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A charge of $10\, e.s.u.$ is placed at a distance of $2\, cm$ from a charge of $40\, e.s.u.$ and $4\, cm$ from another charge of $20\, e.s.u.$ The potential energy of the charge $10\, e.s.u.$ is (in $ergs$)
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 $=1 \mathrm{~g} / \mathrm{cc}$ )
Three capacitors of capacitances $3\,\mu F,\;9\,\mu F$ and $18\,\mu F$ are connected once in series and another time in parallel. The ratio of equivalent capacitance in the two cases $\left( {\frac{{{C_s}}}{{{C_p}}}} \right)$ will be
The electric potential $V(x)$ in a region around the origin is given by $V(x) = 4x^2\,volts$ . The electric charge enclosed in a cube of $1\,m$ side with its centre at the origin is (in coulomb)
A capacitor is charged with a battery and energy stored is $U$. After disconnecting battery another capacitor of same capacity is connected in parallel to the first capacitor. Then energy stored in each capacitor is