HC Verma solutions for Concepts of Physics Vol. 2 [English] Class 11 and 12 chapter 8 - Gauss’s Law [Latest edition]

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 charge Q is uniformly distributed on a 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? Does your answer depend on whether the shell is conducting or non-conducting?

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 deshape 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 fore?

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 with 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 centre of the shell and another charge q₁ is placed outside it as shown in the  following figure . All the three charges are positive. The force on the charge at the centre is ____________.

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

Following Figure (a) shows an imaginary cube of edge L/2. A uniformly charged rod of length (L) moves towards the left at a small but constant speed `nu.` At t = 0, the left end just touches the centre of the face of the cube opposite it. Which of the graphs shown in the figure (b) 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 (see the figure). 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 the following  figure.

(a) M attracts A.
(b) M attracts B.
(c) A attracts B.
(d) B attracts A.

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

(a) the electric field must be zero everywhere on the surface
(b) the electric field may be zero everywhere on the surface
(c) the charge inside the surface must be zero
(d) the charge in the vicinity of the surface must be zero

An electric dipole is placed at the centre of a sphere. Mark the correct options.
(a) The flux of the electric field through the sphere is zero.
(b) The electric field is zero at every point of the sphere.
(c) The electric field is not zero anywhere on the sphere.
(d) The electric field is zero on a circle on the sphere.

In the following 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) A
(b) B
(c) C
(d) D

A closed surface S is constructed around a conducting wire connected to a battery and a switch in the following figure. 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
(a) is increased
(b) is decreased
(c) remains unchanged
(d) remains zero

The following figure shows a closed surface that 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 

`vec"E"= 3/5"E"_0 vec"i" + 4/5 "E"_0 vec "i"  "with" " E"_0 = 2.0 xx 10^3 "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 the cube 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 field in a region is given by `vec"E" = ("E"_0 "x")/"l"  vec"i".` 

Find the charge contained inside the cubical volume bound by the surfaces 

x =0, x =a, y=0, y=a, z=0 and z=a. Take

`"E"_0 = 5 xx 10^3 "N""C"^-1 , "l" =2 "cm" " and" " a" = 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 surface of edge a as shown in the following 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 away from the centre in the following figure.

A charge Q is placed at the centre of an imaginary hemispherical surface. Using symmetry arguments and Gauss's Law, find the flux of the electric field due to this charge through the surface of the hemisphere in the following figure.

A spherical volume contains a uniformly distributed charge of density  2.0 × 10 ^-4 Cm^-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^-10 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 (see the figure). Find the electric field at a point P at a distance x away from the centre for r₁ < x < r. Draw a rough graph showing the electric field as a function of x for 0 < x < 2r₂ (see the figure).

A charge Q is placed at the centre of an uncharged, hollow metallic sphere of radius a. (a) Find the surface. (b) If a charge q is put on the sphere, what would be the surface charge densities on the inner and outer surfaces? (c) Find the electric field inside the sphere at a distance x from the centre in the situations (a) and (b).

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

A long cylindrical wire carries a positive charge of linear density  2.0 × 10^-8 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 (see the figure).

A non-conducting sheet of large surface area and thickness d contains a uniform charge distribution of density $\rho$. 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 with a charge of −2⋅0 × 10⁻⁶ C is placed close to a non-conducting plate with a surface charge density of 4.0 × 10^-6Cm0^-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 non-conducting plate and the other end is fastened to a small ball of mass 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.

One end of a 10 cm long silk thread is fixed to a large vertical surface of a charged non-conducting plate and the other end is fastened to a small ball of mass 10 g and a charge of 4.0× 10^-6 C. In equilibrium, the thread makes an angle of 60° with the vertical (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 and they carry equal and opposite charges with surface density σ as shown in the 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 with a large surface area A (on one side), are placed parallel to each other, as shown in the  following figure . Plate X is given a charge Q,whereas the other is kept neutral. Find (a) the surface charge density at the inner surface of 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 the following figure. The leftmost plate is given a charge Q, the rightmost a charge −2Q and the middle one is kept neutral. Find the charge appearing on the outer surface of the rightmost plate.