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A parallel-plate capacitor consists of a fixed plate and a movable plate that is allowed to slide in the direction parallel to the plates. Let $x$ be the distance of overlap, as shown in the figure. The separation between the plates is fixed. Assume that the plates are electrically isolated, so that their charges $±Q$ are constant. Force on the movable plate is proportional to
Two charged parallel plate capacitors, each with separation between plates equal to $d$, are separated by a large distance $L >> d$. Then the force of interaction between them is proportional to
The electric potential $V$ at any point $O$ ($x$, $y$, $z$ all in metres) in space is given by $V = 4{x^2}\,volt$. The electric field at the point $(1m,\,0,\,2m)$ in $volt/metre$ is
A capacitor of capacitance $C$ is initially charged to a potential difference of $V$ $volt$. Now it is connected to a battery of $2V$ with opposite polarity. The ratio of heat generated to the final energy stored in the capacitor will be
A thin metallic spherical shell contains a charge $Q$ on it. A point charge $+q$ is placed at the centre of the shell and another charge $q'$ is placed outside it as shown in fig. All the three charges are positive. The force on the central charge due to the shell is :-
Two condensers, one of capacity $C$ and other of capacity $C/2$ are connected to a $V-$ volt battery, as shown in the figure. The work done in charging fully both the condensers is
The magnitude of electric field on the surface of a uniformly charged metalic spherical shell is $E$. If a hole is made in it using a insulating device, then the magnitude of electric field in the hole will be