Question
A parallel-plate capacitor with the plate area $100cm^2$ and the separation between the plates 1.0cm is connected across a battery of emf 24 volts. Find the force of attraction between the plates.
✓
Answer
$A = 100cm^2 = 10^{-2}m^2$
$d = 1cm = 10^{-2}m$
$V = 24V_0$
$\therefore$ The capacitance $\text{C}=\frac{\in_0\text{A}}{\text{d}}=\frac{8.85\times10^{-12}\times10^{-2}}{10^{-2}}=8.85\times10^{-12}$
$\therefore$ The energy stored $\text{C}_1=\Big(\frac{1}{2}\Big)\text{CV}^2$
$=\Big(\frac{1}{2}\Big)\times10^{-12}\times(24)^2$
$=2548.8\times10^{-12}$
$\therefore$ The forced attraction between the plates $=\frac{\text{C}_1}{\text{d}}=\frac{2548.8\times10^{-12}}{10^{-2}}=2.54\times10^{-7}\text{N.}$
$d = 1cm = 10^{-2}m$
$V = 24V_0$
$\therefore$ The capacitance $\text{C}=\frac{\in_0\text{A}}{\text{d}}=\frac{8.85\times10^{-12}\times10^{-2}}{10^{-2}}=8.85\times10^{-12}$
$\therefore$ The energy stored $\text{C}_1=\Big(\frac{1}{2}\Big)\text{CV}^2$
$=\Big(\frac{1}{2}\Big)\times10^{-12}\times(24)^2$
$=2548.8\times10^{-12}$
$\therefore$ The forced attraction between the plates $=\frac{\text{C}_1}{\text{d}}=\frac{2548.8\times10^{-12}}{10^{-2}}=2.54\times10^{-7}\text{N.}$
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
Consider the situation shown in figure. The elevator is going up with an acceleration of $2.00m/s^2$ and the focal length of the mirror is 12.0cm. All the surfaces are smooth and the pulley is light. The mass-pulley system is released from rest (with respect to the elevator) at t = 0 when the distance of B from the mirror is 42.0cm. Find the distance between the image of the block B and the mirror at t = 0.200s. Take $g = 10m/s^2.$
→A myopic adult has a far point at 0.1m. His power of accomodation is 4 diopters.
- What power lenses are required to see distant objects?
- What is his near point without glasses?
- What is his near point with glasses? (Take the image distance from the lens of the eye to the retina to be 2cm.)
The deuteron is bound by nuclear forces just as H-atom is made up of p and e bound by electrostatic forces. If we consider the force between neutron and proton in deuteron as given in the form of a Coulomb potential but with an effective charge e':
$\text{F}=\frac{1}{4\pi\in_0}\frac{\text{e}'^2}{\text{r}}$
estimate the value of (e’/e) given that the binding energy of a deuteron is 2.2MeV.
→$\text{F}=\frac{1}{4\pi\in_0}\frac{\text{e}'^2}{\text{r}}$
estimate the value of (e’/e) given that the binding energy of a deuteron is 2.2MeV.
An emf $\varepsilon=100 \sin 314 t$ is applied across a pure capacitor of $637 \mu F$. Find
$i.$ the instantaneous current $I$
$ii.$ instantaneous power $P$
$ii.$ the frequency of power and
$iii.$ the frequency of power and
$iv.$ the maximum energy stored in the capacitor.
→$i.$ the instantaneous current $I$
$ii.$ instantaneous power $P$
$ii.$ the frequency of power and
$iii.$ the frequency of power and
$iv.$ the maximum energy stored in the capacitor.
In a Young's double slit interference experiment the fringe pattern is observed on a screen placed at a distance D from the slits. The slits are separated by a distance d and are illuminated by monochromatic light of wavelength $\lambda$. Find the distance from the central point where the intensity falls to,
→- Half the maximum.
- One fourth of the maximum.
The switch S shown in figure. is kept closed for a long time and is then opened at t = 0. Find the current in the middle $1.0\Omega$ resistor at t = 1ms.
→Electrons emitted with negligible speed from an electron gun are accelerated through a potential difference V along the x-axis. These electrons emerge from a narrow hole into a uniform magnetic field B directed along this axis. However, some of the electrons emerging from the hole make slightly divergent angles, as shown in the figure. Show that these paraxial electrons are refocussed on the x-axis at a distance $\sqrt{\frac{8\pi^2\text{mV}}{\text{eB}^2}}.$
→The $\text{K}_\alpha$ X-rays of aluminium (Z = 13) and zinc (Z = 30) have wavelengths 887pm and 146pm respectively. Use Moseley's law $\sqrt{\text{v}}=\text{a}(\text{z-b})$ to find the wavelengths of the $\text{K}_\alpha$ X-ray of iron (Z = 26).
→- Explain briefly the principle on which a transistor-amplifier works as an oscillator. Draw the necessary circuit diagram and explain its working.
- Identify the equivalent gate for the following circuit and write its truth table.
The optical properties of a medium are governed by the relative permitivity $(\in_\text{r})$ and relative permeability $(\mu_\text{r})$. The refractive index is defined as $\sqrt{\mu_\text{r}\in_\text{r}}=\text{n}$.For ordinary material $\in_\text{r}=0\text{ and }\mu_\text{r}<0$ and the positive sign is taken for the square root. In 1964, a Russian scientist V. Veselago postulated the existence of material with $\in_\text{r}=0\text{ and }\mu_\text{r}<0$. Since then such 'metamaterials' have been produced in the laboratories and their optical properties studied. For such materials $\text{n}=-\sqrt{\mu_1\in_1}$. As light enters a medium of such refractive index the phases travel away from the direction of propagation.
→- According to the description above show that if rays of light enter such a medium from air (refractive index = 1) at an angle ? In $2^{nd}$ quadrant, them the refracted beam is in the $3^{rd}$ quadrant.
- Prove that Snell's law holds for such a medium.