#### Exercise

**Question 1. What is the force between two small charged spheres having charges of 2 x 10-7c and 3 x 10-7 C placed 30 cm apart in air?**

**Question 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?**

**Question 3. Check that the ratio ke2/G me mp is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?**

**Question 4. (a) Explain the meaning of the statement ‘electric charge of a body is quantized**‘.**(b) Why can one ignore the quantization of electric charge when dealing with macroscopic i.e., large-scale charge?**

**Sol. (a) **Quantization of electric charge. It is now a well known fact that all charges occurring in nature are positive or negative integral multiples of a basic unit of electric charge which we take as the magnitude of the charge on an electron. We use symbol e for the amount of charge on an electron. Hence charge on an electron is – e and that on a proton happens to be + e, while charge on a neutron is zero. Any charged

body will have ± ne charge, where n is an integer. This fact is called the quantization of electric charge.

**(b)** At the macroscopic level one deals with charges that are enormous compared to the magnitude of charge e. Since e = 1.6 x 10-19 C, a charge of magnitude, say, 1 µC contains something like 1013 times the electronic charge. At this scale, the fact that charge can increase or decrease only in units of e is not very different from saying that charge can take continuous values. Thus, at the macroscopic level, the quantisation of charge has no practical consequence and can be ignored.

**Question 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.**

**Sol. **Charge is neither created nor destroyed. It is merely transferred from one body to another. Electrons are transferred from glass to silk, so glass has positive charge and silk has negative charge.

**Question 6.Four point charges qA = 2 µC, qB = -5 µC, qc = 2 µC, and q0 = -5 µC are located at the corners of a square ABCD of side 10 cm. What is the force on a charge of 1 µC placed at the centre of the square?**

**Sol. **The center O of the square is at equal distance of 2 cm from each comer. Since opposite comers have equal charges, forces along both diagonals will be balanced. Resultant force on 1 µC charge at the centre of the square ABCD will be zero.

**Question** **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?**

**Sol.** (a) They start from a positive charge and end at a negative charge. They are continuous because force is continuous. They do not have sudden breaks, otherwise a moving test charge will have to take jumps.

(b) Two lines of force do not intersect each other. If they intersect at a point, there will be two directions of the field at that point. Since it is impossible, hence they don’t intersect.

**Note:** Refer to Chapter at a Glance (10)

**Question 8. T wo point charges qA = 3 µC and qB =-3 µC 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 1.5 x 10-9 C is placed at this point, what is the force experienced by the test charge?**

**Question 9. A system has two charges qA = 2.5 x 10-7 C and qB = -2.5 x 10-7 C 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?**

Question 10. An electric dipole with dipole moment 4 x 10^{-9} C-m is aligned at 30° with the direction of a uniform electric field of magnitude 5 x 104 Nc^{-1}. **Calculate the magnitude of the torque acting on the dipole.**

**Question 11. A polythene piece rubbed with wool is found to have a negative charge of 3.2 x 10 ^{-7} C.(a) Estimate the number of electrons transferred (from which to which?)(b) Is there a transfer of mass from wool to polythene?**

**Question** **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 6.5 x 10 ^{-7} 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?**

**Question** **13. Suppose the spheres A and Bin question 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?**

**Question** **14. Figure 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?**

**Question 15. Consider a uniform electric field E = 3 x 10 ^{3} i 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 y-z plane?(b) What is the flux through the same square if the normal to its plane makes a 60° angle with the x-axis?**

**Question 16. What is the net flux of the uniform electric field of question 1.15 through a cube of side 20 cm oriented so that its faces are parallel to the coordinate planes?**

**Sol.** Zero. The number of lines entering the cube is the same as the number of lines leaving the cube.

**Question** **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 8.0 x 10 ^{3} 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? Why or why not?**

**Question** **18. A point charge +10 µC is at a distance 5 cm directly above the center of a square of side 10 cm, as shown in Fig. 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.)**

**Sol.** The situation is shown in figure.

The square can be considered as one of the faces of a cube of each side 10 cm, enclosing the point charge inside it. The cube surface will act as Gaussian surface.

