A parallel plate capacitor has a capacity $C$. The separation between the plates is doubled and a dielectric medium is introduced between the plates. If the capacity now becomes $2C$, the dielectric constant of the medium is
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A parallel plate air capacitor has capacity $C,$ distance of separation between plates is $d$ and potential difference $V$ is applied between the plates. Force of attraction between the plates of the parallel plate air capacitor is
In an isolated parallel plate capacitor of capacitance $C$, the four surface have charges ${Q_1}$, ${Q_2}$, ${Q_3}$ and ${Q_4}$ as shown. The potential difference between the plates is
As shown in figure, on bringing a charge $Q$ from point $A$ to $B$ and from $B$ to $C$, the work done are $2\, joule$ and $-3\, joule$ respectively. The work done to bring the charge from $C$ to $A$ is
A solid sphere of radius $R$ carries a charge $(Q+q)$ distributed uniformly over its volume. A very small point like piece of it of mass $m$ gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge $q.$ If it acquires a speed $v$ when it has fallen through a vertical height $y$ (see figure), then :
Two identical capacitors $1$ and $2$ are connected in series to a battery as shown in figure. Capacitor $2$ contains a dielectric slab of dielectric constant k as shown. $Q_1$ and $Q_2$ are the charges stored in the capacitors. Now the dielectric slab is removed and the corresponding charges are $Q’_1$ and $Q’_2$. Then
A charge of $10 \,\mu C$ is placed at the origin of $x-y$ coordinate system. The potential difference between two points $(0, a)$ and $(a, 0)$ in volt will be
For a uniformly charged thin spherical shell, the electric potential $(V)$ radially away from the center $(O)$ of shell can be graphically represented as
A charge $ + q$ is fixed at each of the points $x = {x_0},\,x = 3{x_0},\,x = 5{x_0}$..... $\infty$, on the $x - $axis and a charge $ - q$ is fixed at each of the points $x = 2{x_0},\,x = 4{x_0},x = 6{x_0}$,..... $\infty$. Here ${x_0}$ is a positive constant. Take the electric potential at a point due to a charge $Q$ at a distance $r$ from it to be $Q/(4\pi {\varepsilon _0}r)$. Then, the potential at the origin due to the above system of charges is