Electrostatic potential energy of given system will be
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A uniformly charged ring of radius $3a$ and total charge $q$ is placed in $xy-$ plane centered at origin. A point charge $q$ is moving towards the ring along the $z-$ axis and has speed $v$ at $z = 4a$. The minimum value of $v$ such that it crosses the origin is
Let $C$ be the capacitance of a capacitor discharging through a resistor $R$. Suppose $t_{1}$ is the time taken for the energy stored in the capacitor to reduce to half its initial value and $t_{2}$ is the time taken for the charge to reduce to one-fourth its initial value. The the ratio $t _{1} / t _{2}$ will be
Three concentric metallic spherical shells of radii $R, 2R, 3R$, are given charges $Q_1, Q_2, Q_3$, respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells, $Q_1 : Q_2 : Q_3$ is
Electric potential in a region is varying according to the relation $V=\frac{3 x^2}{2}-\frac{y^2}{4}$, where $x$ and $y$ are in metre and $V$ is in volt. Electric field intensity (in $N/C$) at a point $(1 \,m , 2 \,m$ ) is ......
A $500 \,\mu F$ capacitor is charged at a steady rate of $100\, \mu C/sec$. The potential difference across the capacitor will be $10\, V$ after an interval of.....$sec$
An infinite number of charges each equal to $0.2\,\mu C$ are arranged in a line at distances $1\,m, 2\,m, 4\,m, 8\,m......$ from a fixed point. The potential at fixed point is ......$kV$
Which one statement is correct ? A parallel plate air condenser is connected with a battery. Its charge, potential, electric field and energy are ${Q_o},\;{V_o},\;{E_o}$ and ${U_o}$ respectively. In order to fill the complete space between the plates a dielectric slab is inserted, the battery is still connected. Now the corresponding values $Q,\;V,\;E$ and $U$ are in relation with the initially stated as