7. A capacitor has been charged by a D C source. What are the magnitude of conduction and displacement current, when it is fully charged?

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1 1. In which Orientation, a dipole placed in uniform electric field is in (a) stable (b) unstable equilibrium. 2. Two point charges having equal charges separated by 1 m in distance experience a force of 8 N. What will be the force experienced by them, If they are held in water, at the same distance. (Dielectric constant of water = 80) 3. Define dielectric Constant of medium. What is the value of dielectric constant for a metal? 4. Charges of magnitude 2Q and Q are located at points (a, o, o ) and (4a, o, o) Find the ratio of the flux of electric field, due to these charges, through concentric spheres of radii 2a & 8a centered at the origin. 5. Figure represents the electric lines of force at constant potentials shown in bracket. At which point A, B and C is the electric field maximum. 6. Two charges 5nC and -2nC are placed at points (5cm, 0, 0) and (23cm, 0, 0) on a region of space where there is no other external field. Calculate the electrostatic potential energy of this charge system. 7. A capacitor has been charged by a D C source. What are the magnitude of conduction and displacement current, when it is fully charged? 8. Sketch a graph to show how the charge Q acquired by a capacitor of capacitance C raises with increase in Potential difference between its plates. 9. A Capacitor is connected to a battery. Is it stored energy equal to less than or greater than the energy drawn from the battery? 10. An uncharged insulated conductor A is brought near a charged insulated conductor B what happens to the charge, potential and capacity of B? 11. A uniform electric field exists between two charged plates as shown in figure. What should be the work done in moving a charge q along the closed rectangular Path ABCDA.

2 12. If a point charge +q is taken from A to C and then from C to B of a circle drawn with another point charge q at its centre, then along which path will more work be done. 13. Why in Millikan s Oil Drop experiment, the charge measured was always found to be of some discrete value and not any arbitrary value? 14. Two electric lines never cross each other. Why? 15.What is meant by electrostatic shielding? 16. Why an electric dipole placed in a uniform electric field does not undergoes acceleration? 17. Why electric field lines (i) Cannot for closed loops sometimes? (ii) Cannot have break in between? 18. State Gauss s law and use this law to derive the electric filed at a point from an infinitely long straight uniformly charged wire. 19. Is it possible that the potential at a point is zero, while there is finite electric field intensity at that point? Give an example. 20. An electric dipole is placed in an electric field due to a point charge. Will there be a force and torque on the dipole? 21. Draw the graph showing the variation of electric potential with distance from the centre of a uniformly charged shell. 22. Find the ratio of the electric field lines starting from a proton kept first in vacuum and then in a medium of dielectric constant Sketch the electric field lines, when a positive charge is kept in the vicinity of an uncharged conducting plate. 24. Compare the electric flux in a cubical surface of side 10 cm and a spherical surface of radius 10 cm, when a change of 5μC is enclosed by them. 25. Two identical metal plates are given positive charges Q1 and Q2, where Q1 > Q2. Find the potential difference between them, if they are now brought together to form a parallel plate capacitor with capacitance C.

3 1. A slab of material of dielectric constant K has the same area as the plates of parallel plate capacitor, but has a thickness( 3 d), where d is the separation of the plates, how is the capacitance change 5 when the slab is inserted between the plates? 2. The battery remains connected to a parallel plate capacitor and a dielectric slab is inserted between the plates. What will be the effect on its - (i) Capacity (ii) Charge (iii) Potential difference (iv) Energy stored? 3. Two uniformly large parallel thin plates having charge densities + σ and - σ are kept in the x-z plane at a distance d apart. Sketch an equipotential surface due to electric field between the plates. If a particle of mass m and charge -q remains stationary between the plates what is the magnitude and direction of this field. 4. A small metal sphere carrying charge +Q is located at the centre of spherical cavity in a large uncharged metal sphere as shown in figure. Use Gauss s theorem to find electric field at points P1 and P2. 5. A charge Q located at a point r is in equilibrium under the combined electric field of three charges q1, q2, q3. If the charges q1, q2 are located at points r1 and r2 respectively, find the direction of the force on Q. Due to q 3 in term of q1, q2, r1, r2 and r. 6. Two large plates P1 and P2, tightly held against each other and placed between two equal and unlike point charges perpendicular to the line joining them. a) What will happen to the plates when they are released? b) Draw the pattern of the electric field lines for the system? 7. Draw equipotential surfaces corresponding to a) a constant electric field in Z direction. b) a field that uniformly increases in magnitude but remains in a constant (say Z) direction. 8. Write the expression for the electric field at point x > r2 from the centre of the shell, having inner and outer radius are r1 and r2 respectively. A charge q is placed at its centre and it has Q charge.

