Q.1. What is the force between two small charged spheres having charges of 2 ×

placed 30 cm apart in air ?

^{10-7 }C and 3 ×^{10-}7 Cplaced 30 cm apart in air ?

Q.2. The electrostatic force on a small sphere 0-4 μ C due to another small sphere of charge – 0.8μ C 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 ?

Force on second sphere due to the first is the same, i.e.,, 0.2 N

Q.3. check that the ratio ke

^{2}/Gm_{e}m_{p}is dimensionless. Look up a table of Physical Constants and determine the value of this ratio. What does the ratio signify ?This is the ratio of electrostatic force to gravitational force between an electron and a proton.

Q.4. (a) Explain the meaning of the statement ‘electric charge of a body is quantized.’

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

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

Sol. (a) the quantization of electric is the property by virtue of which, the charge on a body is integral multiple of a basic unit of charge of an electron/proton, represented by e.

can increase or decrease only in units of ‘e’ when 10

^{12 }electronic charges are involved has almost no singnificance. Thus at the macroscopic level, graininess of electric charge can be considered as continuous.

Q.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. When a glass rod is rubbed with a silk cloth. Charges appear on both. These charges are equal in magnitude and opposite in sing, so that algebraic sum of the charges produced on both is zero. The net charge on the two bodies was zero even before running them. Thus we find that charges can be created only in equal and unlike pairs. This is consistent with the law of conservation of charge.

Q.6. Four point charges q

_{A }= 2 C ; q_{B }= -5μC, qc = 2μC and qD = -5μ C are located at the corners of a square ABCD of side 10 cm. What is the force on a chare of 1 μ placed at the centra of the square ?Q.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.

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

Sol. (a) An electrostatic field line is a continuous curve, because it represents the actual path of a unit positive charge, which experiences a continuous force. It cannot have sudden breaks the moving test charge never jumps from one position to the other.

(b)

(b)

Q.8. Two point charges q

_{A }= 3 C and q_{b}= -3 C are located 20 cm apart in vacuum (a) What is the electric field at the mid point O of the line AB joining the two charges ? (b) If a negative test charge of magnitude 1.5 × 10^{-9}C is placed at the point, What is the force experienced by the test charge ?Q.9. A system has two charges q

_{A}= 2.5 10^{-7}C and q_{b}= -2.5 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?The direction of p is along BA, i.e., along negative Z – axis.

Q.10. An electric dipole with dipole moment 410

^{-9}C m is aligned at 30^{0}with the direction of a uniform electric field of magnitude 5 10^{4}NC^{-1}. Calculate the magnitude of the torque acting on the dipole.Q.11.A polythene piece rubbed with wool is have a negative charge of 310

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

^{-7}C. (a) Estimate the number of electrons transferred (from which to which ?)(b) Is there a transfer of mass from wool to polythene?

Q.12. Two insulated charged copper spheres A and B have their centers separated 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 ? The radii of A and B are negligible compared is charged double the above amount, and the distance between them is halved?Q.13. Suppose the spheres A and B in Q.12 have identical sizes. A third sphere of same size but uncharged is brought in the contact with the first, them brought in contact with the second, and finally removed from both. What is the new force of repulsion between A and B ?

Sol. Here, chare on A = 6.5 10

Their sizes are equal. When third sphere C of same size is brought in contact with A, their charges are equally shared.

^{-7 }C ; charge on B =6.5 10^{-7}CTheir sizes are equal. When third sphere C of same size is brought in contact with A, their charges are equally shared.

The sphere C carrying 3.25 10

^{-7}of charge is brought in contact with B carrying 6.510^{-7}coulomb charge. As their sizes are equal, therefore, charge on each of the spheres B and C becomesQ.14. The given hows 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?

Q.15.consider a uniform electric E = 3 10

^{3}N/C. (a) what is the flux of this 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^{0}angle with the x- axis ?Q.16. What is the net flux of the uniform electric field of Q.15 above through a cube of side 20 cm oriented so that its faces are parallel to the c0-ordinate planes ?

Sol. Net flux over the cube is zero, because the number of lines entering the cube is the same as the number of lines leaving the cube.

Q.17.. Careful measurement of the uniform electric at the surface of a black box indicates that the net outward flux through the surface of the box is 8.0 10

^{3}Nm^{2}/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 ?Q.18. A point charge + 10 μ C is at a distance of 5 cm directly above the centra of a square of side 10 cm A shown of What is the magnitude of the electric flux through the square ? (Hint. Thinks of the square as one face of a cube with edge 10 cm)

Sol. ABCD is a square of side 10 cm. The point charge + 10 μ C is at a distance of 5 cm. directly above the centre of ABCD. We can imagine the square ABCD as one of the six faces of a cube of side 10 cm. The charge + q is at the centrae of this cube.

Q.19. point charge of 2-0 μ C is at the centra of a cubic Gaussian surface 9.0 cm in edge. What is the net electric flux through the surface ?

Q.20. A point charge causes an electric flux of – 1.0 10

^{3}N m^{2}/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 ?Q.21. A conducting sphere of radius 10 cm has an unknown charge. If the electric field 20 cm from the centra of the sphere is 1.510

^{3}N/C and points radially inwards, what is the net charge on the sphere ?Q.22. A uniformly charged conducting sphere of 2.4 m diameter has a surface charge density of 80.0 μ C/M2 . (a) Find the charge on the sphere (b) What is the total electric flux leaving the surface of the sphere ?

Q.23. . An infinite line charge produces a field of 9 10

^{4}N/C at a distance of 2 cm. calculate the linear charge density.Q.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 magnitude 17.0 10

^{-22}C/m^{2}.What is E : in the outer region of the first plate. (b) in the outer region of the second late, (c) between the plates ? see