Electrostatics

A parallel plate capacitor has plate of length ' $$ l', width ' w$$ ' and separation of plates is 'd $$ '. It is connected to a battery of emf V$$ . A dielectric slap of the same thickness 'd $$ ' and of dielectric constant $$ k = 4 is being, inserted between the plates of the capacitor. At what length of the slab inside plates, will be energy stored in the capacitor be two times the initial energy stored?

Ten charges are placed on the circumference of a circle of radius $10\mathrm{s}$ $$ with constant angular separation between successive charges. Alternate charges 1, 3, 5, 7, 9 have charge (+q)$$ each, while $\mathrm{2,4},\mathrm{6,8},10$ $$ have charge $$ (-q)each. The potential v$$ and the electric field $$ E at the centre of the circle are respectively: (Take V = 0 $$ at infinity)

Three charged particles $A,B$ $$ and $C$ $$ with charges $-4q,2q$ $$ and $$ $-2q$  are present on the circumference of a circle of radius $d$ $$ . The charged particles $A,C$ $$ and centre $O$ $$ of the circle formed an equilateral triangle as shown in figure. Electric field at $\mathrm{O}$ $$ along $\mathrm{x}$ $$ -direction is:

A $60\mathrm{p}\mathrm{F}$ capacitor is fully charged by a $20\mathrm{V}$ supply. It is then disconnected from the supply and is connected to another uncharged $60\mathrm{p}\mathrm{F}$ capacitor in parallel. The electrostatic energy that is lost in this process by the time the charge is redistributed between them is (in $\mathrm{n}\mathrm{J}$  )

In a parallel plate capacitor set up, plate area of capacitor is 2 m² and the plates are separated by 1m. If the space between the plates are filled with a dielectric material of thickness 0.5 m and area 2 m² (See fig) the capacitance of the set-up will be ______ ε₀. (Dielectric constant of the material = 3.2) (Round off to the Nearest Integer)

If qf is the free charge on the capacitor plates and qb is the bound charge on the dielectric slab of dielectric constant k placed between the capacitor plates, then bound charge qb can be expressed as:
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A cube of side ‘a’ has point charges +Q located at each of its vertices except at the origin where the charge is -Q. The electric field at the centre of cube is:

Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in

If $c$  is the velocity of light in free space, the correct statements about photon among the following are:

A. The energy of a photon is  $E=hv$ .

B. The velocity of a photon is c.

C. The momentum of a photon,  $p=\frac{hv}{c}$ .

D. In a photon-electron collision, both total energy and total momentum are conserved.

E. Photon possesses positive charge.

Choose the correct answer from the options given below:

In a vernier callipers, $\left(N+1\right)$ divisions of vernier scale coincide with $N$  divisions of main scale. If 1 MSD represents 0.1 mm, the vernier constant (in cm) is: