physics-class-12-unit-02-chapter-02-electric-field-and-potential-and-concept-of-capacitance-l-2-9-snyqlwxcphs

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<h3 id="primary-stylefont-size24pxelectrostaticsprimary"><primary style="font-size:24px;">Electrostatics</primary></h3>
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<ul>
<li>
<p>Let’s recall if you have a collection of charges, then there is potential energy stored in the collection of charges.</p>
</li>
<li>
<p>Potential  is a scalar quantity.</p>
</li>
<li>
<p>Potential of a point charges</p>
</li>
<li>
<p>$V(r)=\frac{Q}{4 \pi \epsilon_0 r}$</p>
</li>
</ul>
</div>
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<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/72aab266-aee5-4e22-6882-84d5185fbe00/public"  width="70%" >


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<footer style = "font-size: 18px">  $\rightarrow$ Electric Field and Potential and Concept Of Capacitance $\rightarrow$ <span style = "color:blue"> Electrostatics </span> $\rightarrow$ Potential of a Point Charges $\rightarrow$ Potential of a Point Charges </footer>

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<h3 id="primary-stylefont-size24pxpotential-of-a-point-chargesprimary"><primary style="font-size:24px;">Potential of a Point Charges</primary></h3>
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<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$V(r)=\frac{Q}{4 \pi \epsilon_0 r}$</p>
</li>
<li>
<p>So, that is a scalar quantity and potential of this point charge depends only on the distance of the point from the point charge.And the potential follows the principle of superposition. So, if you have multiple charges, then the total potential at any point is the sum of the potentials created by each and every individual charge.</p>
</li>
</ul>
</div>
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<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/9b8c8162-e5b8-4424-3a9a-808345fbde00/public"  width="70%" >

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<footer style = "font-size: 18px"> Electric Field and Potential and Concept Of Capacitance $\rightarrow$ Electrostatics $\rightarrow$ <span style = "color:blue"> Potential of a Point Charges </span> $\rightarrow$ Potential of a Point Charges $\rightarrow$ Equipotential Surface </footer>

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<h3 id="primary-stylefont-size24pxequipotential-surfaceprimary"><primary style="font-size:24px;">Equipotential Surface</primary></h3>
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<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>Concept of equipotential surfaces: These are surfaces where the potential electrostatic potentials remain constant.</li>
<li>So, these could be surfaces of arbitrary shapes.</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/264f01c4-533e-4e8c-331d-ed7bc8d00800/public"  width="70%" >

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<footer style = "font-size: 18px"> Potential of a Point Charges $\rightarrow$ Potential of a Point Charges $\rightarrow$ <span style = "color:blue"> Equipotential Surface </span> $\rightarrow$ Equipotential Surface $\rightarrow$ Equipotential Surface </footer>

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<h3 id="primary-stylefont-size24pxequipotential-surfaceprimary-1"><primary style="font-size:24px;">Equipotential Surface</primary></h3>
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<div style='float: left; width:50%; text-align:left;font-size:30px; '>
<ul>
<li>The electric field lines are perpendicular to the equipotential surfaces.</li>
<li>The potential is the same all along the surface which implies that there cannot be a component of the electric field  which is along the equipotential surface.</li>
<li>So, it implies that the electric field lines have o be perpendicular to the equipotential surfaces.</li>
</ul>
</div>
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<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/bc2770d6-f487-4c6c-943d-8912e8485400/public"  width="70%" >

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<footer style = "font-size: 18px"> Potential of a Point Charges $\rightarrow$ Equipotential Surface $\rightarrow$ <span style = "color:blue"> Equipotential Surface </span> $\rightarrow$ Equipotential Surface $\rightarrow$ Electric Field and Potential </footer>

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<h3 id="primary-stylefont-size24pxequipotential-surfaceprimary-2"><primary style="font-size:24px;">Equipotential Surface</primary></h3>
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<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>Equipotentials are another way of representing the electric field distribution or potential distribution which is helpful in understanding and in picturizing the potentials and electric field.</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/8148cb20-92aa-443a-ac9f-b576d5705800/public"  width="70%" >

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<footer style = "font-size: 18px"> Equipotential Surface $\rightarrow$ Equipotential Surface $\rightarrow$ <span style = "color:blue"> Equipotential Surface </span> $\rightarrow$ Electric Field and Potential $\rightarrow$ Electric Field and Potential </footer>

### <Success style="font-size:25px;"> Electric-Field-And-Potential-And-Concept-of-Capacitance L-2 </Success>
### <primary style="font-size:24px;">Electric Field and Potential </primary>
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-  The electric field  line will be perpendicular to the direction to the surface equipotential surface.

