Two capacitors of capacitances $1\ \mu F$ and $3\ \mu F$ are charged to the same voltages $5\,V$. They are connected in parallel with oppositely charged plates connected together. Then:
Diffcult
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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)
A solid sphere of radius $R$ carries a charge $(Q+q)$ distributed uniformly over its volume. A very small point like piece of it of mass $m$ gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge $q.$ If it acquires a speed $v$ when it has fallen through a vertical height $y$ (see figure), then :
A parallel plate capacitor of capacitance $90\ pF$ is connected to a battery of $emf$ $20\ V$. If a dielectric material of dielectric constant $K = \frac{5}{3}$ is inserted between the plates, the magnitude of the induced charge will be.......$n $ $C$
A thin-walled, spherical conducting shell $S$ of radius $R$ is given charge $Q$. The same amount of charge is also placed at its centre $C. $ Which of the following statements are correct ?
A solid conducting sphere having a charge $Q$ is surrounded by an uncharged concentric conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be $V$. If the shell is now given a charge of $-3Q$, the new potential difference between the same two surfaces is......$V$
The diagram shows a small bead of mass $m$ carrying charge $q$. The bead can freely move on the smooth fixed ring placed on a smooth horizontal plane. In the same plane a charge $+Q$ has also been fixed as shown. The potential atthe point $P$ due to $+Q$ is $V$. The velocity with which the bead should projected from the point $P$ so that it can complete a circle should be greater than