**Q1. What is the force between two small charged spheres having charges 2 × 10 ^{-7} C and 3 × 10^{-7} C placed 30cm apart in air ?**

**Sol. Given q _{1} = 2 × 10^{-7} C , q_{2} = 3 × 10^{-7} C ,**

**r = 30 cm = 0.3 m , F = ?**

**By formula ,**

**= 6 × 10 ^{-3} N (repulsive)**

**Q2. 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 ?**

**Sol. Given , q _{1} = 0.4 μC , q_{2} = −0.8 μC**

**F _{12} = 0.2 N**

**(a) We know that**

** r ^{2} = 144 × 10^{-4}**

**and r = 12 × 10 ^{-2} m**

**r = 12 cm**

**(b) Force on second sphere due to first is same i.e. 0.2 N**

**Q3. 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 ?**

**Sol. An electron and proton have a charge of 1.6 × 10 ^{-19} C each and their masses are 9.1×10^{-31} kg and 1.67 ×10^{-27} kg .**

**Electrostatic force b/w electron and proton ,**

**Gravitational force b/w electron and proton ,**

**On dividing ,**

**On putting the values ,**

**The ratio is quite large . This shows that electrostatic forces are much stronger than gravitational forces .**

**A common example is the lifting of a paper by charged comb against the force of entire Earth on that paper .**

**Q: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 ?**

**Sol. (a) Quantisation of electric charge : It is now well known fact that all charges occurring in nature are positive or negative integral multiple of a basic unit of electric charge which we take as the magnitude of the 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 quantisation 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 × 10 ^{-19} C , a charge of magnitude , say 1μC contains something like 10^{13} times the electronic charge . At this scale , the fact that the charge can increase or decrease only in units of e is not very different from saying that charge can take continuous value . Thus at the macroscopic level , the quantisation has no practical consequence and can be ignored .**

**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. Charged 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 .**

**Q:6. Four point charges q _{A} = 2 μC, q_{B} = –5 μC, q_{C} = 2 μC, and q_{D} = –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 square is at equal distance of 10/√2 cm from each corners . Since opposite corners have equal charges , forces along both diagonals will be balanced . Resultant force on 1 μC charge at O will be zero .**

**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 ?**

**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 field at that point . Since it is impossible , hence they don’t intersect .**

**Q: 8. Two point charges q _{A} = 3 μC and q_{B} = -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 × 10**^{-9}C is placed at this point, what is the force experienced by the test charge ?**Sol: q _{A} = 3 μC = 3 × 10^{-6} C and q_{B} = -3 μC = -3 × 10^{-6} C**

**(a) E _{0} = ?,**

**q _{0} = 1.5 × 10^{-9} C ,**

**E at O due to charge at A,**

**= 27 × 10 ^{5} N/C along OB**

**Also, E at O due to charge at B,**

**E _{B} = 27 × 10^{5} N/C along OB**

**Resultant E at O ,**

**E _{O} = E_{A} + E_{B}**

**= 27 × 10 ^{5} + 27 × 10^{5}**

**= 54 × 10 ^{5} N/C along OB**

**(b) For point O, E = 54 × 10 ^{5} N/C , q_{0} = 1.5 × 10^{-9} C ,**

**By relation, F = q _{0} E**

**F = 1.5 × 10 ^{-9} × 54 × 10^{5}**

**= 81 × 10 ^{-4}**

**= 8.0 × 10 ^{-3 N} along OA.**