>$=9 \times 10^9 \frac{\left(5 \times 10^{-9}\right)\left(8 \times 10^{-9}\right)}{0.25}$</p>
</li>
<li>
<p>$=1.44 \times 10^{-6} \hat{x}(N)$</p>
</li>
<li>
<p>$\vec{F_3}=-6.4\times {10^{-7}}\hat{x}+1.44\times {10^{-6}}\hat{x}$</p>
</li>
<li>
<p>$ = 8 \times {10^{-7}}\hat{x} (N)$</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-09-super-position-principle-for-electrostatic-force-l-9_9-zrqxt6j4g_a-0013.jpg"></p>
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<hr>
<footer style = "font-size: 18px"> Example-1(Case-1) $\rightarrow$ Example-1(Case-1) $\rightarrow$ <span style = "color:blue"> Example-1(Case-1) </span> $\rightarrow$ Example-1(Case-2) $\rightarrow$ Example-1(Case-2) </footer>

<h3 id="success-stylefont-size25pxsuperposition-principle-for-electrostatic-force-l-9-success-15"><Success style="font-size:25px;">Superposition Principle for Electrostatic Force L-9 </Success></h3>
<h3 id="primary-stylefont-size24pxexample-1case-2primary"><primary style="font-size:24px;">Example-1(Case-2)</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
</div>
<div style='float: right; width:100%; max-width:400px;'>

<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/106e6f12-5d85-452b-abc0-d7a839e7a800/public" width="50%">
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<hr>
<footer style = "font-size: 18px"> Example-1(Case-1) $\rightarrow$ Example-1(Case-1) $\rightarrow$ <span style = "color:blue"> Example-1(Case-2) </span> $\rightarrow$ Example-1(Case-2) $\rightarrow$ Example-1(Case-2) </footer>

<h3 id="success-stylefont-size25pxsuperposition-principle-for-electrostatic-force-l-9-success-16"><Success style="font-size:25px;">Superposition Principle for Electrostatic Force L-9 </Success></h3>
<h3 id="primary-stylefont-size24pxexample-1case-2primary-1"><primary style="font-size:24px;">Example-1(Case-2)</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$\left|\vec{F_{13}}\right|=\left|\vec{F_{23}}\right|$</p>
</li>
<li>
<p>$\left|\vec{F_{13}}\right|=\frac{1}{4\pi\epsilon_0}\frac{|q_2 q_3 |} {x^2}$</p>
</li>
<li>
<p>$\left|\vec{F_{23}}\right|=\frac{1}{4\pi\epsilon_0}\frac{|q_2 q_3 |} {(x-1)^2}$</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-09-super-position-principle-for-electrostatic-force-l-9_9-zrqxt6j4g_a-0015.jpg"></p>
</main>
<hr>
<footer style = "font-size: 18px"> Example-1(Case-1) $\rightarrow$ Example-1(Case-2) $\rightarrow$ <span style = "color:blue"> Example-1(Case-2) </span> $\rightarrow$ Example-1(Case-2) $\rightarrow$ Example-1(Case-2) </footer>

<h3 id="success-stylefont-size25pxsuperposition-principle-for-electrostatic-force-l-9-success-17"><Success style="font-size:25px;">Superposition Principle for Electrostatic Force L-9 </Success></h3>
<h3 id="primary-stylefont-size24pxexample-1case-2primary-2"><primary style="font-size:24px;">Example-1(Case-2)</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$\frac{1}{4\pi\epsilon_0}\frac{|q_1| |q_3 |} {x^2}=\frac{1}{4\pi\epsilon_0}\frac{|q_2| |q_3 |} {(x-1)^2}$</p>
</li>
<li>
<p>$\frac{(x-1)^2}{x^2}=\frac{\left|q_2\right|}{\left|q_1\right|}=\frac{5 \times 10^{-9}}{20 \times 10^{-9}}=\frac{1}{4}$</p>
</li>
<li>
<p>$\frac{x-1}{x}= \pm \frac{1}{2}$</p>
</li>
<li>
<p><strong>1.</strong> $\frac{x-1}{x}=\frac{+1}{2} \Rightarrow 2(x-1)=x$</p>
</li>
<li>
<p>$\Rightarrow x = 2$</p>
</li>
<li>
<p><strong>2.</strong> $\frac{x-1}{x}=\frac{-1}{2} \Rightarrow 2(x-1)=-x$</p>
</li>
<li>
<p>$ {x = \frac{2}{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-09-super-position-principle-for-electrostatic-force-l-9_9-zrqxt6j4g_a-0016.jpg"></p>
</main>
<hr>
<footer style = "font-size: 18px"> Example-1(Case-2) $\rightarrow$ Example-1(Case-2) $\rightarrow$ <span style = "color:blue"> Example-1(Case-2) </span> $\rightarrow$ Example-1(Case-2) $\rightarrow$ Example-2 </footer>

