Einstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road, New Delhi , Ph. : ,

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1 1 E L E C T R O S TAT I C S 1. Define lines of forces and write down its properties. Draw the lines of force to represent (i) uniform electric field (ii) positive charge (iii) negative charge (iv) two equal and opposite charges separated by some distance (v) two charges q 1 and q 2 separated by some distance d (vi) three equal charges placed at the corners of an equilateral triangle. Why two electric lines of force do not intersect? 2. (a) Define Coulomb. Calculate the charge carried by electrons. (b) Calculate the Coulomb force between a proton and an electron separated by m and compare with the gravitational force between them. Also calculate the Coulomb force between two -particles separated by a distance m. (c) Define charge and write down its properties. What is quantization of electric charge? 3. (a) Define capacitance and its units. Derive an expression for the capacitance of (i) cylindrical capacitor (ii) spherical capacitor (iii) parallel plate capacitor. (b) Derive an expression for the energy stored in a parallel plate capacitor with air as the medium between its plates. How does the total energy stored by the capacitor change when the medium of air is replaced by a medium of dielectric constant K? Explain Show that electric field E itself is a source of energy with energy density 0E Jm. 2 (c) Three capacitors of equal capacitance, when connected in series, have a net capacitance of C 1 and when connected in parallel, have a capacitance of C 2. What will be the value of C 1 /C 2? (d) In a parallel plate capacitor, the capacitance increase from 4 microfarad to 80 microfarad, on introducing a dielectric medium between the plates. What is the dielectric constant of the medium? (e) Define dielectric constant of a medium in terms of force between electric charges. (f) Capacitors P, Q and R have each a capacity C. A battery can charge the capacitor P to a potential difference V. If after charging P, the battery is disconnected from it and the charged capacitor P is connected in following separate instances to Q and R (i) to Q in parallel, and (ii) to R in series, then what will be the potential difference between the plates of P in the two instances? (g) The capacitor is disconnected from the charging battery, explain how the (i) capacitance, (ii) p.d. across the plates, and (iii) energy stored in the parallel plate capacitor change, when a medium of dielectric constant k is introduced between the plates. (h) When two capacitors of capacitance C 1 are connected in series the net capacitance is 3 µf; when connected in parallel its value is 16 µf. Calculate value of C (a) Define electric dipole moment. Derive an expression for the electric field and potential at any point along the (i) equatorial line (ii) axial line of an electric dipole. Show mathematically that the electric field intensity due to a short dipole at a distance d along its axis is twice the intensity at the same distance along the equatorial axis.

2 2 (b) Derive an expression for the total work done in rotating the dipole through an angle in uniform electric field E. Also derive the torque acting on the dipole. (c) What is the force and torque acting on the dipole in the presence of uniform electric field and non-uniform electric field. (d) An electric dipole is held in a uniform electric field. (i) Show that no translatory force acts on it. (ii) The dipole is aligned parallel to the field. Calculate work done in rotating it through (e) An electric dipole, when held at 30 0 with respect to a form electric field of N/C, experiences a torque of Nm. Calculate the dipole moment of the dipole? (f) An electric dipole of dipole moment p is placed along the direction of the uniform external electric field E. It is disturbed from this position by very small angle. Explain what happens to the dipole on being released. 5. Three capacitors of capacitance X 1, X 2 and X 3 are connected (i) in series and (ii) in parallel. Derive expressions for the equivalent capacitance X for each of these combinations. 6. If an oil drop of weight N is balanced in an electric field of V/m, find the charge on the oil drop. 7. (a) Define electric field at a point and its unit. Is electric field intensity a scalar or a vector quantity? Two points charges q and q are placed a distance 2a apart Calculate the electric field at a point P situated at a distance r along the perpendicular bisector of the line joining the charges. What is the field when r > > a? (b) Find the electric field between two metal plate 3 mm. apart, connected to a 12 V battery. (c) Define electric potential and its unit. Derive the expression for the electric field and potential at a distance r from a point charge Q. (d) Two point electric charges of unknown magnitude and sign are placed a distance d apart. The electric field intensity is zero at a point, not between the charges but on the line joining them. Write two essential conditions for this to happen. (e) In an electric field an electron is kept freely. If the electron is replaced by a proton, what will be the relationship between the force experienced by them? 8. Explain the construction, basic principle and working of a Van de Graff generator with the help of a diagram. 9. (a) State Coulomb s law of force in electrostatics. (b) State Gauss s theorem in electrostatics. Apply this to calculate the field intensity (i) at a point near an infinite plane sheet of charge of uniform charge density. (ii) at any point inside and outside a hollow and solid charged conducting sphere. (iii) at a point from a infinite line charge of charge per unit length. (iv) at any point inside and outside of the solid non-conducting charged sphere also draw the variation of electric field with distance in (ii) and (iv). 10. Define equipotential surfaces and how it is related with the electric field. Draw the equipotential surfaces (i) for a given point charge (ii) uniform electric field 11. You are given an isolated parallel plate capacitor of capacitance C charged to a potential difference V. What will happen to the following when the separation between the plates is doubled with the help of insulating handles attahced to the plates?

