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Transcript

HOLIDAY HOMEWORK, KENDRIYA VIDYALAYA O.F DUM DUM 1. Two point charges qA = 3 μC and qB = - 3 μC are located 20 cm apart in vacuum, (i) Find the electric field at the mid point of the line AB joining the two charges, (ii) If a negative test charge of magnitude 1.5 × 10 – 9 is placed at the centre, find the force experienced by the test charge. 2. Obtain the expression for the capacitance of a parallel plate capacitor. Three capacitors of capacitances C1, C2 and C3 are connected (i) in series, (ii) in parallel. Show that the energy stored in the series combination is the same as that in the parallel combination. 3. Sketch a graph to show how the charge 'Q' acquired by a capacitor of capacitance 'C' varies with increase in potential difference between its plates. Hence find its capacitance 4. Sketch electric field lines for an isolated positive point charge, between +q and –q, between +2q and +q and answer why lines of forces can never intersect each other? 5. State Gauss' theorem in electrostatics. A charge of 17.7 x 10 -4 C is distributed uniformly over a large sheet of area 200 m2.Calculate the electric field intensity at a distance 20 cm from it in air Or Electric field intensity at point 'B' due to a point charge 'Q' kept at point 'A' is 24 NC-1 and the electric potential at point 'B' due to same charge is 12 JC-1 . Calculate the distance AB and also the magnitude of charge Q. 6. Find the equivalent capacitance between the points A and B of the given combination of capacitors. If a battery of e.m.f. 10 V is connected between the points A and B, calculate the total charge in the circuit. 7. An electric dipole of length 4 cm, when placed with its axis making an angle of 300 with a uniform electric field experiences a torque of 4 Nm. Calculate the (i) magnitude of the electric field. (ii) potential energy of the dipole, If the dipole has charges of 10 C 8. The graph shows the variation of voltage, ‘V’ across the plates of two capacitors A and B versus increase of charge, ‘Q’ stored on them. Which of the two capacitors has higher capacitance? Give reason for your answer. [2 9. State Gauss’ theorem in electrostatics. Using this theorem, derive the expression for the electric field intensity at any point outside a uniformly charged thin spherical shell. MD M ALAM 9681527043 HOLIDAY HOMEWORK, KENDRIYA VIDYALAYA O.F DUM DUM 10. The graph shows the variation of voltage, ‘V’ across the plates of two capacitors A and B versus increase of charge ‘Q’ stored on them. Which of the two capacitors has lower capacitance? Give reason for your answer. [2 11. State Gauss’ theorem in electrostatics. Using this theorem, derive an expression for the electric field intensity due to an infinitely long, straight wire of linear charge density Cm 1 . 12. Two point charges equal to 10 μC and – 10μC are separated by a distance of 40 cm in air. (i) Calculate the electrostatic potential energy of the system, assuming the zero of the potential energy to be at infinity. (ii) Draw an equipotential surface of the system. 13. X and Y are two parallel plate capacitors having the same area of plates and same separation between the plates. ’X has are between the plates and Y contains a dielectric medium of εr = 5. (i) Calculate the potential difference between the plates of X and Y. (ii) What lithe ratio of electrostatic energy stored In X and Y’ 14. Name the dielectric whose molecules have (i) non-zero, (ii) zero dipole moment. Define the term ‘dielectric constant’ for a medium. 15. Find (i) the equivalent capacitance and (ii) the total energy stored in the system of capacitors given in the network. The charging battery has an emf of 4 V. 16. In the figure shown, calculate the total flux of the electrostatic field through the spheres S1 and S2. The wire, AB, shown here, has a linear charge density, λ, given by λ= kx where x is the distance measured along the wire, from the end A. MD M ALAM 9681527043 HOLIDAY HOMEWORK, KENDRIYA VIDYALAYA O.F DUM DUM 17. (a) Define the term ‘electrostatic potential ’.Give the dependence of electrostatic potential due to a small electric dipole at a far off point lying on (i) the axial line and (ii) equatorial line. (b) Briefly explain the principle of a capacitor. Obtain the expression for the capacitance of a parallel plate capacitor. 18. Two fixed point charges – 4e and +e units are separated by a distance 'a'. Where should the third point charge be placed for it to be in equilibrium? Or A 4 μF capacitor is charged by a 200 V supply. The supply is then disconnected and the charged capacitor is connected to another uncharged 2 μF capacitor. How much electrostatic energy of the first capacitor is lost in the process of attaining the steady situation? 19. An electric dipole of dipole moment 20 × 10 – 6 Cm is enclosed by a closed surface. What is the net flux coming out of the surface? 20. Define 'electric line of force' and give its two important properties. 21. (a) Why does the electric field inside a dielectric decrease when it is placed in an external electric field? (b) A parallel plate capacitor with air between the plates has a capacitance of 8 pF. What will be the capacitance if the distance between the plates he reduced by half and the space between them is filled with a substance of dielectric constant K=6? Or There point charges of + 2 μC, - 3 μC and - 3 μC are kept at the vertices, A, B and C respectively of an equilateral triangle of side 20 cm as shown in the figure. What should be the sign and magnitude of the charge to be placed at the mid-point (M) of side BC so that the charge at A remains in equilibrium? 22. An electric dipole is held in a uniform electric field. (1) Using suitable diagram, show that it does not undergo any translatory motion, and (ii) derive an expression for the torque acting on it and specify its direction. 23. Two dielectric slabs of dielectric constants K1 and K2 are filled in between the two plates, each of area A, of the parallel plate capacitor as shown in the figure. Find the net capacitance of the capacitor. MD M ALAM 9681527043 HOLIDAY HOMEWORK, KENDRIYA VIDYALAYA O.F DUM DUM Or A small metal sphere carrying charge + Q is located at the centre of a spherical cavity in a large uncharged metal sphere as shown in the figure. Use Gauss's theorem to find electric field at points P1 and P2. 24. Define the term electric field intensity. Write its SI unit. Derive an expression for the electric field intensity at a point on the axis of an electric dipole. Or State Gauss theorem in electrostatics. Use it to obtain an expression for the electric field intensity at a point near a uniformly charged infinite plane sheet. MD M ALAM 9681527043