Ncert solution class 12 physics
Electric Charges and Fields
1.1 What is the force between two small charged spheres havingcharges of 2 × 10–7C and 3 × 10–7C placed 30 cm apart in air?1.2 The electrostatic force on a small sphere of charge 0.4 μC due toanother small sphere of charge – 0.8 μC in air is 0.2 N. (a) What isthe distance between the two spheres? (b) What is the force on thesecond sphere due to the first?
1.3 Check that the ratio ke2/G memp is dimensionless. Look up a Tableof Physical Constants and determine the value of this ratio. Whatdoes the ratio signify?
1.4 (a) Explain the meaning of the statement ‘electric charge of a bodyis quantised’.(b) Why can one ignore quantisation of electric charge when dealingwith macroscopic i.e., large scale charges?
1.5 When a glass rod is rubbed with a silk cloth, charges appear onboth. A similar phenomenon is observed with many other pairs ofbodies. Explain how this observation is consistent with the law ofconservation of charge.
1.6 Four point charges qA = 2 μC, qB = –5 μC, qC = 2 μC, and qD = –5 μC arelocated at the corners of a square ABCD of side 10 cm. What is theforce on a charge of 1 μC placed at the centre of the square?
1.7 (a) An electrostatic field line is a continuous curve. That is, a fieldline cannot have sudden breaks. Why not?(b) Explain why two field lines never cross each other at any point?
1.8 Two point charges qA = 3 μC and qB = –3 μC are located 20 cm apartin vacuum.(a) What is the electric field at the midpoint O of the line AB joiningthe two charges?(b) If a negative test charge of magnitude 1.5 × 10–9 C is placed atthis point, what is the force experienced by the test charge?
1.9 A system has two charges qA = 2.5 × 10–7 C and qB = –2.5 × 10–7 Clocated 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 4 × 10–9 C m is aligned at 30°with the direction of a uniform electric field of magnitude 5 × 104 NC–1.Calculate the magnitude of the torque acting on the dipole.
1.11 A polythene piece rubbed with wool is found to have a negativecharge of 3 × 10–7 C.(a) Estimate the number of electrons transferred (from which towhich?)(b) Is there a transfer of mass from wool to polythene?
1.12 (a) Two insulated charged copper spheres A and B have their centresseparated by a distance of 50 cm. What is the mutual force of electrostatic repulsion if the charge on each is 6.5 × 10–7 C? Theradii of A and B are negligible compared to the distance ofseparation.(b) What is the force of repulsion if each sphere is charged doublethe 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 uniformelectrostatic field. Give the signs of the three charges. Which particlehas the highest charge to mass ratio?FIGURE 1.33
1.15 Consider a uniform electric field E = 3 × 103 î N/C. (a) What is theflux of this field through a square of 10 cm on a side whose plane isparallel to the yz plane? (b) What is the flux through the samesquare 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 1.15through a cube of side 20 cm oriented so that its faces are parallelto the coordinate planes?
1.17 Careful measurement of the electric field at the surface of a blackbox indicates that the net outward flux through the surface of thebox is 8.0 × 103 Nm2/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? Whyor Why not?
1.18 A point charge +10 μC is a distance 5 cm directly above the centreof a square of side 10 cm, as shown in Fig. 1.34. What is themagnitude of the electric flux through the square? (Hint: Think ofthe square as one face of a cube with edge 10 cm.)
1.19 A point charge of 2.0 μC is at the centre of a cubic Gaussiansurface 9.0 cm on edge. What is the net electric flux through thesurface?
1.20 A point charge causes an electric flux of –1.0 × 103 Nm2/C to passthrough a spherical Gaussian surface of 10.0 cm radius centred onthe charge. (a) If the radius of the Gaussian surface were doubled,how much flux would pass through the surface? (b) What is thevalue of the point charge?
1.21 A conducting sphere of radius 10 cm has an unknown charge. Ifthe electric field 20 cm from the centre of the sphere is 1.5 × 103 N/Cand points radially inward, what is the net charge on the sphere?
1.22 A uniformly charged conducting sphere of 2.4 m diameter has asurface charge density of 80.0 μC/m2. (a) Find the charge on thesphere. (b) What is the total electric flux leaving the surface of thesphere?
1.23 An infinite line charge produces a field of 9 × 104 N/C at a distanceof 2 cm. Calculate the linear charge density.
1.24 Two large, thin metal plates are parallel and close to each other. Ontheir inner faces, the plates have surface charge densities of oppositesigns and of magnitude 17.0 × 10–22 C/m2. What is E: (a) in the outerregion of the first plate, (b) in the outer region of the second plate,and (c) between the plates?
ADDITIONAL EXERCISES
1.25 An oil drop of 12 excess electrons is held stationary under a constantelectric field of 2.55 × 104 NC–1 in Millikan’s oil drop experiment. Thedensity of the oil is 1.26 g cm–3. Estimate the radius of the drop.(g = 9.81 m s–2; e = 1.60 × 10–19 C).
1.26 Which among the curves shown in Fig. 1.35 cannot possiblyrepresent electrostatic field lines?
1.27 In a certain region of space, electric field is along the z-directionthroughout. The magnitude of electric field is, however, not constantbut increases uniformly along the positive z-direction, at the rate of105 NC–1 per metre. What are the force and torque experienced by asystem having a total dipole moment equal to 10–7 Cm in the negativez-direction ?
1.28 (a) A conductor A with a cavity as shown in Fig. 1.36(a) is given acharge Q. Show that the entire charge must appear on the outersurface of the conductor. (b) Another conductor B with charge q isinserted into the cavity keeping B insulated from A. Show that thetotal charge on the outside surface of A is Q + q [Fig. 1.36(b)]. (c) Asensitive instrument is to be shielded from the strong electrostaticfields 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 (σ/2ε0) ˆn , where ˆn is theunit vector in the outward normal direction, and σ is the surfacecharge density near the hole.
1.30 Obtain the formula for the electric field due to a long thin wire ofuniform linear charge density λ without using Gauss’s law. [Hint:Use Coulomb’s law directly and evaluate the necessary integral.]
1.31 It is now believed that protons and neutrons (which constitute nucleiof ordinary matter) are themselves built out of more elementary unitscalled 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+ (2/3) e, and the ‘down’ quark (denoted by d) of charge (–1/3) e,together with electrons build up ordinary matter. (Quarks of othertypes have also been found which give rise to different unusualvarieties of matter.) Suggest a possible quark composition of aproton and neutron.
1.32 (a) Consider an arbitrary electrostatic field configuration. A smalltest charge is placed at a null point (i.e., where E = 0) of theconfiguration. Show that the equilibrium of the test charge isnecessarily unstable.(b) Verify this result for the simple configuration of two charges ofthe same magnitude and sign placed a certain distance apart.
1.33 A particle of mass m and charge (–q) enters the region between thetwo charged plates initially moving along x-axis with speed vx (likeparticle 1 in Fig. 1.33). The length of plate is L and an uniformelectric field E is maintained between the plates. Show that thevertical deflection of the particle at the far edge of the plate isqEL2/(2m vx2).Compare this motion with motion of a projectile in gravitational fielddiscussed in Section 4.10 of Class XI Textbook of Physics.
1.34 Suppose that the particle in Exercise in 1.33 is an electron projectedwith velocity vx = 2.0 × 106 m s–1. If E between the plates separatedby 0.5 cm is 9.1 × 102 N/C, where will the electron strike the upperplate? (|e|=1.6 × 10–19 C, me = 9.1 × 10–31 kg.)
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