A parallel plate capacitor has a uniform electric field $E$ in the space between the plates. If the distance between the plates is $d$ and area of each plate is $A$ , the energy stored in the capacitor is
$\frac{1}{2}{\varepsilon _0}{E^2}Ad$
${\varepsilon _0}{E}Ad$
$\frac{1}{2}{\varepsilon _0}{E^2}$
${E^2}Ad/{\varepsilon _0}$
In the figure shown, the potential difference between points $A$ and $B$ is......$V$
Two point charges $+8q$ and $-2q$ are located at $x = 0$ and $x = L$ respectively. The location of a point on the $x-$ axis at which net electric field due to these two point charges is zero, is
A network of four capacitors of capacity equal to $C_1 = C, C_2 = 2C, C_3 = 3C$ and $C_4=4C$ are conducted to a battery as shown in the figure. The ratio of the charges on $C_2$ and $C_4$ is
A finite ladder is constructed by connecting several sections of $2\,\mu F$ , $4\,\mu F$ capacitor combinations as shown in the figure. It is terminated by a capacitor of capacitance $C$. What value should be chosen for $C$ such that the equivalent capacitance of the ladder between the points $A$ and $B$ becomes independent of the number of sections in between.......$\mu F$
In a parallel plate air capacitor, a cathode beam comprising $n = 10^6$ electrons is emitted with a velocity $v_0 = 10^8\ m/s$ into the space between the plates. The potential difference between the plate is $\phi = 400\ V$ ,the seperation between the plates is $d = 2\ cm$ and the area of each plate is $l^2 = 100\ cm^2$ . The deflection of the electron beam, is ........... $mm$