-   E cos $\theta$ is the component of the electric field vector along the length direction A B.

</div>
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</main>
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<footer style = "font-size: 18px"> Equipotential Surface $\rightarrow$ Equipotential Surface $\rightarrow$ <span style = "color:blue"> Electric Field and Potential </span> $\rightarrow$ Electric Field and Potential $\rightarrow$ Electric Field and Potential </footer>

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<h3 id="primary-stylefont-size24pxelectric-field-and-potentialprimary"><primary style="font-size:24px;">Electric Field and Potential</primary></h3>
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<div>
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<div style='float: left; width:100%;font-size:30px;text-align:left;'>
<ul>
<li>
<p>Work done in moving a unit charge from A to B = $\left(V_0+d V\right)-V_0  =d V $</p>
</li>
<li>
<p>Work done =  $ -\vec{E} \cdot \vec{dl}=-E dl \cos \theta $</p>
</li>
<li>
<p>$=-E_l \cdot dl $ $ -E_l dl =dV $</p>
</li>
<li>
<p>$\Rightarrow \quad E_l=-\frac{d V}{dl}$</p>
</li>
</ul>
</div>
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<footer style = "font-size: 18px"> Equipotential Surface $\rightarrow$ Electric Field and Potential $\rightarrow$ <span style = "color:blue"> Electric Field and Potential </span> $\rightarrow$ Electric Field and Potential $\rightarrow$ Electric Field and Potential </footer>

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<h3 id="primary-stylefont-size24pxelectric-field-and-potential-primary"><primary style="font-size:24px;">Electric Field and Potential </primary></h3>
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<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>$ \vec{\mu} =d \vec{x}$</li>
</ul>
<ul>
<li>
<p>$ E_x  =-\frac{\partial V}{\partial x}$</p>
</li>
<li>
<p>$E_y  =-\frac{\partial V}{\partial y}$</p>
</li>
<li>
<p>$E_z  =-\frac{\partial V}{\partial z}$</p>
</li>
</ul>
<ul>
<li>
<p>$ \vec{E} =\hat{\imath} E_x+ \hat {j} E_y+\hat{\imath} E_z$</p>
</li>
<li>
<p>$=-\left(\hat{\imath} \frac{\partial V}{\partial x}+\hat{\jmath} \frac{\partial V}{\partial y}+ \hat{\imath} \frac{\partial V}{\partial z}\right)$</p>
</li>
</ul>
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</div>
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<footer style = "font-size: 18px"> Electric Field and Potential $\rightarrow$ Electric Field and Potential $\rightarrow$ <span style = "color:blue"> Electric Field and Potential </span> $\rightarrow$ Electric Field and Potential $\rightarrow$ Electric Field and Potential </footer>

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<h3 id="primary-stylefont-size24pxelectric-field-and-potential-primary-1"><primary style="font-size:24px;">Electric Field and Potential </primary></h3>
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<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<p><strong>Example:</strong></p>
<ul>
<li>
<p>$V(r)=\frac{Q}{4 \pi \epsilon_0 r}$</p>
</li>
<li>
<p>$r=\sqrt{x^2+y^2+z^2}$</p>
</li>
<li>
<p>$V(x, y, z)=\frac{Q}{4 \pi \epsilon_0 \sqrt{x^2+y^2+z^2}} $</p>
</li>
<li>
<p>$E_x=-\frac{\partial V}{\partial x}=-\frac{Q}{4 \pi \epsilon_0} \frac{1}{\left(x^2+y^2+z^2\right)^{3 / 2}}\left(-\frac{1}{2}\right) \cdot 2 x$</p>
</li>
<li>
<p>$=\frac{a}{4 \pi \epsilon_0\left(x^2+y^2+z^2) \right.} \frac{x}{\sqrt{x^2+y^2+z^2}}$</p>
</li>
</ul>
</div>
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<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/df0d2431-f3e8-49cf-25e3-e905205b9800/public"  width="70%" >