4 9. Show that the electric field at the surface of a charged conductor as given by = σ ^ where σ is the E n surface charge density and ^ a unit vector normal to the surface in the outward direction. n 10. Plot a graph showing the variation of column b force (F) versus ( 1 r2) whose r is the distance between the two charges of each pair of charges (1μC, 2μC) and (2μC, -3μC). Interpret the graphs obtained. 11. Two insulated charged copper spheres A and B of identical size have charges qa and qb respectively A third sphere C of the same size but uncharged is brought in contact with the first and then in contact with the second and finally removed from both. What are the new charges on A and B? 12. Consider two conducting spheres of radii R1, and R2 with R1 > R2. If the two are at the same potential, the larger sphere has more charge than the smaller sphere. State whether the charge density of the smaller sphere is more or less than that of the larger one. 13.A charge A situated outside an uncharged hollow conductor experience a force if another charge B is placed inside the conductor, but B does not experience any force. Why? Does it not violate the third law of motion. 14. Define electric flux. Write its S.I unit. A charge q is enclosed by a spherical surface of radius R. If the radius is reduced to half, how would the electric flux through the surface change? 15. A 4μF 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 1 st capacitor is lost in the process of attaining the steady situation? 16. A test charge q is moved without acceleration from A to C along the path from A to B and then from B to C in electric field E as shown in figure B to C in electric field E as shown in figure. a) Calculate the potential difference between A and C. b) At which point (of the two) is the electric potential more and why? 17. Two point charges q1 = 10x10-8 C and q2=-2x10-8 C are separated by a distance of 60 cm in air. a) Find at what distance from the 1 st charge q1, would the electric potential be zero? b) Also calculate the electrostatic potential energy of the system Figure shows a sheet of aluminum foil of negligible thickness placed between the plates of a capacitor. How will its capacitance be affected ifa) The foil is electrically insulated? b) The foil is connected to the upper plate with a conducting wire?

5 19. Can two equipotential surfaces intersect each other? Give reasons. Two charges (-q) and (+q) are located at points A(0, 0,-a) and B(o, o, +a) respectively. How much work is done in moving a test charge from point P(7, 0, 0) to Q(-3, 0, 0)? 20.. Two charges of 5nC and -2nC are placed at points (5cm, 0, 0) and (23cm, 0, 0) in region of space where there is no other external field. Calculate the electrostatic potential energy of this charge system. 21. In the given figure, calculate the total flux of the electrostatic field through the spheres S1 and S2. The wire AB shown here has a line as charge density, given as.= kx, where x is distance measured along the wire, from the end A. 22. A thin straight infinitely long conducting wire having charge density, is enclosed by a cylindrical surface of radius r and length l, its axis coinciding with the length of the wire. Find the expression for electric flux through the surface of the cylinder. 23. A uniformly charged rod with linear charge density λ of length L is inserted into a hollow cubical structure of side L with constant velocity and moves out from the opposite face. Draw the graph between flux and time. 24. Draw a graph showing the variation of potential with distance from the positive charge to negative charge of a dipole, by choosing the mid-point of the dipole as the origin. 25. The spherical shell of a Van de Graff generator is to be charged to a potential of 2 million volt. Calculate the minimum radius the shell can have, if the dielectric strength of air is 0.8 kv/mm. 26. A pith ball of mass 0.2 g is hung by insulated thread between the plates of a capacitor of separation 8cm. Find the potential difference between the plates to cause the thread to incline at an angle 150 with the vertical, if the charge in the pith ball is equal to 10-7C. 27. Net capacitance of three identical capacitors in series is 1μf. What will be their net capacitance if connected in parallel? Find the ratio of energy stored in the two configurations, if they are both connected to the same source. 28. Find the capacitance of a system of three parallel plates each of area A m2 separated by d1 and d2 m respectively. The space between them is filled with dielectrics of relative dielectric constant є1 and є Three point charges of 1C, 2C & 3C are placed at the corners of an equilateral triangle of side 1m. Calculate the work done to move these charges to the corners of a smaller equilateral triangle of sides 0.5m. 30. How will you connect seven capacitors of 2μf to obtain an effective capacitance of 10/11 μf.

