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A parallel plate capacitor of capacitance $C$ has spacing $d$ between two plates having area $A$. The region between the plates is filled with $N$ dielectric layers, parallel to its plates, each with thickness $\delta=\frac{ d }{ N }$. The dielectric constant of the $m ^{\text {th }}$ layer is $K _{ m }= K \left(1+\frac{ m }{ N }\right)$. For a very large $N \left(>10^3\right)$, the capacitance $C$ is $\alpha\left(\frac{ K \varepsilon_0 A }{ d \;ln 2}\right)$. The value of $\alpha$ will be. . . . . . . .
Four capacitors of each of capacity $3\,\mu F$ are connected as shown in the adjoining figure. The ratio of equivalent capacitance between $A$ and $B$ and between $A$ and $C$ will be
The figure gives the electric potential $V$ as a function of distance through five regions on $x$-axis. Which of the following is true for the electric field $E$ in these regions
Four point charges $-Q, -q, 2q$ and $2Q$ are placed, one at each comer of the square. The relation between $Q$ and $q$ for which the potential at the centre of the square is zero is
A parallel plate air capacitor of capacitance $C$ is connected to a cell of emf $V$ and then disconnected from it. A dielectric slab of dielectric constant $K,$ which can just fill the air gap of the capacitor, is now inserted in it. Which of the following is incorrect $?$
In the following circuit, the switch $S$ is closed at $t = 0.$ The charge on the capacitor $C_1$ as a function of time will be given by $\left( {{C_{eq}}\, = {\kern 1pt} \,\frac{{{C_1}{C_2}}}{{{C_1} + {C_2}}}} \right).$
A point chargr $Q$ is fixed A small charge $q$ and mass $m$ is given a velocity $v_0$ from infinity & perpendicular distance $r_0$ as shown. If distance of closest approach is $r_0/2$. The value of $q$ is [Given $mv_0^2 = \frac{{{Q^2}}}{{4\pi { \in _0}\,{r_0}}}$]