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<footer style = "font-size: 18px"> Electric Field and Potential $\rightarrow$ Electric Field and Potential $\rightarrow$ <span style = "color:blue"> Electric Field and Potential </span> $\rightarrow$ Electric Field and Potential $\rightarrow$ Electric Field and Potential </footer>

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<h3 id="primary-stylefont-size24pxelectric-field-and-potential-primary-2"><primary style="font-size:24px;">Electric Field and Potential </primary></h3>
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<div style='float: left; width:100%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$E_x  =\frac{Q}{4 \pi \epsilon_0 r^2} \frac{x}{r}$</p>
</li>
<li>
<p>$E_y  =\frac{Q}{4 \pi \epsilon_0 r^2} \cdot \frac{y}{r}$</p>
</li>
<li>
<p>$E_z  =\frac{Q}{4 \pi \epsilon_0 r^2} \cdot \frac{z}{r}$</p>
</li>
<li>
<p>$\vec{E}  =\imath E_x+\hat{\jmath} E_y+\hat{\imath} E_z$ $=\frac{Q}{4 \pi \epsilon_0 r^2} \frac{\left(\hat{\epsilon} x+\hat{\jmath} y+\hat{\tau}_z\right)}{r}$</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-02-electric-field-and-potential-and-concept-of-capacitance-l-2_9-snyqlwxcphs-007.jpg"></p>
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<footer style = "font-size: 18px"> Electric Field and Potential $\rightarrow$ Electric Field and Potential $\rightarrow$ <span style = "color:blue"> Electric Field and Potential </span> $\rightarrow$ Electric Field and Potential $\rightarrow$ Conductors with Cavity </footer>

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<h3 id="primary-stylefont-size24pxelectric-field-and-potential-primary-3"><primary style="font-size:24px;">Electric Field and Potential </primary></h3>
<hr>
<main>
<div style='float: left; width:100%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$\vec{E}=\frac{Q}{4 \pi \epsilon_0 r^2} \frac{\vec{r}}{r}=\frac{Q \vec{r}}{4 \pi \epsilon_0 r^2}$</p>
</li>
<li>
<p>We know V as a function of x, y and z, I can use these three relationships to calculate $ E_x, E_y and E_z$ and from there  the total electric field $\vec E$.</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-02-electric-field-and-potential-and-concept-of-capacitance-l-2_9-snyqlwxcphs-008.jpg"></p>
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<footer style = "font-size: 18px"> Electric Field and Potential $\rightarrow$ Electric Field and Potential $\rightarrow$ <span style = "color:blue"> Electric Field and Potential </span> $\rightarrow$ Conductors with Cavity $\rightarrow$ Cavity with the Conductor </footer>

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<h3 id="primary-stylefont-size24pxconductors-with-cavityprimary"><primary style="font-size:24px;">Conductors with Cavity</primary></h3>
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<div style='float: left; width:50%;text-align:left;font-size:30px;'> 
<ul>
<li>
<p>Arbitrary relationship conductor.</p>
</li>
<li>
<p>No excess charges within the conductor.</p>
</li>
<li>
<p>$\sigma=\frac{Q}{4 \pi R^2}$</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"> Conductors with Cavity </span> $\rightarrow$ Cavity with the Conductor $\rightarrow$ Cavity with the Conductor </footer>

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<h3 id="primary-stylefont-size24pxcavity-with-the-conductorprimary"><primary style="font-size:24px;">Cavity with the Conductor</primary></h3>
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<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>We have a conductor of arbitrary shape and I have a cavity.</p>
</li>
<li>
<p>This is the Gaussian surface enclosing the cavity and that Gaussian surface lies entirely within the conductor.</p>
</li>
<li>
<p>Gaussian Surface</p>
</li>
<li>
<p>$\oint \vec{E} \cdot \overrightarrow{d l}=0$</p>
</li>
<li>
<p>$\oint_C \vec{E} \cdot \vec{d l} \neq 0$</p>
</li>
<li>
<p>There can be no access charge on the inner surface</p>
</li>
</ul>
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<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/fa88513a-39ef-4fef-a573-e59373405b00/public"  width="70%" >

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<footer style = "font-size: 18px"> Electric Field and Potential $\rightarrow$ Conductors with Cavity $\rightarrow$ <span style = "color:blue"> Cavity with the Conductor </span> $\rightarrow$ Cavity with the Conductor $\rightarrow$ Cavity with the Conductor </footer>