3 (a) charge on the plates (b) potential difference across the plates (c) field between the plates (d) energy stored in the capacitor 12. Derive the expression for a equivalent capacity of two capacitors of capacitances C 1, connected in series. 13. Calculate the distance between two protons such that the electrical repulsive force between them is equal to the weight of either. 14. Obtain the energy in joules acquired by an electron beam when accelerated through a potential difference of 2000 V. Also find the speed of the particle. 15. The electric field at a point due to a point charge is 20 N/C and the electric potential at that point is 10 J/C. Calculate the distance of the point from the charge and the magnitude of the charge. 16. Force between two point electric charges kept at a distance d apart in air is F. If these charges are kept at the same distance in water, how does the force between them charge? 17. An -particle and a proton are accelerated through the same potential difference. Calculate the ratio of velocities acquired by the two particles. 18. Two point changes +4µC and 6µC are separated by a distance of 20 cm in air. At what point on the line joining the two charges is the electric potential zero? 19. Two point electric charges of values q and 2q are keep at a distance d apart from each other in air. A third charge Q is to be kept along the same line in such a way that the net force acting on q and 2q is zero. Calculate the position of charge Q in terms of q and d. 20. Two identical point charges of charge Q are kept at a distance r from each other. A third point charge is placed on the line joining the above two charges such that all the three charges in equilibrium. Calculate the magnitude and location of the third charge. 21. A proton, placed in a uniform electric field of magnitude NC 1, moves from a point A to B in the direction of electric field. If AB = 0.05m, calculate the (i) potential difference between A and B, and (ii) work done in moving the proton from A to B. 22. Two point charges 20 µc and 40 µc are separated by a distance r in air. If an additional charge of 16µC is given to each, by what factor does the force between the charges change? 23. An electric flux of Nm 2 /C passed normally through a spherical Gaussian surface of radius 10 cm, due to a point charge placed at the centre. (i) What is the charge enclosed by the Gaussian surface? (ii) If the radius of the Gaussian surface is doubled, how much flux would pass through the surface? 24. How does the force between two point charges change, if the dielectric constant of the medium in which they are kept, increases? 25. An infinite plane sheet of charge density 10 8 C/m 2, is held in air. In this situation how far apart are two equipotential surfaces, whose p.d. is 5 V? 26. A charge of +10µC is given to a hollow metallic sphere of radius 0.1 m. Find the potential at the (i) outer surface, and (ii) centre of the sphere. 27. What is the amount of work done in moving a 100 nc charge between two points 5 cm apart on an equipotential surface? 3

4 4 28. An electric dipole of length 2 cm is placed with its axis making an angle of 60 0 to a uniform electric field of 10 5 N/C. If it experiences a torque of 8 3 Nm, calculate the (i) magnitude of the charge on the dipole, and (ii) potential energy of the dipole. 29. Calculate the potential and field at the centre of a square of side 2 m, which carries at its four corners charges of +2 nc, + 1nC, 2 nc and 3 nc respectively. Also calculate the work done to carry a charge particle of +10nC from infinity to the center of the square. 30. An electric dipole is placed in a uniform electrostatic field. Will the net force experienced by it be zero even when the torque experienced by it is maximum? 31. There is a point charge q each at the four corners of a square. What will be the ratio of force between the charges at adjacent corners and the charges at opposite corners of the square? 32. Two conducting spheres of equal size carry 40µC and 20µC charge respectively. What will be the charges on them after they have been brought in contact and separated? Also find the work done. 33. A point charge q goes around another point charge Q in a semi conductor path of radius R. What will be the change in electrostatic potential energy of the system of charges? 34. Can any set of parallel field represent a uniform electrostatic field? Justify your answer. 35. At which of the points A, B and C in a uniform electrostatic field as shown, will the electric potential be (a) minimum (b) maximum 36. Two like point charges q each at a separation R in air exert a force of magnitude F. They are now immersed in a non-conducting oil of dielectric constant 16. What should the new separation between the charges be so that the force between them remains unchanged? 37. A metal wire is bent in the shape of a circle of radius 10 cm. It is given a charge of 20µC, which is spread uniformly over it. Calculate electrical potential at the centre of the circle. 38. Two capacitors of capacitance 10µF and 2µF are connected in series with a 6V battery. If E is the energy stored in the 10µF capacitor what will be the total energy supplied by the battery in terms of E. 39. A 10µF capacitor can withstand a maximum voltage of 100 volts across it whereas another 20µF capacitor can withstand a maximum voltage of only 25 volts. What is the maximum voltage that can be put across their series combination? 40. A parallel plate capacitor has capacitance of 30pF. What will its capacitance become in the two cases shown below when it is half-filled with a dielectric of dielectric constant?

5 41. Find the equivalent capacitance of the following network between A and B. 5 (a) (b)