Electrostatics

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:

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:

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: The potential ( $V$ ) at any axial point, at 2 m distance ( $r$ ) from the centre of the dipole of dipole moment vector $\dot{P}$ of magnitude, $4*10^{-6}Cm$ , is $\pm 9*10^3 V$ .

(Take $\frac{1}{4\pi {ϵ}_0}=9*10^9$ SI units)

Reason R :  $V=\pm \frac{2P}{4\pi {?}_0{r}^2}$ , where $r$  is the distance of any axial point, situated at 2 m from the centre of the dipole.

In the light of the above statements, choose the correct answer from the options given below:

In the following circuit, the equivalent capacitance between terminal $A$ and terminal $B$  is :