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<h3 id="primary-stylefont-size24pxcavity-with-the-conductorprimary-1"><primary style="font-size:24px;">Cavity with the Conductor</primary></h3>
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<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>A conductor like this, any arbitrary conductor.</li>
<li>All charges are sitting excess charge, all the excess charge with the output.</li>
</ul>
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<footer style = "font-size: 18px"> Conductors with Cavity $\rightarrow$ Cavity with the Conductor $\rightarrow$ <span style = "color:blue"> Cavity with the Conductor </span> $\rightarrow$ Cavity with the Conductor $\rightarrow$ Cavity with the Conductor </footer>

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<h3 id="primary-stylefont-size24pxcavity-with-the-conductorprimary-2"><primary style="font-size:24px;">Cavity with the Conductor</primary></h3>
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<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>A spherical conductor and let’s some cavity here.</li>
<li>If you now take a Gaussian surface like this, which is lying within the conductor, the next flux must be 0 and the next charge enclosed also of accumulated charge on the inner surface of the conductor.</li>
</ul>
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<footer style = "font-size: 18px"> Cavity with the Conductor $\rightarrow$ Cavity with the Conductor $\rightarrow$ <span style = "color:blue"> Cavity with the Conductor </span> $\rightarrow$ Cavity with the Conductor $\rightarrow$ Problem </footer>

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<h3 id="primary-stylefont-size24pxcavity-with-the-conductorprimary-3"><primary style="font-size:24px;">Cavity with the Conductor</primary></h3>
<hr>
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<div style='float: left; width:100%; font-size:30px; text-align:left;'>
<ul>
<li>If the conductor is a spherical conductor, that positive charge will get equally distributed all across the surface of the conductor.</li>
<li>The net  charge enclosed by this Gaussian surface is 0.</li>
<li>And, these negative charges will leave an equal amount of positive charge on the outer surface of the conductor.</li>
</ul>
</div>
<div>
</div>
</main>
<hr>
<footer style = "font-size: 18px"> Cavity with the Conductor $\rightarrow$ Cavity with the Conductor $\rightarrow$ <span style = "color:blue"> Cavity with the Conductor </span> $\rightarrow$ Problem $\rightarrow$ Problem </footer>

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<h3 id="primary-stylefont-size24pxproblemprimary"><primary style="font-size:24px;">Problem</primary></h3>
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<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>Conductor a spherical conductor with a spherical cavity  cetered in the
conductor</p>
</li>
<li>
<p>A charge -Q in place at the centerd of the cavity</p>
</li>
<li>
<p>a) Calculate the surface charge density on the inner & outer surface</p>
</li>
<li>
<p>b) Calculate the electric field every here</p>
</li>
</ul>
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<footer style = "font-size: 18px"> Cavity with the Conductor $\rightarrow$ Cavity with the Conductor $\rightarrow$ <span style = "color:blue"> Problem </span> $\rightarrow$ Problem $\rightarrow$ Problem </footer>

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<h3 id="primary-stylefont-size24pxproblemprimary-1"><primary style="font-size:24px;">Problem</primary></h3>
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<main>
<div style='float: left; width:60%;text-align:left;font-size:30px;'>
<ul>
<li>Conductor sphere of radius a.</li>
<li>Conducting wire of radius b.</li>
<li>I throw a charge on the system. So, the charge will, because these are conductors oined by another conductor here, the charge will distribute itself.</li>
<li>If there was a potential difference then that will lead to an electric field and that electric  field will ensure the charges then move and until the potential becomes equal all along the conductor.</li>
</ul>
</div>
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<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/7347ce8d-fd0a-47fd-e973-146b75f09500/public"  width="100%" >

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<hr>
<footer style = "font-size: 18px"> Cavity with the Conductor $\rightarrow$ Problem $\rightarrow$ <span style = "color:blue"> Problem </span> $\rightarrow$ Problem $\rightarrow$ Problem </footer>

<h3 id="success-stylefont-size25px-electric-field-and-potential-and-concept-of-capacitance-l-2-success-18"><Success style="font-size:25px;"> Electric-Field-And-Potential-And-Concept-of-Capacitance L-2 </Success></h3>
<h3 id="primary-stylefont-size24pxproblemprimary-2"><primary style="font-size:24px;">Problem</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$ V_a=\frac{q_a}{4 \pi \epsilon_0 a} $</p>
</li>
<li>
<p>$V_b=\frac{q_b}{4 \pi \epsilon_0 b} $</p>
</li>
<li>
<p>$V_a=V_b $</p>
</li>
</ul>
<p>-$ \Rightarrow \frac{q_a}{a}=\frac{q_b}{b} $</p>
<ul>
<li>Surface charge  density $\sigma_a$ & $\sigma_b $</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:380px;'>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/f155097d-6da5-4d6a-1caa-d12f082e7d00/public"  width="100%" >

