A small plane area is rotated in an electric field. In which orientation of the area is the flux of the electric field through the area maximum? In which orientation is it zero?

A circular ring of radius r made of a non-conducting material is placed with its axis parallel to a uniform electric field. The ring is rotated about a diameter through 180°. Does the flux of electric field change? If yes, does it decrease or increase?

A charge Q is uniformly distributed on a thin spherical shell. What is the field at the centre of the shell? If a point charge is brought close to the shell, will the field at the centre change? Do your answer depend on whether the shell is conducting or nonconducting?

A spherical shell made of plastic, contains a charge Q distributed uniformly over its surface. What is the electric field inside the shell? If the shell is hammered to de-shape it without altering the charge, will the field inside be changed? What happens if the shell is made of a metal?

A point charge q is placed in a cavity in a metal block. If a charge Q is brought outside the metal, will the charge q feel an electric force?

A rubber balloon is given a charge Q distributed uniformly over its surface. Is the field inside the balloon zero everywhere if the balloon does not have a spherical surface?

It is said that any charge given to a conductor comes to its surface. Should all the protons come to the surface? Should all the electrons come to the surface? Should all the free electrons come to the surface?

A charge Q is uniformly distributed over a large plastic plate. The electric field at a point P close to the centre of the plate is 10 V m^–1. If the plastic plate is replaced by a copper plate of the same geometrical dimensions and carrying the same charge Q, the electric field at the point P will become

A metallic particle having no net charge is placed near a finite metal plate carrying a positive charge. The electric force on the particle will be

A thin, metallic spherical shell contains a charge Q on it. A point charge q is placed at the center of the shell, and another charge q₁ is placed outside it as shown in the figure. All three charges are positive. The force on the charge at the centre is:

Consider the situation of the previous problem. The force on the central charge due to the shell is

Electric charges are distributed in a small volume. The flux of the electric field through a spherical surface of radius 10 cm surrounding the total charge is 25 V m. The flux over a concentric sphere of radius 20 cm will be

Figure shows an imaginary cube of edge L/2. A uniformly charged rod of length L moves towards left at a small but constant speed v. At t = 0, the left end just touches the centre of the face of the cube opposite it. Which of the graphs shown in figure represents the flux of the electric field through the cube as the rod goes through it?

A charge q is placed at the centre of the open end of a cylindrical vessel. The flux of the electric field through the surface of the vessel is

Mark the correct options:

A positive point charge Q is brought near an isolated metal cube.

A large non-conducting sheet M is given a uniform charge density. Two uncharged small metal rods A and B are placed near the sheet as shown in figure.

If the flux of the electric field through a closed surface is zero.

An electric dipole is placed at the centre of a sphere. Mark the correct options:

Figure shows a charge q placed at the centre of a hemisphere. A second charge Q is placed at one of the positions A, B, C and D. In which position(s) of this second charge, the flux of the electric field through the hemisphere remains unchanged?

A closed surface S is constructed around a conducting wire connected to a battery and a switch. As the switch is closed, the free electrons in the wire start moving along the wire. In any time interval, the number of electrons entering the closed surface S is equal to the number of electrons leaving it. On closing the switch, the flux of the electric field through the closed surface.

Figure shows a closed surface which intersects a conducting sphere. If a positive charge is placed at point P, the flux of the electric field through the closed surface.

The electric field in a region is given by with E₀ = 2.0 × 10³ N C^–1. Find the flux of this field through a rectangular surface of area 0.2 m² parallel to the y–z plane.

A charge Q is uniformly distributed over a rod of length ℓ. Consider a hypothetical cube of edge ℓ with the centre of he cub at one end of the rod. Find the minimum possible flux of the electric field through the entire surface of the cube.

Show that there can be no net charge in a region in which the electric field is uniform at all points.

The electric filed in a region is given by Find the charge contained inside a cubical volume bounded by the surfaces x = 0, x = a, y = 0, y = a, z = 0 and z = a. Take E₀ = 5 × 10³ NC^–1, ℓ = 2 cm and α = 1 cm.

A charge Q is placed at the centre of a cube. Find the flux of the electric field through the six surfaces of the cube.

A charge Q is placed at a distance a/2 above the centre of a horizontal, square of edge a as shown in figure. Find the flux of the electric field through the square surface.

