At a certain distance from a point charge, the field intensity is $500\, Vm^{-1}$ and the potential is $-3000\, V$. The distance to the charge and the magnitude of the charge respectively are
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From a supply of identical capacitors rated $8\ \mu F$, $250\ V$, the minimum number of capacitors required to form a composite $16$ $\mu F$, $1000$ $V$ is :
A parallel plate capacitor is charged and then disconnected from the source of potential difference. If the plates of the condenser are then moved farther apart by the use of insulated handle, which one of the following is true?
A two point charges $4 q$ and $-q$ are fixed on the $x-$axis at $x=-\frac{d}{2}$ and $x=\frac{d}{2},$ respectively. If a third point charge $'q'$ is taken from the origin to $x = d$ along the semicircle as shown in the figure, the energy of the charge will
A small sphere carrying a charge ‘$q$’ is hanging in between two parallel plates by a string of length $L$. Time period of pendulum is ${T_0}$. When parallel plates are charged, the time period changes to $T$. The ratio $T/{T_0}$ is equal to
The diagram shows three infinitely long uniform line charges placed on the $X, Y $ and $Z$ axis. The work done in moving a unit positive charge from $(1, 1, 1) $ to $(0, 1, 1) $ is equal to
A thin metal plate $P$ is inserted half way between the plates of a parallel plate capacitor of capacitance $C$ in such a way that it is parallel to the two plates. The capacitance now becomes
A particle of charge $Q$ and mass $M$ moves in a circular path of radius $R$ in a uniform magnetic field of magnitude $B$. The same particle now moves with the same speed in a circular path of same radius $R$ in the space between the cylindrical electrodes of the cylindrical capacitor. The radius of the inner electrode is $R/2$ while that of the outer electrode is $ 3R/2.$ Then the potential difference between the capacitor electrodes must be