The mean electric energy density between the plates of a charged capacitor is (here $q$= charge on the capacitor and $A$= area of the capacitor plate)
A$\frac{{{q^2}}}{{2{\varepsilon _0}{A^2}}}$
B$\frac{q}{{2{\varepsilon _0}{A^2}}}$
C$\frac{{{q^2}}}{{2{\varepsilon _0}A}}$
D
None of the above
Medium
Download our app for free and get started
A$\frac{{{q^2}}}{{2{\varepsilon _0}{A^2}}}$
a (a) Energy density $ = \frac{1}{2}{\varepsilon _0}{E^2} = \frac{1}{2}{\varepsilon _0}{\left( {\frac{\sigma }{{{\varepsilon _0}}}} \right)^2} = \frac{{{\sigma ^2}}}{{2{\varepsilon _0}}} = \frac{{{q^2}}}{{2{\varepsilon _0}{A^2}}}$
Download our app
and 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.*
Two capacitors of capacities $2 {C}$ and ${C}$ are joined in parallel and charged up to potential ${V}$. The battery is removed and the capacitor of capacity $C$ is filled completely with a medium of dielectric constant ${K}$. The potential difference across the capacitors will now be
Sixty-four drops are jointed together to form a bigger drop. If each small drop has a capacitance $C$, a potential $V$, and a charge $q$, then the capacitance of the bigger drop will be
The figure gives the electric potential $V$ as a function of distance through five regions on $x$-axis. Which of the following is true for the electric field $E$ in these regions
A small sphere of mass $m =\ 0.5\, kg$ carrying a positive charge $q = 110\ \mu C$ is connected with a light, flexible and inextensible string of length $r = 60 \ cm$ and whirled in a vertical circle. If a vertically upwards electric field of strength $E = 10^5 NC^{-1}$ exists in the space, The minimum velocity of sphere required at highest point so that it may just complete the circle........$m/s$ $(g = 10\, ms^{-2})$
A square of side ‘$a$’ has charge $Q$ at its centre and charge ‘$q$’ at one of the corners. The work required to be done in moving the charge ‘$q$’ from the corner to the diagonally opposite corner is
A parallel plate capacitor with air between the plates has a capacitance of $9\,pF$. The separation between its plates is $'d'$. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant $K_1=3$ and thickness $\frac {d}{3}$ while the other one has dielectric constant $K_2 = 6$ and thickness $\frac {2d}{3}$ . Capacitance of the capacitor is now........$pF$
A ball of mass $1\, g$ and charge ${10^{ - 8}}\,C$ moves from a point $A$. where potential is $600\, volt$ to the point $B$ where potential is zero. Velocity of the ball at the point $B$ is $20\, cm/s$. The velocity of the ball at the point $A$ will be