HC Verma solutions for Concepts of Physics Vol. 2 [English] Class 11 and 12 chapter 7 - Electric Field and Potential [Latest edition]

The charge on a proton is +1.6 × 10⁻¹⁹ C and that on an electron is −1.6 × 10⁻¹⁹ C. Does it mean that the electron has 3.2 × 10⁻¹⁹ C less charge than the proton? 

Consider the situation shown in the figure. What are the signs of q₁ and q₂? If the lines are drawn in proportion to the charges, what is the ratio q₁/q₂? 

Figure shows some of the electric field lines corresponding to an electric field. The figure suggests that

When the separation between two charges is increased, the electric potential energy of the charges

If a positive charge is shifted from a low-potential region to a high-potential region, the electric potential energy 

Two equal positive charges are kept at points A and B. The electric potential at the points between A and B (excluding these points) is situated while moving from A to B. The potential  

The electric field at the origin is along the positive x-axis. A small circle is drawn with the centre at the origin, cutting the axes at points A, B, C and D with coordinates (a, 0), (0, a), (−a, 0), (0, −a), respectively. Out of the points on the periphery of the circle, the potential is minimum at  

If a body is charged by rubbing it, its weight

An electric dipole is placed in a uniform electric field. The net electric force on the dipole 

Consider the situation in the figure. The work done in taking a point charge from P to Ais W_A, from P to B is W_B and from P to C is W_C. 

A point charge q is rotated along a circle in an electric field generated by another point charge Q. The work done by the electric field on the rotating charge in one complete revolution is 

Mark out the correct options.

A point charge is brought inside an electric field. The electric field at a nearby point
(a) will increase if the charge is positive
(b) will decrease if the charge is negative
(c) may increase if the charge is positive
(d) may decrease if the charge is negative

The electric field and the electric potential at a point are E and V, respectively.  

Electric potential decreases uniformly from 120 V to 80 V, as one moves on the x-axis from x = −1 cm to x = +1 cm. The electric field at the origin 

(a) must be equal to 20 Vcm⁻¹
(b) may be equal to 20 Vcm⁻¹
(c) may be greater than 20 Vcm⁻¹
(d) may be less than 20 Vcm⁻¹ 

Which of the following quantities does not depend on the choice of zero potential or zero potential energy?

An electric dipole is placed in an electric field generated by a point charge.

A proton and an electron are placed in a uniform electric field.

The electric field in a region is directed outward and is proportional to the distance rfrom the origin. Taking the electric potential at the origin to be zero, 

Suppose all the electrons of 100 g water are lumped together to form a negatively-charged particle and all the nuclei are lumped together to form a positively-charged particle. If these two particles are placed 10.0 cm away from each other, find the force of attraction between them. Compare it with your weight.

Consider a gold nucleus to be a sphere of radius 6.9 fermi in which protons and neutrons are distributed. Find the force of repulsion between two protons situated at largest separation. Why do these protons not fly apart under this repulsion?

Suppose an attractive nuclear force acts between two protons which may be written as F=Ce^−kr/r². Write down the dimensional formulae and appropriate SI units of C and k.   

Suppose an attractive nuclear force acts between two protons which may be written as F=Ce^−kr/r². Suppose that k = 1 fermi⁻¹ and that the repulsive electric force between the protons is just balanced by the attractive nuclear force when the separation is 5 fermi. Find the value of C. 

Two charged particles with charge 2.0 × 10⁻⁸ C each are joined by an insulating string of length 1 m and the system is kept on a smooth horizontal table. Find the tension in the string.

Two identical balls, each with a charge of 2.00 × 10−7 C and a mass of 100 g, are suspended from a common point by two insulating strings, each 50 cm long. The balls are held at a separation 5.0 cm apart and then released. Find. 

(a) the electric force on one of the charged balls

(b) the components of the resultant force on it along and perpendicular to the string

(c) the tension in the string

(d) the acceleration of one of the balls. Answers are to be obtained only for the instant just after the release.

Two small spheres, each with a mass of 20 g, are suspended from a common point by two insulating strings of length 40 cm each. The spheres are identically charged and the separation between the balls at equilibrium is found to be 4 cm. Find the charge on each sphere. 

