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Electric potential in a region is varying according to the relation $V=\frac{3 x^2}{2}-\frac{y^2}{4}$, where $x$ and $y$ are in metre and $V$ is in volt. Electric field intensity (in $N/C$) at a point $(1 \,m , 2 \,m$ ) is ......
A capacitor of capacity $C$ is charged to a steady potential difference $V$ and connected in series with an open key and a pure resistor $'R'$. At time $t = 0$, the key is closed. If $I =$ current at time $t$, a plot of log $I$ against $'t'$ is as shown in $(1)$ in the graph. Later one of the parameters i.e. $V, R$ or $C$ is changed keeping the other two constant, and the graph $(2)$ is recorded. Then
Two metallic plates form a parallel plate capacitor. The distance between the plates is $'d'.$ A metal sheet of thickness $\frac{d}{2}$ and of area equal to area of each plate is introduced between the plates. What will be the ratio of the new capacitance to the original capacitance of the capacitor $?$
Consider a sphere of radius $R$ with uniform charge density and total charge $Q$. The electrostatic potential distribution inside the sphere is given by $\theta_{(r)}=\frac{Q}{4 \pi \varepsilon_{0} R}\left(a+b(r / R)^{C}\right)$. Note that the zero of potential is at infinity. The values of $(a, b, c)$ are
The plates of a parallel plate capacitor of capacity $50\,\mu C$ are charged to a potential of $100\;volts$ and then separated from each other so that the distance between them is doubled. How much is the energy spent in doing so
A composite parallel plate capacitor is made up of two different dielectric materials with different thickness $\left(t_{1}\right.$ and $\left.t_{2}\right)$ as shown in figure. The two different dielectric material are separated by a conducting foil $F$. The voltage of the conducting foil is $.....V$
Consider a spherical shell of radius $R$ with a total charge $+ Q$ uniformly spread on its surface (centre of the shell lies at the origin $x=0$ ). Two point charges $+q$ and $-q$ are brought, one after the other from far away and placed at $x=-a / 2$ and $x=+a / 2( < R)$, respectively. Magnitude of the work done in this process is
A charge of $5\,C$ is given a displacement of $0.5\,m$. The work done in the process is $10\,J$. The potential difference between the two points will be.......$V$
The expression for the capacity of the capacitor formed by compound dielectric placed between the plates of a parallel plate capacitor as shown in figure, will be (area of plate $ = A$)