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If ${q}_{{f}}$ is the free charge on the capacitor plates and ${q}_{{b}}$ is the bound charge on the dielectric slab of dielectric constant $k$ placed between the capacitor plates, then bound charge $q_{b}$ can be expressed as
Figure $(A)$ shows two capacitors connected in series and joined to a battery. The graph in figure $(B)$ shows the variation in potential as one moves from left to right on the branch containing the capacitors, if
The distance between the plates of a charged parallel plate capacitor is $5\ cm$ and electric field inside the plates is $200\ Vcm^{-1}$. An uncharged metal bar of width $2\ cm$ is fully immersed into the capacitor. The length of the metal bar is same as that of plate of capacitor. The voltage across capacitor after the immersion of the bar is......$V$
A parallel plate capacitor has plate area $100\, m ^{2}$ and plate separation of $10\, m$. The space between the plates is filled up to a thickness $5\, m$ with a material of dielectric constant of $10 .$ The resultant capacitance of the system is $'x'$ $pF$. The value of $\varepsilon_{0}=8.85 \times 10^{-12} F \cdot m ^{-1}$ The value of $'x'$ to the nearest integer is............
A point charge of magnitude $+ 1\,\mu C$ is fixed at $(0, 0, 0) $. An isolated uncharged spherical conductor, is fixed with its center at $(4, 0, 0).$ The potential and the induced electric field at the centre of the sphere is
Two capacitors of capacitances $3\,\mu \,F$ and $6\,\mu F$ are charged to a potential of $12 \,V$ each. They are now connected to each other, with the positive plate of each joined to the negative plate of the other. The potential difference across each will be......$volt$