Chapter 1:  Electric Charges and Fields

Class 12 Chapter 1:  Electric Charges and Fields Internal Example Questions and Answers :

Example 1.1 How can you charge a metal sphere positively without touching it?

Example 1.2 If  electrons move out of a body to another body every second, how much time is required to get a total charge of 1 C on the other body?

Example 1.3 How much positive and negative charge is there in a cup of water?

Example 1.4 Coulomb’s law for electrostatic force between two point charges and Newton’s law for gravitational force between two stationary point masses, both have inverse-square dependence on the distance between the charges and masses respectively.

(a) Compare the strength of these forces by determining the ratio of their magnitudes (i) for an electron and a proton and (ii) for two protons. (b) Estimate the accelerations of electron and proton due to the electrical force of their mutual attraction when they are 1 Å (=  m) apart? (  =  kg ,  =  kg)

Example 1.5 A charged metallic sphere A is suspended by a nylon thread. Another charged metallic sphere B held by an insulating handle is brought close to A such that the distance between their centres is 10 cm, as shown in Fig. 1.7(a). The resulting repulsion of A is noted (for example, by shining a beam of light and measuring the deflection of its shadow on a screen). Spheres A and B are touched by uncharged spheres C and D respectively, as shown in Fig. 1.7(b). C and D are then removed and B is brought closer to A to a distance of 5.0 cm between their centres, as shown in Fig. 1.7(c). What is the expected repulsion of A on the basis of Coulomb’s law? Spheres A and C and spheres B and D have identical sizes. Ignore the sizes of A and B in comparison to the separation between their centres.

                         FIGURE 1.7

Example 1.6 Consider three charges ,  ,  each equal to q at the vertices of an equilateral triangle of side  . What is the force on a charge Q (with the same sign as ) placed at the centroid of the triangle, as shown in Fig. 1.9?

   

Example 1.7 Consider the charges  , and –  placed at the vertices of an equilateral triangle, as shown in Fig. 1.10. What is the force on each charge ?

   

Example 1.8 An electron falls through a distance of 1.5 cm in a uniform electric field of magnitude  N  [Fig. 1.13(a)]. The direction of the field is reversed keeping its magnitude unchanged and a proton falls through the same distance [Fig. 1.13(b)]. Compute the time of fall in each case. Contrast the situation with that of ‘free fall under gravity’.

 

Example 1.9 Two point charges  and  , of magnitude +  C and  C, respectively, are placed 0.1 m apart. Calculate the electric fields at points A, B and C shown in Fig. 1.14 .

Example 1.10 Two charges ±10 μC are placed 5.0 mm apart. Determine the electric field at (a) a point P on the axis of the dipole 15 cm away from its centre O on the side of the positive charge, as shown in Fig. 1.21(a), and (b) a point Q, 15 cm away from O on a line passing through O and normal to the axis of the dipole, as shown in Fig. 1.21(b).

Example 1.11 The electric field components in Fig. 1.27 are  ,  , in which  = 800 N/C . Calculate (a) the flux through the cube, and (b) the charge within the cube. Assume that  = 0.1 m.

Example 1.12 An electric field is uniform, and in the positive  direction for positive , and uniform with the same magnitude but in the negative  direction for negative . It is given that  N/C for  and  N/C for  . A right circular cylinder of length 20 cm and radius 5 cm has its centre at the origin and its axis along the x-axis so that one face is at x=+10 cm and the other is at  cm (Fig. 1.28). (a) What is the net outward flux through each flat face? (b) What is the flux through the side of the cylinder? (c) What is the net outward flux through the cylinder? (d) What is the net charge inside the cylinder?

Example 1.13 An early model for an atom considered it to have a positively charged point nucleus of charge , surrounded by a uniform density of negative charge up to a radius . The atom as a whole is neutral. For this model, what is the electric field at a distance  from the nucleus?

   

Class 12 Chapter 1:  Electric Charges and Fields Exercise Questions and Answers :

1.1 What is the force between two small charged spheres having charges of  and  placed 30 cm apart in air ?

1.2 The electrostatic force on a small sphere of charge 0.4 μC due to another small sphere of charge – 0.8 μC in air is 0.2 N. (a) What is the distance between the two spheres? (b) What is the force on the second sphere due to the first?

1.3 Check that the ratio  is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?

1.4 (a) Explain the meaning of the statement ‘electric charge of a body is quantised’.

(b) Why can one ignore quantisation of electric charge when dealing with macroscopic i.e., large scale charges?

1.5 When a glass rod is rubbed with a silk cloth, charges appear on both. A similar phenomenon is observed with many other pairs of bodies. Explain how this observation is consistent with the law of conservation of charge.

1.6 Four point charges  ,  , and are located at the corners of a square ABCD of side 10 cm. What is the force on a charge of 1  placed at the centre of the square?

1.7 (a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?

(b) Explain why two field lines never cross each other at any point?

1.8 Two point charges  and  are located 20 cm apart in vacuum.

(a) What is the electric field at the midpoint O of the line AB joining the two charges?

(b) If a negative test charge of magnitude  C is placed at this point, what is the force experienced by the test charge?

1.9 A system has two charges  and  located at points A: (0, 0, –15 cm) and B: (0,0, +15 cm), respectively. What are the total charge and electric dipole moment of the system?

1.10 An electric dipole with dipole moment  C m is aligned at 30° with the direction of a uniform electric field of magnitude  N . Calculate the magnitude of the torque acting on the dipole.