Two identically-charged particles are fastened to the two ends of a spring of spring constant 100 N m⁻¹ and natural length 10 cm. The system rests on a smooth horizontal table. If the charge on each particle is 2.0 × 10⁻⁸ C, find the extension in the length of the spring. Assume that the extension is small as compared to the natural length. Justify this assumption after you solve the problem.  

Two particles A and B, each carrying a charge Q, are held fixed with a separation dbetween them. A particle C of mass m and charge q is kept at the middle point of the line AB. If it is displaced through a distance x perpendicular to AB, what would be the electric force experienced by it?  

Two particles A and B, each carrying a charge Q, are held fixed with a separation dbetween them. A particle C of mass m and charge q is kept at the middle point of the line AB.  Assuming x<<d, show that this force is proportional to x.

Two particles A and B, each carrying a charge Q, are held fixed with a separation dbetween them. A particle C of mass m and charge q is kept at the middle point of the line AB.   Under what conditions will the particle C execute simple harmonic motion if it is released after such a small displacement? Find the time period of the oscillations if these conditions are satisfied.

Two particles A and B possessing charges of +2.00 × 10⁻⁶ C and of −4.00 × 10⁻⁶ C, respectively, are held fixed at a separation of 20.0 cm. Locate the points (s) on the line AB, where (a) the electric field is zero (b) the electric potential is zero.  

Three identical charges, each with a value of 1.0 × 10⁻⁸ C, are placed at the corners of an equilateral triangle of side 20 cm. Find the electric field and potential at the centre of the triangle. 

A positive charge q is placed in front of a conducting solid cube at a distance d from its centre. Find the electric field at the centre of the cube to the charges appearing on its surface.

A particle of mass 1 g and charge 2.5 × 10⁻⁴ C is released from rest in an electric field of 1.2 × 10 ⁴ N C⁻¹. Find the electric force and the force of gravity acting on this particle. Can one of these forces be neglected in comparison with the other for approximate analysis?

A particle of mass 1 g and charge 2.5 × 10⁻⁴ C is released from rest in an electric field of 1.2 × 10 ⁴ N C⁻¹.   How long will it take for the particle to travel a distance of 40 cm?

A particle of mass 1 g and charge 2.5 × 10⁻⁴ C is released from rest in an electric field of 1.2 × 10 ⁴ N C⁻¹. What will be the speed of the particle after travelling this distance? 

A particle of mass 1 g and charge 2.5 × 10⁻⁴ C is released from rest in an electric field of 1.2 × 10 ⁴ N C⁻¹. How much is the work done by the electric force on the particle during this period?

A ball of mass 100 g and with a charge of 4.9 × 10⁻⁵ C is released from rest in a region where a horizontal electric field of 2.0 × 10⁴ N C⁻¹ exists. (a) Find the resultant force acting on the ball. (b) What will be the path of the ball? (c) Where will the ball be at the end of 2 s?

The bob of a simple pendulum has a mass of 40 g and a positive charge of 4.0 × 10⁻⁶ C. It makes 20 oscillations in 45 s. A vertical electric field pointing upward and of magnitude 2.5 × 10⁴ NC⁻¹ is switched on. How much time will it now take to complete 20 oscillations? 

A block of mass m with a charge q is placed on a smooth horizontal table and is connected to a wall through an unstressed spring of spring constant k, as shown in the figure. A horizontal electric field E, parallel to the spring, is switched on. Find the amplitude of the resulting SHM of the block. 

A block of mass containing a net positive charge q is placed on a smooth horizontal table which terminates in a vertical wall as shown in the figure. The distance of the block from the wall is d. A horizontal electric field E towards the right is switched on. Assuming elastic collisions (if any), find the time period of the resulting oscillatory motion. Is it a simple harmonic motion? 

Two equal charges, 2.0 × 10⁻⁷ C each, are held fixed at a separation of 20 cm. A third charge of equal magnitude is placed midway between the two charges. It is now moved to a point 20 cm from both the charges. How much work is done by the electric field during the process?

An electric field of 20 NC⁻¹ exists along the x-axis in space. Calculate the potential difference V_B − V_A where the points A and B are
(a) A = (0, 0); B = (4 m, 2m)
(b) A = (4 m, 2 m); B = (6 m, 5 m)
(c) A = (0, 0); B = (6 m, 5 m)
Do you find any relation between the answers of parts (a), (b) and (c)?  