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

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<h3 id="primary-stylefont-size24pxproblemprimary-3"><primary style="font-size:24px;">Problem</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$ V(r)=\frac{Q}{4 \pi \epsilon_0 r} $</p>
</li>
<li>
<p>at  r=R</p>
</li>
<li>
<p>$ V(R)=\frac{Q}{4 \pi \epsilon_0 R}$</p>
</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:350px;'>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/393a5998-4b8e-416a-b437-60896566f500/public"  width="70%" >

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

<h3 id="success-stylefont-size25px-electric-field-and-potential-and-concept-of-capacitance-l-2-success-20"><Success style="font-size:25px;"> Electric-Field-And-Potential-And-Concept-of-Capacitance L-2 </Success></h3>
<h3 id="primary-stylefont-size24pxproblemprimary-4"><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>$ q_a=\sigma_a \cdot 4 \pi a^2 $</p>
</li>
<li>
<p>$ q_b=\sigma_b \cdot 4 \pi b^2 $</p>
</li>
<li>
<p>$ \frac{\sigma_a \cdot 4 \pi a^2}{a}=\frac{\sigma_b \cdot 4 \pi b^2}{b} $</p>
</li>
<li>
<p>$ \sigma_a a=\sigma_b b $</p>
</li>
<li>
<p>Electric field = $ \frac{\sigma}{\epsilon_0} $</p>
</li>
<li>
<p>There will be some positive charges and they will there will be more positive charge accumulated here.</p>
</li>
<li>
<p>So, the positive charge density will increase.</p>
</li>
</ul>
</div>
<div style='float: right; width:0%; max-width:400px;'>

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

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<h3 id="primary-stylefont-size24pxproblemprimary-5"><primary style="font-size:24px;">Problem</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px'>
<ul>
<li>
<p>$  E_a=\frac{\sigma_a}{\epsilon_0} $ ; $ E_b=\frac{\sigma_b}{\epsilon_0}$</p>
</li>
<li>
<p>$ E_a a=E_b, b $</p>
</li>
<li>
<p>$ \frac{E_b}{E_a}=\frac{a}{b} $</p>
</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/d163ab9f-a7e9-4a72-0bdd-8e4f78ddf400/public"  width="100%" >

</main>
<hr>
<footer style = "font-size: 18px"> Problem $\rightarrow$ Problem $\rightarrow$ <span style = "color:blue"> Problem </span> $\rightarrow$ Lightning Rod $\rightarrow$ Capacitors and Capacitance </footer>

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<h3 id="primary-stylefont-size24pxlightning-rodprimary"><primary style="font-size:24px;">Lightning Rod</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px'>
<ul>
<li>Sharp edges conducted with the sharp edge on top of the residence and this conductor is joined by conducting wire to the ground.</li>
<li>Electric field lines crowd along  the corner of around sharp edges.</li>
<li>Conductors are equipotential surfaces charges put on conductors reside on  the outer surface of the conductor.</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/472305c2-3cc0-44bf-955a-f24e215d3a00/public"  width="100%" >

</main>
<hr>
<footer style = "font-size: 18px"> Problem $\rightarrow$ Problem $\rightarrow$ <span style = "color:blue"> Lightning Rod </span> $\rightarrow$ Capacitors and Capacitance $\rightarrow$ Parallel Plate Capacitor </footer>

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<h3 id="primary-stylefont-size24pxcapacitors-and-capacitanceprimary"><primary style="font-size:24px;">Capacitors and Capacitance</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px'>
<ul>
<li>Two conductors carrying equal and opposite charges.</li>
<li>Two conductors I move some electrons from one conductor to the other conductor.</li>
<li>So, I have two conductors which are oppositely charged and kept this particular configuration forms what is called as a capacitor.</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/007c0dc6-85dd-469f-f5b6-b0d19ad67700/public"  width="70%" >

