Three charges $Q,\, + q$ and $ + q$ are placed at the vertices of a right-angled isosceles triangle as shown. The net electrostatic energy of the configuration is zero if $Q$ is equal to
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Two parallel plate capacitors have their plate areas $100 \,cm ^2$ and $500 \,cm ^2$ respectively. If they have the same charge and potential and the distance between the plates of the first capacitor is $0.5 \,mm$, then the distance between the plates of the second capacitor is ........ $cm$
$0.2\, F$ capacitor is charged to $600\, V$ by a battery. On removing the battery. It is connected with another parallel plate condenser of $1\, F$. The potential decreases to....$V$
Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle $\theta$ with each other. When suspended in water the angle remains the same. If density of the material of the sphere is $1.5 \mathrm{~g} / \mathrm{cc}$, the dielectric constant of water will be
(Take density of water $=1 \mathrm{~g} / \mathrm{cc}$ )
A hollow conducting sphere of radius $R$ has a charge $( + Q)$ on its surface. What is the electric potential within the sphere at a distance $r = \frac{R}{3}$ from its centre