Electric Charges and Field (12Acd01)

Sheet 01 Coulomb’s Law in Electro Statics

1. Justify the statement that “1 Coulomb is a very large unit of electric charge for practical purpose.
   
2. A free pith ball P of 10g carries a charge of \(\left(5\times10^{-8}\right)C\). What must be the nature and the magnitude of charge that should be given to another pith ball Q fixed 7cm below the former ball, so that upper ball is stationary?
   
   Ans: \(\left(1.067\times 10^{-6}\right)C\).
   
   
3. Two point charges +4Q and +Q are fixed and separated by a distance of a in air. Where should be third point charge q be placed on line joining two charges so that it may be in equilibrium ? In which case equilibrium will be stable and in which case will be unstable?
   
   Ans: \(x=\frac{2a}{3}\).
   
   
4. Two charges each of +Q units are placed along a line. A third charge q is placed in between them on line joining two charges so that the system of charges will be is in equilibrium. What is the position and magnitude of the charge q?
   
   Ans: \(x=\frac{R}{2}\), \(q=\frac{Q}{4}\).
   
   
5. Force of attraction between two point charges placed at a distance “d” is F. What distance apart should be they be kept to same medium, so that force between them is 2F?
   
   Ans: \(r=\frac{d}{\sqrt{2}}\).
   
   
6. A charge Q is divided into two parts \(q\) and \(\left(Q-q\right)\). How the charge Q and q be related so that when \(q\) and \(\left(Q-q\right)\) are placed at a certain distance apart, experiences maximum electrostatic repulsion.
   
   Ans: \(Q=2q\).
   
   
7. (a) Two insulated charged copper spheres A and B have their center separated by a distance of \(50cm\). What is the mutual force of electrostatic repulsion if the charge on each is \(\left(6.5\times10^{-7}\right)C\)? The radii of A and B are negligible compared to the distance of separation between them.
   |(b) What is the force of repulsion, if
   (i) Each sphere is charged double the above amount and distance between them is halved?
   (ii) The two spheres are placed in water?[ Given: Dielectric Constant of water = 80.]
   
   Ans: (a) \(\left(1.5\times 10^{-2}\right)N\).
   (b)(i) 0.24N.
   (b)(ii) \(\left(1.9\times 10^{-4}\right)N\).
   
   
8. Suppose the spheres A and B in example 15 have identical sizes. A third sphere of same size and 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?
   
   Ans: \(\left(5.7\times 10^{-3}\right)N\).
   
   
9. Two particles, each having a mass of \(5g\) and charge \(\left(1.0\times10^{-7}\right)C\), stay in limiting equilibrium on a horizontal table with a separation of \(10cm\) between them. The co-efficient of friction between the each particle and and the table is same. Find: \(\mu\).
   
   Ans: \(\mu=0.18\).
   
   
10. Two small spheres, each of mass \(m\) kg and charge \(q\) Coulomb are suspended from a point by insulating threads each of length \(l\) meter but of negligible mass. If, \(\theta\) be the angle each string makes with the vertical when equilibrium is reached, show that \(q^{2}=\left(4.mg.l^{2}Sin^{2}\theta .tan\theta\right)\) .
    
11. Two identical charged sphere are suspended in air by strings of equal weights and make an angle of \(30^{o}\) with each other. When suspended in a liquid of density \(800\frac{kg}{m^{3}}\), angle remains same. What is the dielectric constant of the liquid? The density of the material of the sphere is \(1600\frac{kg}{m^{3}}\).
    
    
    Ans: \(\epsilon_{r}=2\).
    
    
12. Two identical spheres, having charges of opposite sign attract each other with a force of \(0.108N\) when separated by a distance of \(0.5m\). The spheres are now connected by a conducting wire, which then after some times removed, and thereafter they repel each other with a force of \(0.036N\). What were the initial charges on the spheres?
    
    Ans: \(q_{1}=\left(3\times 10^{6}\right)C\) and \(q_{2}=10^{-6}C\).
    
    
13. A particle of mass m and carrying a charge \(-q_{1}\) is moving around a charge \(+q_{2}\) along a circular path of radius r. Prove that: the period of revolution of the charge \(-q_{1}\) about \(+q_{2}\) is given by \(T=\sqrt{\frac{16\pi^{2}\epsilon_{o}mr^{3}}{q_{1}.q_{2}}}\).
14. Two point electric charges q and 2q are kept at a distance d apart from each other in air. A third charge Q is to be kept along the same line in such away that the net force acting on q and 2q is Zero. Calculate: the position of charge Q in terms of q and d.
    
    Ans: \(x=\left(\sqrt{2}-1\right)\times d\) from charge q.