Electrostatic P...

Match the following two columns:

A very thin metal sheet is inserted halfway between the parallel plates of an air-gap capacitor. The sheet is thin compared to the distance between the plates, and it does not touch either plate when fully inserted. The system had capacitance, $$C$$, before the plate is inserted.
What is the equivalent capacitance of the system after the sheet is fully inserted?

The plates of a parallel plate capacitor are charged upto $$100 V$$.A $$2 mm$$ thick insulator shunt is inserted between the plates . Then to maintain the same potential difference ,the distance between the same potential difference , the distance between the capacitor plates is increased by $$ 1.6 mm$$.The dielectric constant of the insulator is 

A uniform electric field of magnitude $$290 V/m$$ is directed in the positive $$x$$ direction. A $$+13.0 \mu C$$ charge moves from the origin to the point $$(x, y) = (20.0 cm, 50.0 cm).$$

What is the change in the potential energy of the charge field system?

The area of the plates of a parallel plate capacitor is $$A$$ and the gap between them is $$d$$. The gap is filled with a non-homogeneous dielectric whose dielectric constant varies with the distance $$'y'$$from one plate as : $$K\ =\ \lambda \sec \left(\frac{\pi y}{2d}\right)$$ , where $$\lambda$$ is a dimensionless constant. The capacitance of this capacitor is

Five conducting plates are placed parallel to each other Separation between them is $$d$$ and area of each plate is $$A$$. Plate number $$1,2$$ and $$3$$ are connected with each other and at the same time through a cell of emf $$E$$. The charge on plate number $$1$$ is

A capacitor of capacitance $${ C }_{ 1 }=1\mu F$$ can with stand maximum voltage $${ V }_{ 1 }=6kV$$ (kilo-volt) and another capacitor of capacitance $${ C }_{ 2 }=3\mu F$$ can withstand maximum voltage $${ V }_{ 2 }=4kV$$. When the two capacitors are connected in series, the combined system can withstand a maximum voltage of:

In a quark model of elemetary particles, a neutron is made of one up quark of charge $$\cfrac{2}{3}e$$ and two down quark of charges $$\left( -\cfrac { 1 }{ 3 } e \right) $$. If they have a triangle configuration with side length of the order of $${ 10 }^{ -15 }m$$. The electrostatic potential energy of neutron in $$MeV$$ is

A solid conducting sphere of radius $${R_1}$$ is surrounded by another concentric hollow conducting sphere of radius $${R_2}$$. the capacitance of this assembly is proportional to:-

The gravitational field strength $$\vec {E}$$ and gravitational potential $$V$$ are related as $$\vec {E} = -\left (\dfrac {\partial V}{\partial x} \hat {i} + \dfrac {\partial V}{\partial y} \hat {j} + \dfrac {\partial V}{\partial z}\hat {k}\right )$$
In the figure, transversal lines represent equipotential surfaces. A particle of mass $$m$$ is released from rest at the origin. The gravitational unit of potential, $$1\overline {V} = 1\ cm^{2}/ s^{2}$$.
Speed of the particle $$(v) (y$$ is in cm $$v$$ is in $$cm/s$$) as function of its y-co-ordinate is