<h3 id="success-stylefont-size25pxsuperposition-principle-for-electrostatic-force-l-9-success-18"><Success style="font-size:25px;">Superposition Principle for Electrostatic Force L-9 </Success></h3>
<h3 id="primary-stylefont-size24pxexample-1case-2primary-3"><primary style="font-size:24px;">Example-1(Case-2)</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>
<ol>
<li>To the right of $q_2$ ${x = 2m}$</li>
</ol>
</li>
<li>
<ol start="2">
<li>Between ${q_1} ~and ~{q_2} ~x = \frac{2}{3}m$</li>
</ol>
</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>

<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/92910e9f-3a75-4560-99e0-b1ccf3250b00/public" width="50%">

</main>
<hr>
<footer style = "font-size: 18px"> Example-1(Case-2) $\rightarrow$ Example-1(Case-2) $\rightarrow$ <span style = "color:blue"> Example-1(Case-2) </span> $\rightarrow$ Example-2 $\rightarrow$ Example-2 </footer>

<h3 id="success-stylefont-size25pxsuperposition-principle-for-electrostatic-force-l-9-success-19"><Success style="font-size:25px;">Superposition Principle for Electrostatic Force L-9 </Success></h3>
<h3 id="primary-stylefont-size24px-example---2primary"><primary style="font-size:24px;"> Example - 2</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>What is the force on ${q_3}?$</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>

<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/08ef717d-de19-4890-27d3-ff40e4f24300/public" width="70%">
</main>
<hr>
<footer style = "font-size: 18px"> Example-1(Case-2) $\rightarrow$ Example-1(Case-2) $\rightarrow$ <span style = "color:blue"> Example-2 </span> $\rightarrow$ Example-2 $\rightarrow$ Example-2 </footer>

<h3 id="success-stylefont-size25pxsuperposition-principle-for-electrostatic-force-l-9-success-20"><Success style="font-size:25px;">Superposition Principle for Electrostatic Force L-9 </Success></h3>
<h3 id="primary-stylefont-size24px-example---2primary-1"><primary style="font-size:24px;"> Example - 2</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$\overrightarrow{r_{1}} = 0.1\hat{y}$</p>
</li>
<li>
<p>$\vec{r_2}=-0.1\hat{y}$</p>
</li>
<li>
<p>$\vec{r_3}=0.1\hat{x}$</p>
</li>
<li>
<p>$\vec{r_{31}}=\vec{r_3}-\vec{r_1}=0.1(\hat{x}-\hat{y})$</p>
</li>
<li>
<p>$\vec{r_{32}}=\vec{r_3}-\vec{r_2}=0.1(\hat{x}+\hat{y})$</p>
</li>
<li>
<p>$\hat{r_{31}}=\frac{\vec{r_{31}}}{\left|\vec{r}_{31}\right|}$</p>
</li>
<li>
<p>$=\frac{0.1(\hat{x}-\hat{y})}{\sqrt{0.1(\hat{x}-\hat{y}) \times 0.1(\hat{x}-\hat{y})}}$</p>
</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>
 
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/1921325e-47fe-4381-2c44-b75431129c00/public" width="70%">
</main>
<hr>
<footer style = "font-size: 18px"> Example-1(Case-2) $\rightarrow$ Example-2 $\rightarrow$ <span style = "color:blue"> Example-2 </span> $\rightarrow$ Example-2 $\rightarrow$ Example-2 </footer>

<h3 id="success-stylefont-size25pxsuperposition-principle-for-electrostatic-force-l-9-success-21"><Success style="font-size:25px;">Superposition Principle for Electrostatic Force L-9 </Success></h3>
<h3 id="primary-stylefont-size24px-example---2primary-2"><primary style="font-size:24px;"> Example - 2</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$\hat{r_{31}}=\frac{\vec{r_{31}}}{|\vec{r_{31}}|} = \frac{0.1(\hat{x}-\hat{y})}{\left|\vec{r}_{31}\right|}$</p>
</li>
<li>
<p>$\left|\vec{r}_{31}\right|=[0.1(\hat{x}-\hat{y}) \cdot(0.1(\hat{x}-\hat{y}))]^{1 / 2}=[0.01(1+1)]^{1 /2}$</p>
</li>
<li>
<p>$ =\sqrt{0.02}=\sqrt{2}\times{0.1}$</p>
</li>
<li>
<p>$\hat{r}_{31}=\frac{1}{\sqrt{2}}(\hat{x}-\hat{y})$</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-09-super-position-principle-for-electrostatic-force-l-9_9-zrqxt6j4g_a-0020.jpg"></p>
</main>
<hr>
<footer style = "font-size: 18px"> Example-2 $\rightarrow$ Example-2 $\rightarrow$ <span style = "color:blue"> Example-2 </span> $\rightarrow$ Example-2 $\rightarrow$ Example-2 </footer>

