Twenty seven drops of same size are charged at $220\, \mathrm{~V}$ each. They combine to form a bigger drop. Calculate the potential of the bigger drop. (In $\mathrm{~V}$)
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A parallel plate capacitor is charged to a potential difference of $100\,V$ and disconnected from the source of $emf$ . A slab of dielectric is then inserted between the plates. Which of the following three quantities change?
For changing the capacitance of a given parallel plate capacitor, a dielectric material of dielectric constant $K$ is used, which has the same area as the plates of the capacitor. The thickness of the dielectric slab is $\frac{3}{4} d$, where $'d'$ is the separation between the plates of parallel plate capacitor. The new capacitance $(C')$ in terms of original capacitance $\left( C _{0}\right)$ is given by the following relation
The figure shows a family of parallel equipotential surfaces and four paths along which an electron is made to move from one surface to another as shown in the figur
$(I)$ What is the direction of the electric field ?
$(II)$ Rank the paths according to magnitude of work done, greatest first
Figure shows a solid metal sphere of radius $‘a’$ surrounded by a concentric thin metal shell of radius $2a$ . Initially both are having charges $Q$ each. When the two are connected by a conducting wire as shown in the figure, then amount of heat produced in this process will be
A charge of $10 \,\mu C$ is placed at the origin of $x-y$ coordinate system. The potential difference between two points $(0, a)$ and $(a, 0)$ in volt will be
Charges $-q,\, q,\,q$ are placed at the vertices $A$, $B$, $C$ respectively of an equilateral triangle of side $'a'$ as shown in the figure. If charge $-q$ is released keeping remaining two charges fixed, then the kinetic energy of charge $(-q)$ at the instant when it passes through the mid point $M$ of side $BC$ is
A particle of mass $m$ and charge $q$ is kept at the top of a fixed frictionless sphere. $A$ uniform horizontal electric field $E$ is switched on. The particle looses contact with the sphere, when the line joining the center of the sphere and the particle makes an angle $45^o$ with the vertical. The ratio $\frac{qE}{mg}$ is :-
A slab of dielectric constant $K$ has the same crosssectional area as the plates of a parallel plate capacitor and thickness $\frac{3}{4}\,d$, where $d$ is the separation of the plates. The capacitance of the capacitor when the slab is inserted between the plates will be.(Given $C _{0}=$ capacitance of capacitor with air as medium between plates.)