Which of the following correctly represents the variation of electric potential $$(\mathrm{V})$$ of a charged spherical conductor of radius $$(\mathrm{R})$$ with radial distance $$(\mathrm{r})$$ from the center?

As shown in the figure, a point charge $Q$ is placed at the centre of conducting spherical shell of inner radius $a$ and outer radius $b$. The electric field due to charge $\mathrm{Q}$ in three different regions $\mathrm{I},\mathrm{II}$ and $\mathrm{III}$ is given by: $(\mathrm{I}:rb$ )

Electric field in a certain region is given by $$\overrightarrow{\mathrm{E}}=\left(\frac{\mathrm{A}}{x^2}\hat{i}+\frac{\mathrm{B}}{y^3}\hat{j}\right)\text{. The }\mathrm{SI}\text{ unit of }\mathrm{A}\text{ and }\mathrm{B}$$ are :

Two isolated metallic solid spheres of radii $$\mathrm{R}$$ and $$2\mathrm{R}$$ are charged such that both have same charge density $$\sigma$$. The spheres are then connected by a thin conducting wire. If the new charge density of the bigger sphere is $${\sigma }^{\prime }$$. The ratio $$\frac{{\sigma }^{\prime }}{\sigma }$$ is :

A point charge $$2\times 10^{-2}\mathrm{C}$$ is moved from P to S in a uniform electric field of $$30\mathrm{N}{\mathrm{C}}^{-1}$$ directed along positive x-axis. If coordinates of P and S are (1, 2, 0) m and (0, 0, 0) m respectively, the work done by electric field will be

In a cuboid of dimension $$2\mathrm{L}\times 2\mathrm{L}\times \mathrm{L}$$, a charge $$q$$ is placed at the center of the surface '$$\mathrm{S}$$' having area of $$4{\mathrm{L}}^2$$. The flux through the opposite surface to '$$\mathrm{S}$$' is given by

A point charge of 10 $$\mu$$C is placed at the origin. At what location on the X-axis should a point charge of 40 $$\mu$$C be placed so that the net electric field is zero at $$x=2$$cm on the X-axis?

The electric potential at the centre of two concentric half rings of radii R$${}_1$$ and R$${}_2$$, having same linear charge density $$\lambda$$ is :

If two charges q$${}_1$$ and q$${}_2$$ are separated with distance 'd' and placed in a medium of dielectric constant K. What will be the equivalent distance between charges in air for the same electrostatic force?

The electric field due to a short electric dipole at a large distance $(r)$ from center of dipole on the equatorial plane varies with distance as :

A $$10\mu \mathrm{C}$$ charge is divided into two parts and placed at $$1\mathrm{cm}$$ distance so that the repulsive force between them is maximum. The charges of the two parts are:

Two charges each of magnitude $$0.01\mathrm{C}$$ and separated by a distance of $$0.4\mathrm{mm}$$ constitute an electric dipole. If the dipole is placed in an uniform electric field '$$\vec{E}$$' of 10 dyne/C making $$30^{\circ }$$ angle with $$\vec{E}$$, the magnitude of torque acting on dipole is:

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : If an electric dipole of dipole moment $$30\times 10^{-5}\mathrm{C}\mathrm{m}$$ is enclosed by a closed surface, the net flux coming out of the surface will be zero. Reason R : Electric dipole consists of two equal and opposite charges. In the light of above, statements, choose the correct answer from the options given below.

In a metallic conductor, under the effect of applied electric field, the free electrons of the conductor

Electric potential at a point '$$\mathrm{P}$$' due to a point charge of $$5\times 10^{-9}\mathrm{C}$$ is $$50\mathrm{V}$$. The distance of '$$\mathrm{P}$$' from the point charge is: (Assume, $$\frac{1}{4\pi {\epsilon }_0}=9\times 10^{+9}{\mathrm{Nm}}^2{\mathrm{C}}^{-2}$$ )

Graphical variation of electric field due to a uniformly charged insulating solid sphere of radius $$\mathrm{R}$$, with distance $$r$$ from the centre O is represented by:

For a uniformly charged thin spherical shell, the electric potential (V) radially away from the centre (O) of shell can be graphically represented as -

A dipole comprises of two charged particles of identical magnitude $$q$$ and opposite in nature. The mass 'm' of the positive charged particle is half of the mass of the negative charged particle. The two charges are separated by a distance '$$l$$'. If the dipole is placed in a uniform electric field '$$\bar{E}$$'; in such a way that dipole axis makes a very small angle with the electric field, '$$\bar{E}$$'. The angular frequency of the oscillations of the dipole when released is given by:

A child stands on the edge of the cliff $$10\mathrm{m}$$ above the ground and throws a stone horizontally with an initial speed of $$5{\mathrm{ms}}^{-1}$$. Neglecting the air resistance, the speed with which the stone hits the ground will be $${\mathrm{ms}}^{-1}$$ (given, $$g=10{\mathrm{ms}}^{-2}$$ ).

The initial speed of a projectile fired from ground is $$\mathrm{u}$$. At the highest point during its motion, the speed of projectile is $$\frac{\sqrt{3}}{2}u$$. The time of flight of the projectile is :