Energy per unit volume for a capacitor having area $A$ and separation $d$ kept at potential difference $V$ is given by
AIPMT 2001, Medium
Download our app for free and get started
For a parallel plate capacitor: $\quad C =\frac{ A \varepsilon_{0}}{ d }$
Volume of capacitor $= Ad$
Energy stored in a capacitor $= E =\frac{1}{2} CV ^{2}$
Energy stored per unit volume $= E ^{\prime}=\frac{\frac{1}{2} CV ^{2}}{ Ad }$
$E ^{\prime}=\frac{1}{2} \frac{\frac{A \varepsilon_{0}}{ d } V ^{2}}{ Ad }=\frac{1}{2} \varepsilon_{0} \frac{ V ^{2}}{ d ^{2}}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1View SolutionElectrostatic potential energy of given system will be
- 2A parallel - plate capacitor with plate area $A$ has separation $d$ between the plates. Two dielectric slabs of dielectric constant ${K}_{1}$ and ${K}_{2}$ of same area $\frac A2$ and thickness $\frac d2$ are inserted in the space between the plates. The capacitance of the capacitor will be given by :View Solution
- 3View SolutionThe separation between the plates of a isolated charged parallel plate capacitor is increased. Which of the following quantities will change?
- 4In the given circuit, a charge of $+80\, \mu C$ is given to the upper plate of the $4\,\mu F$ capacitor. Then in the steady state, the charge on the upper plate of the $3\,\mu F$ capacitor is.....$\mu C$View Solution
- 5Four plates of equal area $A$ are separated by equal distances $d$ and are arranged as shown in the figure. The equivalent capacity isView Solution
- 6If some charge is given to a solid metallic sphere, the field inside remains zero and by Gauss's law all the charge resides on the surface. Now, suppose that Coulomb's force between two charges varies as $1 / r^{3}$. Then, for a charged solid metallic sphereView Solution
- 7View SolutionWhen a test charge is brought in from infinity along the perpendicular bisector of an electric dipole, the work done is ..........
- 8Charges are placed on the vertices of a square as shown. Let $E$ be the electric field and $V$ the potential at the centre. If the charges on $A$ and $B$ are interchanged with those on $D$ and $C$ respectively, thenView Solution
- 9The capacity and the energy stored in a parallel plate condenser with air between its plates are respectively ${C_o}$ and ${W_o}$. If the air is replaced by glass (dielectric constant $= 5$ ) between the plates, the capacity of the plates and the energy stored in it will respectively beView Solution
- 10$A B C$ is a right angled triangle situated in a uniform electric field $\vec{E}$ which is in the plane of the triangle. The points $A$ and $B$ are at the same potential of $15 \,V$ while the point $C$ is at a potential of $20 \,V . A B=3 \,cm$ and $B C=4 \,cm$. The magnitude of electric field is (in $S.I.$ Units)View Solution
