The two metallic plates of radius $r$ are placed at a distance $d$ apart and its capacity is $C$. If a plate of radius $r/2$ and thickness $d$ of dielectric constant $6$ is placed between the plates of the condenser, then its capacity will be
A$7C/2$
B$3C/7$
C$7C/3$
D$9C/4$
Diffcult
Download our app for free and get started
D$9C/4$
d (d) Area of the given metallic plate $A = \pi r^2$
Area of the dielectric plate $A' = \pi \,{\left( {\frac{r}{2}} \right)^2} = \frac{A}{4}$
Uncovered area of the metallic plates
$ = A - \frac{A}{4} = \frac{{3A}}{4}$
The given situation is equivalent to a parallel combination of two capacitor. One capacitor $(C')$ is filled with a dielectric medium $(K = 6)$ having area $\frac{A}{4}$ while the other capacitor $(C'')$ is air filled having area $\frac{{3A}}{4}$
Hence
$ = \frac{{{\varepsilon _0}A}}{d}\left( {\frac{K}{4} + \frac{3}{4}} \right)$$ = \frac{{{\varepsilon _0}A}}{d}\,\left( {\frac{6}{4} + \frac{3}{4}} \right) = \frac{9}{4}\,C$
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.*
In a region, the potential is represented by $V(x, y, z) = 6x - 8xy - 8y + 6yz$, where $V$ is in volts and $x, y, z$ are in metres. The electric force experienced by a charge of $2$ coulomb situated at point $( 1, 1, 1)$ is
A table tennis ball which has been covered with conducting paint is suspended by a silk thread so that it hang between two plates, out of which one is earthed and other is connected to a high voltage generator. This ball
A simple pendulum with a bob of mass $m = 1\ kg$ , charge $q = 5\mu C$ and string length $l = 1\ m$ is given a horizontal velocity $u$ in a uniform electric field $E = 2 × 10^6\ V/m$ at its bottom most point $A$ , as shown in figure. It is given a speed $u$ such that the particle leave the circular path at its topmost point $C$ . Find the speed $u$ . (Take $g = 10\ m/s^2$ )
A spherical charged conductor has surface charge density $\sigma $ . The electric field on its surface is $E$ and electric potential of conductor is $V$ . Now the radius of the sphere is halved keeping the charge to be constant. The new values of electric field and potential would be
An uncharged parallel plate capacitor having a dielectric of constant $K$ is connected to a similar air-cored parallel capacitor charged to a potential $V$. The two share the charge and the common potential is $V'$. The dielectric constant $K$ is
An empty thick conducting shell of inner radius $a$ and outer radius $b$ is shown in figure.If it is observed that the inner face of the shell carries a uniform charge density $-\sigma$ and the surface carries a uniform charge density $ '\sigma '$
If a point charge $q_A$ is placed at the center of the shell, then choose the correct statement $(s)$