**Question 19. A point charge of 2.0 µC is at the centre of a cubic Gaussian surface 9.0 cm on edge. What is the net electric flux through the Surface ?**

**Question** **20. A point charge causes an electric flux of – 1.0 x 10 ^{3} Nm2/C to pass through a spherical Gaussian surface of 10.0 cm radius centred on the charge. (a) H 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?**

**Question** **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 1.5 x 10 ^{3} N/C and points radially inward, what is the net charge on the sphere?**

**Question** **22. A uniformly charged conduction sphere of 2.4 m diameter has a surface charge density of 80.0 µC/m2. (a) Find the charge on the sphere. (b) What is the total electric flux leaving the surface of the sphere?**

**Question 23. An infinite line charge produces a field of 9 x 10 ^{4} N/C at a distance of 2 cm. Calculate the linear charge density.**

**Question** **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 17.0 x 10 ^{-22} C/m2. 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?**

### Additional NCERT Exercise

**Question 25. An oil drop of 12 excess electrons is held stationary under a constant electric field of 2.55×10 ^{4} Vm^{-1} in Millikan’s oil drop experiment. The density of the oil is 1.26 g cm^{-3}. Estimate the radius of the drop (g = 9.81 m s^{-2}; e = 1.60 x 10^{-19} C).**

**Question** **26. Which among the curves shown in Fig. cannot possibly represent electrostatic field lines?**

**Sol.** Only (c) is right; the rest cannot represent electrostatic field lines, because field lines

must be normal to a conductor ; cannot start from a negative charge; cannot intersect each other;They do not form closed loops

**Question** **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 10 ^{5} NC^{-1} per metre. What are the force and torque experienced by a system having a total dipole moment equal to 10^{-7} cm in the negative Z-direction?**

**Question** **28. (a) A conductor A with a cavity as shown in Fig. (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 q is inserted into the cavity keeping B insulated from A. Show that the total charge on the outside surface of A is Q + q [Fig. (b)].(c) A sensitive instrument is to be shielded from the strong electrostatic field in its environment. Suggest a possible way.**

**Sol.** (a) Taking a close Gaussian surface just inside touching the outer surface of the conductor (A).

Since electric field inside the Gaussian surface is zero.

Hence there is no charge inside the Gaussian surface and whole charge Q lies on the outer surface of conductor A.

(b) Charge+ Q appears on conductor A forming cavity. Induced charge q appears on outer surface of A. Therefore, total charge (Q + q) appears on outer surface of A.

(c) The instrument should be enclosed inside a metallic case to make its environment field free.

**Question** **29. A hollow charged conductor has a tiny hole cut into its surface. Showthat the electric field in the hole is (cr / 2s0) II , where II is the unit vector in the outward normal direction, and cr is the surface charge density near the hole.**

**Question** **30. Obtain the formula for the electric field due to a long thin wire ofuniform linear charge density )… without using Gauss’s law. [Hint: Use Coulomb’s law directly and evaluate the necessary integral.**

**Question 31. It is now believed 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+ (2/3) e, and the ‘down’ quark (denoted by d) of charge (-1/3) e, 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.**

**Question** **2. (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.**

**Sol.(a) **Proving it by contradiction. Suppose the equilibrium is stable; then the test charge displaced slightly in any direction will experience a restoring force towards the null-point. That is, all field lines near the null point should be directed inwards towards the null point. That is, there is a net inward flux of electric field through a closed surface around the null-point. But by Gauss’s law, the flux of electric field through a surface, not enclosing any charge, must be zero. Hence, the equilibrium cannot be stable.

**(b)** The mid-point of the line joining the two charges is a null-point. Displace a test charge from the null-point slightly along the line. There is a restoring force. But displace it, say, normal to the line. You will see that the net force takes it away from the null-point. Remember, stability of equilibrium needs restoring force in all directions

**Question 33. A particle of mass m and charge (-q) enters the region between the two charged plates initially moving along x-axis with speed vx” The length of plate is L and an uniform electric field Eis maintained between the plates. Show that the vertical deflction 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 Text book of physics.**

**Sol.** Let the point at which the charged particle enters the electric field, be origin 0 (0, 0), then after traveling a horizontal displacement L, it gets deflected by displacement y in vertical direction as it comes out of the electric field. So, co

ordinates of its initial position are x1 = 0 and y1 = 0 and of final position on coming out of the electric field are

**Question 34. Suppose that the particle in Q.1.33 is an electron projected with velocity vx = 2.0 x 10 ^{6} ms^{-1}. If E between the plates separated by 0.5 cm is 9.1 x 10^{2} N/ C, where will the electron strike the upper plate? Charge of electron, e = l.6×10^{-19} C and mass of electron, me= 9.lxl0^{-31} kg.**

**Related Articles:**

- NCERT Solutions for Class 12 (All Subjects)
- NCERT Solutions for Class 12 Physics
- Electrical Charges and Fields Class 12 Notes Physics Chapter 1