A parallel plate capacitor of capacitance $C$ is connected to a battery and is charged to a potential difference $V$ . Another capacitor of capacitance $2C$ is similarly charged to a potential difference $2V$ . The charging battery is now disconnected and the capacitors are connect in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is
zero
$\frac{3}{2}\,C{V^2}$
$\frac{25}{6}\,C{V^2}$
$\frac{9}{2}\,C{V^2}$
Force between $A$ and $B$ is $F$. If $75\%$ charge of $A$ is transferred to $B$ then force between $A$ and $B$ is
Potential in the $x-y$ plane is given as $V = 5(x^2 + xy)\, volts$. The electric field at the point $(1, -2)$ will be
The conducting spherical shells shown in the figure are connected by a conductor. The capacitance of the system 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 dielectric has dielectric constant $K_1 = 6$ and thickness $\frac {d}{3}$ while the other one has dielectric constant $K_2 = 12$ and thickness $\frac {2d}{3}$ . Capacitance of the capacitor is now ......... $pF$
Consider a solid insulating sphere of radius $R$ with charge density varying as $\rho = \rho _0r^2$ ($\rho _0$ is a constant and $r$ is measure from centre). Consider two points $A$ and $B$ at distance $x$ and $y$ respectively $(x < R, y > R)$ from the centre. If magnitudes of electric fields at points $A$ and $B$ are equal, then