Question
A parallel plate capacitor is connected to a battery. The plates are pulled apart with a uniform speed. If $x$ is the separation between the plates, the time rate of change of electrostatic energy of capacitor is proportional to
✓
Answer
(a) $U = \frac{1}{2}C{V^2} = \frac{1}{2}\left( {\frac{{{\varepsilon _0}A}}{x}} \right)\,{V^2}$
$\frac{{dU}}{{dt}} = \frac{1}{2}{\varepsilon _0}A{V^2}\left( { - \frac{1}{{{x^2}}}\frac{{dx}}{{dt}}} \right)$ $==>$ $\frac{{dU}}{{dt}} \propto {x^{ - 2}}$
$\frac{{dU}}{{dt}} = \frac{1}{2}{\varepsilon _0}A{V^2}\left( { - \frac{1}{{{x^2}}}\frac{{dx}}{{dt}}} \right)$ $==>$ $\frac{{dU}}{{dt}} \propto {x^{ - 2}}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Two plates $A$ and $B$ have thermal conductivities $84\,Wm ^{-1}\,K ^{-1}$ and $126\,Wm ^{-1}\,K ^{-1}$ respectively. They have same surface area and same thickness. They are placed in contact along their surfaces. If the temperatures of the outer surfaces of $A$ and $B$ are kept at $100^{\circ}\,C$ and $0{ }^{\circ}\,C$ respectively, then the temperature of the surface of contact in steady state is $..........\,{ }^{\circ} C$.
→The $K, L$ and $M$ energy levels of platinum lie roughly at $78, 12$ and $3\ keV$ respectively. The ratio of wavelength of $K_{\alpha}$ line to that of $K_{\beta}$ line in $X-$ ray spectrum is :
→A force of $6.4\, N$ stretches a vertical spring by $0.1 \,m$. The mass that must be suspended from the spring so that it oscillates with a period of $\left( {\frac{\pi }{4}} \right)sec$. is ... $kg$
→In the figure, the potentiometer wire $AB$ of length $L$ and resistance $9r$ is joined to the cell $D$ of $emf$ $\varepsilon $ and internal resistance $r$. The cell $C's$ $emf$ is $\frac{\varepsilon }{2}$and its internal resistance is $2r$. The galvanometer $G$ will show no deflection when the length $AJ$ is
→If the overbridge is concave instead of being convex, the thrust on the road at the lowest position will be
The $ i-V$ characteristic of a $P-N$ junction diode is shown below. The approximate dynamic resistance of the $P-N$ junction when a forward bias of $2\;volt $ is applied.......$\Omega$
→$Assertion$ : Mountain roads rarely go straight up the slope.
$Reason$ : Slope of mountains are large, therefore more chances of vehicle to slip from roads
→$Reason$ : Slope of mountains are large, therefore more chances of vehicle to slip from roads
Formaldehyde reacts with ammonia to give urotropine. The formula of urotropine is
A perfect smooth sphere $A$ of mass $2\ kg$ is in contact with a rectangular block $B$ of mass $4\ kg$ and vertical wall as shown in the figure. All surfaces are smooth. Find normal reaction by vertical wall on sphere $A$ .......... $N$
→$A$ $4$ -kilogram disk slides over level ice toward the east at a velocity of $1$ meter per second, as shown. The disk strikes a post and rebounds toward the north at the same speed. The change in the magnitude of the eastward component of the momentum of the disk is ............. $\mathrm{kg}$ $ \cdot $ $\mathrm{m}/ \mathrm{s}$
→