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A parallel plate capacitor is made of two plates of length $l$, width $w$ and separated by distance $d$. A dielectric slab ( dielectric constant $K$) that fits exactly between the plates is held near the edge of the plates. It is pulled into the capacitor by a force $F = -\frac{{\partial U}}{{\partial x}}$ where $U$ is the energy of the capacitor when dielectric is inside the capacitor up to distance $x$ (See figure). If the charge on the capacitor is $Q$ then the force on the dielectric when it is near the edge is
Two capacitors each of $1\,\mu F$ capacitance are connected in parallel and are then charged by $200\;volts$ $d.c.$ supply. The total energy of their charges (in $joules$) is
A point dipole $\vec p = - {p_0}\hat x$ is kept at the origin. The potential and electric field due to this dipole on the $y-$ axis at a distance $d$ are, respectively : (Take $V = 0$ at infinity)
Five capacitors, each of capacitance value $C$ are connected as shown in the figure. The ratio of capacitance between $P$ and $R$, and the capacitance between $P$ and $Q$, is
A circuit shown in the figure consists of a battery of $emf$ $10$ $V$ and two capacitance $C_1$ and $C_2 $ of capacitances $1.0$ $ \mu F$ and $2.0$ $\mu F$ respectively. The potential difference $V_A - V_B$ is $5\,V$
A parallel plate capacitor of capacitance $5\,\mu F$ and plate separation $6\, cm$ is connected to a $1\, V$ battery and charged. A dielectric of dielectric constant $4$ and thickness $4\, cm$ is introduced between the plates of the capacitor. The additional charge that flows into the capacitor from the battery is........$\mu C$
The equivalent capacitance of three capacitors of capacitance ${C_1},{C_2}$ and ${C_3}$ are connected in parallel is $12$ units and product ${C_1}.{C_2}.{C_3} = 48$. When the capacitors ${C_1}$ and ${C_2}$ are connected in parallel, the equivalent capacitance is $6$ units. Then the capacitance are