</main>
<hr>
<footer style = "font-size: 18px"> Problem $\rightarrow$ Lightning Rod $\rightarrow$ <span style = "color:blue"> Capacitors and Capacitance </span> $\rightarrow$ Parallel Plate Capacitor $\rightarrow$ Parallel Plate Capacitor </footer>

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<h3 id="primary-stylefont-size24pxparallel-plate-capacitor-primary"><primary style="font-size:24px;">Parallel Plate Capacitor </primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px'>
<ul>
<li>This is essentially the conductor which we will discuss which in terms of parallel bit capacitor</li>
<li>This process of putting charges on these conductors is called charging of the conductors.</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>
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<hr>
<footer style = "font-size: 18px"> Lightning Rod $\rightarrow$ Capacitors and Capacitance $\rightarrow$ <span style = "color:blue"> Parallel Plate Capacitor </span> $\rightarrow$ Parallel Plate Capacitor $\rightarrow$ Capacitance </footer>

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<h3 id="primary-stylefont-size24pxparallel-plate-capacitor-primary-1"><primary style="font-size:24px;">Parallel Plate Capacitor </primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px'>
<ul>
<li>
<p>Plate area : A</p>
</li>
<li>
<p>Plate separation : d</p>
</li>
<li>
<p>Potential difference</p>
</li>
<li>
<p>$ V=E \cdot d =\frac{\sigma d }{\epsilon_0} $</p>
</li>
<li>
<p>$ \sigma=\frac{Q}{A} $</p>
</li>
<li>
<p>$V=Q \cdot \frac{d}{\epsilon_0 A}$</p>
</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>
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<hr>
<footer style = "font-size: 18px"> Capacitors and Capacitance $\rightarrow$ Parallel Plate Capacitor $\rightarrow$ <span style = "color:blue"> Parallel Plate Capacitor </span> $\rightarrow$ Capacitance $\rightarrow$ Example </footer>

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<h3 id="primary-stylefont-size24pxcapacitanceprimary"><primary style="font-size:24px;">Capacitance</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;text-align:left;font-size:30px'>
<ul>
<li>
<p>$ V=Q \cdot \frac{d}{\epsilon_0 A} $</p>
</li>
<li>
<p>$ C=\frac{\epsilon_0 A}{d} $ Capacitance</p>
</li>
<li>
<p>$ V=\frac{Q}{C} $</p>
</li>
<li>
<p>$ Q=C V $</p>
</li>
<li>
<p>C : Capacitance parameter</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-02-electric-field-and-potential-and-concept-of-capacitance-l-2_9-snyqlwxcphs-0022.jpg"></p>
</main>
<hr>
<footer style = "font-size: 18px"> Parallel Plate Capacitor $\rightarrow$ Parallel Plate Capacitor $\rightarrow$ <span style = "color:blue"> Capacitance </span> $\rightarrow$ Example $\rightarrow$ Thankyou </footer>

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<h3 id="primary-stylefont-size24pxexampleprimary"><primary style="font-size:24px;">Example</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;text-align:left;font-size:30px'>
<ul>
<li>
<p>$ d=1 \mathrm{~mm} $</p>
</li>
<li>
<p>A=10 $ \mathrm{~cm}^2 $</p>
</li>
<li>
<p>Capacitance C= $ \frac{\epsilon_0 A}{d}$$ = \frac{8.85 \times 10^{-12} \times 10 \times 10^{-4}}{10^{-3}} = 8.85 \mathrm{pF} $</p>
</li>
<li>
<p>$ C=8.85 \times 10^{-12} \mathrm{~F} $</p>
</li>
<li>
<p>Potential difference $ V$</p>
</li>
<li>
<p>$ Q=C V =8.85 \times 10^{-12}(\mathrm{~F}) \times 1(\mathrm{V}) $ $ =8.85 \times 10^{-12} \mathrm{C}  =8.85 \mathrm{kC} $</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-02-electric-field-and-potential-and-concept-of-capacitance-l-2_9-snyqlwxcphs-0023.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-02-electric-field-and-potential-and-concept-of-capacitance-l-2_9-snyqlwxcphs-0024.jpg"></p>
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<hr>
<footer style = "font-size: 18px"> Parallel Plate Capacitor $\rightarrow$ Capacitance $\rightarrow$ <span style = "color:blue"> Example </span> $\rightarrow$ Thankyou $\rightarrow$ </footer>