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$\begin{array}{l}C=\frac{Q}{V}=\frac{Q}{\frac{Q}{{\epsilon }_{0}A}\cdot d}\\ C=\frac{{\epsilon }_{0}A}{d}\end{array}$ For capacitor $C_2$$\text{ Charge }{q}_1=C_{2}r=3\times 10^{-1}\times 200=6\times 10^{-4}C$ For capacitor $C$, $\text{ Charge, }{q}_3=C_{2}r=4\times 10^{-}\times 200=8\times 10^{-1}\mathrm{C}$ SAQ 17. Derive an expression for the eleciric potential due to a point charge Ans : Electric Potentiat: Elecric potental at any point is defined as the positive charge from infinity to that point in the presence of electric work done in bringing a ty Expression for Electric Potential due to a Point Charge: Conside origin ' $O$ ', ' $P$ ' be the point at a distance ' $r$ ' from $O$, and $E$ is the $e^{\prime }$ a chit positive charge ' $Q$ ' at Figure Assume the unit charge is moved from $r_1$ to $r_3+\Delta r_1$ Then the work done in moving the charge from $r_1$ to $r_1+\Delta r_1$ is given as, \[ \begin{array}{l} \Delta W=-E \Delta r_{1} \\ \Delta W=-\frac{Q}{4 \pi \varepsilon_{e}\left(r_{1}\right)^{2}} \Delta r_{1} \quad\left[E=\frac{Q}{4 \pi \varepsilon_{e} r^{2}}\right] \end{array} \] Negative sign indicates that $\Delta r_3<0$ : Total work done in moving unit positive charge from $r_1=\infty$ to a point $r_1=r$ is given \[ \begin{aligned} W & =-\int_{\infty}^{r} \frac{Q}{4 \pi \varepsilon_{e} r_{1}^{2}} d r_{1} \\ & =\frac{-Q}{4 \pi \varepsilon_{e}}\left[\frac{r_{1}^{-2+1}}{-2+1}\right]_{\infty}^{r}=\frac{+Q}{4 \pi \varepsilon_{0}}\left[\frac{1}{r_{1}}\right]_{\infty}^{r} \\ W & =\frac{Q}{4 \pi \varepsilon_{e} r} \end{aligned} \] This work done gives the potential at point ' $P$ ' due to charge $Q$. $V=\frac{1}{4\pi {\epsilon }_e}\frac{Q}{r}$ SAQ19. Explain the behavlour of dielectrics in an Ans: Behaviour of Dlelectrics in an Electric Field: The m polar and non-polar. Polar molecule: In a polar molecule, the centre coincide 1. They have asymmetrical charge distribution and the range of dipole moment is $10^{-10}\mathrm{cm}$ Hence, these molecules are called permanent electric dipoles. 2. When a polar molecule is placed in a electric field, molecules arrange themselv: in the direction of electric field. $\mathrm{A}$ bett alignment is at low temperature and strong electric fields. 3. In the absence of electric field, molect dipole moment occurs in random dire electric dipole moment per unit volum Examples: ${\mathrm{NO}}_2,{\mathrm{H}}_2\mathrm{O},{\mathrm{NH}}_3$ etc Non-Polar Molecule: In a non-polar mole coincide with each other. They do not exhit 1 in the presence of electric field. protons (positive charge) move in the direction of electric field, while electrons (negative charges) move in opposite direction. 2. The displacement of two charges occur until the external forces and the internal forces are balanced. 28

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Updated on: Dec 31, 2023