Find the flux of the electric field through a spherical surface of radius R due to a charge of 10^–7 C at the centre and another equal charge at a point 2R way from the centre.

A charge Q is placed at the centre of an imaginary hemispherical surface. Using symmetry arguments and the Gauss’s law, find the flux of the electric field due to this charge through the surface of the hemisphere (figure).

A spherical volume contains a uniformly distributed charge of density 2.0 × 10^–4 C m^–3. Find the electric field at a point inside the volume at a distance 4.0 cm from the centre.

The radius of a gold nucleus (Z = 79) is about 7.0 × 10^–15 m. Assume that the positive charge is distributed uniformly throughout the nuclear volume. Find the strength of the electric field at

(a) the surface of the nucleus and

(b) at the middle point of a radius.

Remembering that gold is a conductor, is it justified to assume that the positive charge is uniformly distributed over the entire volume of the nucleus and does not come to the outer surface?

A charge Q is distributed uniformly within the material of a hollow sphere of inner and outer radii r₁ and r₂ figure. Find the electric field at a point P a distance x away from the centre for r₁ < x < r₂. Draw a rough graph showing the electric field as a function of x for 0 < x < 2r₂ figure.

A charge Q is placed at the centre of an uncharged, hollow metallic sphere of radius a.

(a) Find the surface charge density on the inner surface and on the outer surface.

(b) If a charge q is put on the sphere, what would be he surface charge densities on the inner and the outer surfaces?

(c) Final the electric field inside the sphere at a distance x from the centre in the situations (a) and (b).

Consider the following very rough model of a beryllium atom. The nucleus has four protons and four neutrons confined to a small volume of radius 10^–15 m. The two 1s electrons make a spherical charge cloud at an average distance of 1.3 × 10¹¹ m from the nucleus, whereas the two 2s electrons make another spherical cloud at an average distance of 5.2 × 10^–11 m from the nucleus. Find the electric field at

(a) a point just inside the 1s cloud and (b) a point just inside the 2s cloud.

Find the magnitude of the electric field at a point 4 cm away from a line charge of density 2 × 10^–6 C m^–1.

A long cylindrical wire carries a positive charge of linear density 2.0 × 10^–6 C m^–1. An electron revolves around it in a circular path under the influence of the attractive electrostatic force. Find the kinetic energy of the electron. Note that it is independent of the radius.

A long cylindrical volume contains a uniformly distributed charge of density ρ. Find the electric field at a point P inside the cylindrical volume at a distance x from its axis.

A nonconducting sheet of large surface area and thickness d contains uniform charge distribution of density ρ. Find the electric field at a point P inside the plate, at a distance x from the central plane. Draw a qualitative graph of E against x for 0 < x < d.

A charged particle having a charge of –2.0 × 10^–6 C is placed close to a nonconducting plate having a surface charge density 4.0 × 10^–6 C m^–2. Find the force of attraction between the particle and the plate.

One end of a 10 cm long silk thread is fixed to a large vertical surface of a charged nonconducting plate and the other end is fastened to a small ball having a mass of 10 g and a charge of 4.0 × 10^–6 C. In equilibrium, the thread makes an angle of 60° with the vertical. Find the surface charge density on the plate.

Consider the situation of the previous problem.

(a) Find the tension in the string in equilibrium.

(b) Suppose the ball is slightly pushed aside and released. Find the time period of the small oscillations.

Two large conducting plates are placed parallel to each other with a separation of 2.00 cm between them. An electron starting from rest near one of the plates reaches the other plate in 2.00 microseconds. Find the surface charge density on the inner surfaces.

Two large conducting plates are placed parallel to each other and the carry equal and opposite charges with surface density σ as shown in figure. Find the electric field

(a) at the left of the plates.

(b) in between the plates and

(c) at the right of the plates.

Two conducting plates X and Y, each having large surface area A (on one side), are placed parallel to each other as shown in figure. The plate X is given a charge Q whereas the other is neutral. Find:

(a) the surface charge density at the inner surface of the plate X,

(b) the electric field at a point to the left of the plates

(c) the electric field at a point in between the plates and

(d) the electric field at a point to the right of the plates

Three identical metal plates with large surface areas are kept parallel to each other as shown in figure. The leftmost plate is given a charge Q, the rightmost a charge –2Q and the middle one remains neutral. Find the charge appearing on the outer surface of the rightmost plate.