If the electric potential at any point (x, y, z) m in space is given by V = 3x2 volt. The electric field at the point (1, 0, 3) m will be :

Two point charges A and B of magnitude +8 $$\times$$ 10$$-$$6 C and $$-$$8 $$\times$$ 10$$-$$6 C respectively are placed at a distance d apart. The electric field at the middle point O between the charges is 6.4 $$\times$$ 104 NC$$-$$1. The distance 'd' between the point charges A and B is :

Given below are two statements : Statement I : A point charge is brought in an electric field. The value of electric field at a point near to the charge may increase if the charge is positive. Statement II : An electric dipole is placed in a non-uniform electric field. The net electric force on the dipole will not be zero. Choose the correct answer from the options given below :

The three charges q/2, q and q/2 are placed at the corners A, B and C of a square of side 'a' as shown in figure. The magnitude of electric field (E) at the corner D of the square, is :

If a charge q is placed at the centre of a closed hemispherical non-conducting surface, the total flux passing through the flat surface would be :

Three identical charged balls each of charge 2 C are suspended from a common point P by silk threads of 2 m each (as shown in figure). They form an equilateral triangle of side 1m. The ratio of net force on a charged ball to the force between any two charged balls will be :

Given below two statements : One is labelled as Assertion (A) and other is labelled as Reason (R). Assertion (A) : Non-polar materials do not have any permanent dipole moment. Reason (R) : When a non-polar material is placed in an electric field, the centre of the positive charge distribution of it's individual atom or molecule coincides with the centre of the negative charge distribution. In the light of above statements, choose the most appropriate answer from the options given below.

Sixty four conducting drops each of radius 0.02 m and each carrying a charge of 5 $$\mu$$C are combined to form a bigger drop. The ratio of surface density of bigger drop to the smaller drop will be :

In the figure, a very large plane sheet of positive charge is shown. P1 and P2 are two points at distance l and 2l from the charge distribution. If $$\sigma$$ is the surface charge density, then the magnitude of electric fields E1 and E2 at P1 and P2 respectively are :

Two identical charged particles each having a mass 10 g and charge 2.0 $$\times$$ 10$$-$$7C are placed on a horizontal table with a separation of L between them such that they stay in limited equilibrium. If the coefficient of friction between each particle and the table is 0.25, find the value of L. [Use g = 10 ms$$-$$2]

A long cylindrical volume contains a uniformly distributed charge of density $$\rho$$. The radius of cylindrical volume is R. A charge particle (q) revolves around the cylinder in a circular path. The kinetic energy of the particle is :

A vertical electric field of magnitude 4.9 $$\times$$ 105 N/C just prevents a water droplet of a mass 0.1 g from falling. The value of charge on the droplet will be : (Given : g = 9.8 m/s2)

Two uniformly charged spherical conductors $$A$$ and $$B$$ of radii $$5\mathrm{mm}$$ and $$10\mathrm{mm}$$ are separated by a distance of $$2\mathrm{cm}$$. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitudes of the electric fields at the surface of the sphere $$A$$ and $$B$$ will be :

Two identical positive charges $$Q$$ each are fixed at a distance of '2a' apart from each other. Another point charge $$q_0$$ with mass 'm' is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge $${\mathrm{q}}_0$$ executes $$\mathrm{SHM}$$. The time period of oscillation of charge $${\mathrm{q}}_0$$ will be :

A charge of $$4\mu \mathrm{C}$$ is to be divided into two. The distance between the two divided charges is constant. The magnitude of the divided charges so that the force between them is maximum, will be :

A uniform electric field $$\mathrm{E}=(8\mathrm{m}/\mathrm{e})\mathrm{V}/\mathrm{m}$$ is created between two parallel plates of length $$1\mathrm{m}$$ as shown in figure, (where $$\mathrm{m}=$$ mass of electron and e = charge of electron). An electron enters the field symmetrically between the plates with a speed of $$2\mathrm{m}/\mathrm{s}$$. The angle of the deviation $$(\theta )$$ of the path of the electron as it comes out of the field will be _________.

A spherically symmetric charge distribution is considered with charge density varying as $$\rho (r)=\{\begin{array}{ll}{\rho }_0\left(\frac{3}{4}-\frac{r}{R}\right)& \text{ for }r\le R\\ \text{ zero }& \text{ for }r>R\end{array}$$ Where, $$r(r<R)$$ is the distance from the centre O (as shown in figure). The electric field at point P will be:

Given below are two statements. Statement I : Electric potential is constant within and at the surface of each conductor. Statement II : Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point. In the light of the above statements, choose the most appropriate answer from the options given below.

Two identical metallic spheres $$\mathrm{A}$$ and $$\mathrm{B}$$ when placed at certain distance in air repel each other with a force of $$\mathrm{F}$$. Another identical uncharged sphere $$\mathrm{C}$$ is first placed in contact with $$\mathrm{A}$$ and then in contact with $$\mathrm{B}$$ and finally placed at midpoint between spheres A and B. The force experienced by sphere C will be:

A person can throw a ball upto a maximum range of 100 m. How high above the ground he can throw the same ball?