Consider the situation of the previous problem. A charge of −2.0 × 10⁻⁴ C is moved from point A to point B. Find the change in electrical potential energy U_B − U_A for the cases (a), (b) and (c). 

An electric field  $$\overrightarrow{E}=(\overrightarrow{i}20+\overrightarrow{j}30){NC}^{-1}$$  exists in space. If the potential at the origin is taken to be zero, find the potential at (2 m, 2 m).

An electric field  $$\overrightarrow{E}=\overrightarrow{i}$$  Ax exists in space, where A = 10 V m⁻². Take the potential at (10 m, 20 m) to be zero. Find the potential at the origin.

The electric potential existing in space is $$V(x,y,z)=A(xy+yz+zx).$$ (a) Write the dimensional formula of A. (b) Find the expression for the electric field. (c) If A is 10 SI units, find the magnitude of the electric field at (1 m, 1 m, 1 m).

Two charged particles, with equal charges of 2.0 × 10⁻⁵ C, are brought from infinity to within a separation of 10 cm. Find the increase in the electric potential energy during the process 

Some equipotential surface is shown in the figure. What can you say about the magnitude and the direction of the electric field? 

An electric field of magnitude 1000 NC⁻¹ is produced between two parallel plates with a separation of 2.0 cm, as shown in the figure. (a) What is the potential difference between the plates? (b) With what minimum speed should an electron be projected from the lower place in the direction of the field, so that it may reach the upper plate? (c) Suppose the electron is projected from the lower place with the speed calculated in part (b). The direction of projection makes an angle of 60° with the field. Find the maximum height reached by the electron.

A uniform field of 2.0 NC⁻¹ exists in space in the x-direction. (a) Taking the potential at the origin to be zero, write an expression for the potential at a general point (x, y, z). (b) At which point, the potential is 25 V? (c) If the potential at the origin is taken to be 100 V, what will be the expression for the potential at a general point? (d) What will be the potential at the origin if the potential at infinity is taken to be zero? Is it practical to choose the potential at infinity to be zero?  

How much work has to be done in assembling three charged particles at the vertices of an equilateral triangle, as shown in the figure?

Two particles of masses 5.0 g each and opposite charges of +4.0 × 10⁻⁵ C and −4.0 × 10⁻⁵ C are released from rest with a separation of 1.0 m between them. Find the speeds of the particles when the separation is reduced to 50 cm.  

A sample of HCI gas is placed in an electric field of 2.5 × 10⁴ NC⁻¹. The dipole moment of each HCI molecule is 3.4 × 10⁻³⁰ Cm. Find the maximum torque that can act on a molecule. 

Two particles A and B, of opposite charges 2.0 × 10⁻⁶ C and −2.0 × 10⁻⁶ C, are placed at a separation of 1.0 cm. Two particles A and B, of opposite charges 2.0 × 10⁻⁶ C and −2.0 × 10⁻⁶ C, are placed at a separation of 1.0 cm. 

Two particles A and B, of opposite charges 2.0 × 10⁻⁶ C and −2.0 × 10⁻⁶ C, are placed at a separation of 1.0 cm. Calculate the electric field at a point on the axis of the dipole 1.0 cm away from the centre. 

Two particles A and B, of opposite charges 2.0 × 10⁻⁶ C and −2.0 × 10⁻⁶ C, are placed at a separation of 1.0 cm. Calculate the electric field at a point on the perpendicular bisector of the dipole and 1.0 m away from the centre. 

Three charges are arranged on the vertices of an equilateral triangle, as shown in the figure. Find the dipole moment of the combination. 

Find the magnitude of the electric field at the point P in the configuration shown in the figure for d >> a.

Two particles, carrying charges −q and +q and and of mass m each, are fixed at the ends of a light rod of length a to form a dipole. The rod is clamped at an end and is placed in a uniform electric field E with the axis of the dipole along the electric field. The rod is slightly tilted and then released. Neglecting gravity, find the time period of small oscillations.  

Assume that each atom in a copper wire contributes one free electron. Estimate the number of free electrons in a copper wire of mass 6.4 g (take the atomic weight of copper to be 64 g mol⁻¹).