<h3 id="success-stylefont-size25pxsuperposition-principle-for-electrostatic-force-l-9-success-22"><Success style="font-size:25px;">Superposition Principle for Electrostatic Force L-9 </Success></h3>
<h3 id="primary-stylefont-size24px-example---2primary-3"><primary style="font-size:24px;"> Example - 2</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$\hat{r_{31}}=\frac{\vec{r_{31}}}{|\vec{r_{31}}|}=\frac{0.1(\hat{x}-\hat{y})}{\left|\vec{r}_{31}\right|}$</p>
</li>
<li>
<p>$\left|\vec{r}_{31}\right|=[0.1(\hat{x}-\hat{y}) \cdot(0.1(\hat{x}-\hat{y}))]^{1 / 2}$</p>
</li>
<li>
<p>$=[0.01(1+1)]^{1 / 2}=\sqrt{0.02}=\sqrt{2}\times{0.1}$</p>
</li>
<li>
<p>$\hat{r}_{31}=\frac{1}{\sqrt{2}}(\hat{x}-\hat{y})$</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-09-super-position-principle-for-electrostatic-force-l-9_9-zrqxt6j4g_a-0020.jpg"></p>
</main>
<hr>
<footer style = "font-size: 18px"> Example-2 $\rightarrow$ Example-2 $\rightarrow$ <span style = "color:blue"> Example-2 </span> $\rightarrow$ Example-2 $\rightarrow$ Example-2 </footer>

<h3 id="success-stylefont-size25pxsuperposition-principle-for-electrostatic-force-l-9-success-23"><Success style="font-size:25px;">Superposition Principle for Electrostatic Force L-9 </Success></h3>
<h3 id="primary-stylefont-size24pxexample-2primary"><primary style="font-size:24px;">Example-2</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$\hat{r}_{32}=\frac{1}{\sqrt{2}}(\hat{x}+\hat{y})$</p>
</li>
<li>
<p>$\vec{F_3}=\vec{F_{31}}+\vec{F_{32}}$</p>
</li>
<li>
<p>$=\frac{1}{4 \pi \epsilon_0} \frac{q_1 q_3}{r_{31}^2} \cdot\hat{r_{31}}+\frac{1}{4 \pi \epsilon_0} \frac{q_2 q_3}{r_{32}^2} \hat{r}_{32}$</p>
</li>
<li>
<p>$=\frac{1}{4 \pi \epsilon_0} q_1[\frac{q_1}{r_{31}^2} \hat{r_{31}}+\frac{q_2}{r_{32}^2} \hat{r_{32}}]$</p>
</li>
<li>
<p>$=\frac{1}{4 \pi \epsilon_0} \frac{q_1 q_3}{r_{31}^2}(\hat{r_{31}}+\hat{r_{32}})$</p>
</li>
<li>
<p>$\hat{r_{32}}=\hat{r_{31}}$</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-09-super-position-principle-for-electrostatic-force-l-9_9-zrqxt6j4g_a-0022.jpg"></p>
</main>
<hr>
<footer style = "font-size: 18px"> Example-2 $\rightarrow$ Example-2 $\rightarrow$ <span style = "color:blue"> Example-2 </span> $\rightarrow$ Example-2 $\rightarrow$ Thankyou </footer>

<h3 id="success-stylefont-size25pxsuperposition-principle-for-electrostatic-force-l-9-success-24"><Success style="font-size:25px;">Superposition Principle for Electrostatic Force L-9 </Success></h3>
<h3 id="primary-stylefont-size24pxexample-2primary-1"><primary style="font-size:24px;">Example-2</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>${q_2} = {q_1}$</p>
</li>
<li>
<p>$\hat{r_{31}}=\frac{1}{\sqrt{2}}(\hat{x}-\hat{y})$</p>
</li>
<li>
<p>$\hat{r_{32}}=\frac{1}{\sqrt{2}}(\hat{x}+\hat{y})$</p>
</li>
<li>
<p>$\hat{r_{31}}+\hat{r_{32}}=\frac{2}{\sqrt{2}} \hat{x}$</p>
</li>
<li>
<p>$\vec{F_3}=\frac{1}{4 \pi \epsilon_0} \frac{q_1 q_3}{r_{31}^2} \sqrt{2} \hat{x}$</p>
</li>
<li>
<p>$=9 \times 10^9 \times \frac{10 \times 10^{-9} \times 5 \times 10^{-9}}{0.02} \times \sqrt{2} \cdot \hat{x}$</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-09-super-position-principle-for-electrostatic-force-l-9_9-zrqxt6j4g_a-0023.jpg"></p>
</main>
<hr>
<footer style = "font-size: 18px"> Example-2 $\rightarrow$ Example-2 $\rightarrow$ <span style = "color:blue"> Example-2 </span> $\rightarrow$ Thankyou $\rightarrow$ </footer>