1.11 A polythene piece rubbed with wool is found to have a negative charge of  C.

(a) Estimate the number of electrons transferred (from which to which?)

(b) Is there a transfer of mass from wool to polythene?

1.12 (a) Two insulated charged copper spheres A and B have their centres separated by a distance of 50 cm. What is the mutual force of electrostatic repulsion if the charge on each is C ? The radii of A and B are negligible compared to the distance of separation.

(b) What is the force of repulsion if each sphere is charged double the above amount, and the distance between them is halved?

1.13 Suppose the spheres A and B in Exercise 1.12 have identical sizes. A third sphere of the same size but uncharged is brought in contact with the first, then brought in contact with the second, and finally removed from both. What is the new force of repulsion between A and B?

1.14 Figure 1.33 shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

1.15 Consider a uniform electric field  N/C. (a) What is the flux of this field through a square of 10 cm on a side whose plane is parallel to the yz plane? (b) What is the flux through the same square if the normal to its plane makes a 60° angle with the x-axis?

1.16 What is the net flux of the uniform electric field of Exercise 1.15 through a cube of side 20 cm oriented so that its faces are parallel to the coordinate planes?

1.17 Careful measurement of the electric field at the surface of a black box indicates that the net outward flux through the surface of the box is N/C . (a) What is the net charge inside the box?

(b) If the net outward flux through the surface of the box were zero, could you conclude that there were no charges inside the box? Why or Why not?

1.18 A point charge  is a distance 5 cm directly above the centre of a square of side 10 cm, as shown in Fig. 1.34. What is the magnitude of the electric flux through the square? (Hint: Think of the square as one face of a cube with edge 10 cm.)

    

1.19 A point charge of 2.0  is at the centre of a cubic Gaussian surface 9.0 cm on edge. What is the net electric flux through the surface?

1.20 A point charge causes an electric flux of   N /C to pass through a spherical Gaussian surface of 10.0 cm radius centred on the charge. (a) If the radius of the Gaussian surface were doubled, how much flux would pass through the surface? (b) What is the value of the point charge?

1.21 A conducting sphere of radius 10 cm has an unknown charge. If the electric field 20 cm from the centre of the sphere is N/C and points radially inward, what is the net charge on the sphere?

1.22 A uniformly charged conducting sphere of 2.4 m diameter has a surface charge density of 80.0 μC/ . (a) Find the charge on the sphere. (b) What is the total electric flux leaving the surface of the sphere?

1.23 An infinite line charge produces a field of  N/C at a distance of 2 cm. Calculate the linear charge density.

1.24 Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude   C/  . What is E: (a) in the outer region of the first plate, (b) in the outer region of the second plate, and (c) between the plates?

Class 12 Chapter 1:  Electric Charges and Fields Additional Exercise Questions and Answers :

1.25 An oil drop of 12 excess electrons is held stationary under a constant electric field of  N  (Millikan’s oil drop experiment). The density of the oil is 1.26 g  . Estimate the radius of the drop.  ( g = 9.81 m  ; e = C).

1.26 Which among the curves shown in Fig. 1.35 cannot possibly represent electrostatic field lines?

1.27 In a certain region of space, electric field is along the z-direction throughout. The magnitude of electric field is, however, not constant but increases uniformly along the positive z-direction, at the rate of   N  per metre. What are the force and torque experienced by a system having a total dipole moment equal to   Cm in the negative z-direction ?

1.28 (a) A conductor A with a cavity as shown in Fig. 1.36(a) is given a charge Q. Show that the entire charge must appear on the outer surface of the conductor. (b) Another conductor B with charge  is inserted into the cavity keeping B insulated from A. Show that the total charge on the outside surface of A is Q +  [Fig. 1.36(b)]. (c) A sensitive instrument is to be shielded from the strong electrostatic fields in its environment. Suggest a possible way.

  

1.29 A hollow charged conductor has a tiny hole cut into its surface. Show that the electric field in the hole is  , where  is the unit vector in the outward normal direction, and  is the surface charge density near the hole.

1.30 Obtain the formula for the electric field due to a long thin wire of uniform linear charge density E without using Gauss’s law. [Hint: Use Coulomb’s law directly and evaluate the necessary integral.]

1.31 It is now established that protons and neutrons (which constitute nuclei of ordinary matter) are themselves built out of more elementary units called quarks. A proton and a neutron consist of three quarks each. Two types of quarks, the so called ‘up’ quark (denoted by u) of charge  , and the ‘down’ quark (denoted by d) of charge  , together with electrons build up ordinary matter. (Quarks of other types have also been found which give rise to different unusual varieties of matter.) Suggest a possible quark composition of a proton and neutron.

1.32 (a) Consider an arbitrary electrostatic field configuration. A small test charge is placed at a null point (i.e., where E = 0) of the configuration. Show that the equilibrium of the test charge is necessarily unstable.

(b) Verify this result for the simple configuration of two charges of the same magnitude and sign placed a certain distance apart.

1.33 A particle of mass m and charge () enters the region between the two charged plates initially moving along -axis with speed  (like particle 1 in Fig. 1.33). The length of plate is L and an uniform electric field E is maintained between the plates. Show that the vertical deflection of the particle at the far edge of the plate is  . Compare this motion with motion of a projectile in gravitational field discussed in Section 4.10 of Class XI Textbook of Physics.

1.34 Suppose that the particle in Exercise in 1.33 is an electron projected with velocity   m  . If E between the plates separated by 0.5 cm is    N/C, where will the electron strike the upper plate? (  C ,  kg )