6 1. Two Point charges of magnitude +q and q are placed at ( -d, o, o) and (+d, o, o) respectively, Find 2 2 The equation of the equi potential surface where the potential is zero. 2. Deduce the expression for the potential energy of two point charges q1 and q2 brought from infinity to the point r1 and r2 respectively in the presence of eternal electric field E. 3. A parallel plate is charged by a battery. When the battery remains connected, a dielectric slab is inserted in the space between the plate. Explain what changes if any, occur in the values of (i) Potential difference between the plates (ii) Electric field strength between the plates (iii) Capacitance (iv) Charge on the plate (v) Energy stored in the capacitor? 3. Two idential parallel plate (air) Capacitors C 1 and C 2 have capacitances C each. The space between their plates is now filled with dielectric as shown. If the two capacitors still have equal Capacitance Obtain the relation between dielectric Constants K, K 1, & K (a) What happens to the energy stored in a Capacitor if after disconnecting the battery, the plates of a charged capacitor are moved farther. (b) When a Capacitors is charged by a battery, does the energy stored by a Capacitors remain same as energy supplied by the battery? (c ) What is the physical significance of lim q 0 in the expression E=lim q 0 F/q 5. Find the potential differences between the left and right place of each capacitor is the circuit shown is the figure. 6. Define an expression for the potential energy of an electric dipole of dipole moment P is an electric field E. 7. State and Prove Gauss theorem is electrostatics.

7 8. (a) Show mathematically that the potential on the equatorial line of an electric dipole is zero. (b) Define electric line of force and give its two properties. 9. A molecule of a substance has a permanent electric dipole moment of magnitude cm. A mole of this substance is polarized at low temperature by applying a strong electrostatic field of magnitude 10 6 Vm -1. The direction of the field is suddenly changed by an angle of Estimate the heat released by the substance in aligning its dipoles along the new direction of the field. For simplicity assume 100% polarization of sample. 10. Two small identical electric dipole AB and CD, each of dipole moment p are kept at an angle of as shown in figure. What is the resultant dipole moment of this combination? If this system is subjected to electric field ( E ) directed along +X direction. What will be the magnitude and direction of the torque acting on this? 11. Figure shows two identical capacitance C1 and C2 each of the 1πF capacitance connected to a battery of 6V. Initially switch S is closed. After sometime S is left open and dielectric slabs of dielectric constant K = 3 are inserted to fill completely the space between the plates of the two capacitors. How will the (i) Charge and (ii) Potential difference between the plates of the capacitors be affected after the slabs are inserted? 12. Show that the potential of a charged spherical conductor, kept at the centre of a charged hollow spherical conductor is always greater than that of the hollow spherical conductor, irrespective of the charge accumulated on it. 13. Derive the expression for the potential due to a dipole. Find the ratio of the potential along the equatorial and axial line of a dipole.

8 14. Two point charges 4Q, Q are separated by 1m in air. At what point on the line joining the charges B the electric field intensity zero? Also calculate the electrostatic potential energy of the system of charges taking the value of charge Q = 2x10-7 C. 15.Three points charges of +2πC, -3πC are kept at the vertices A, B and C respectively of an equilateral triangle of side 20 cm as shown in figure. What should be the sign and magnitude of charge to be placed at the need point M of side BC so that charge at A remains in equilibrium? 16. A cube of side 6 has a charge q at each of its vertices. Determine the potential and electric field due to this charge at the centre of the cube. 17.If one of the two electrons of a hydrogen molecule is removed, we get a hydrogen molecular ion H + 2. This ion consists of two protons and an electron. If at any instant the two protons be separated by a distance of 1.5A 0 and electrons by 1A 0 from each proton. Calculate the potential energy of system specify your choice of zero P.E. 18. A network of four capacitor each of 12μF capacitance is connected to a 500 V supply as shown in figure. Determine (a) Equivalent capacitance of the network and (b) Charge on each capacitor.

9 19. A potential difference of 1200 V is established between two parallel plates of a capacitor. The plates of the capacitor are at a distance of 2 cm apart. An electron is released from the negative plate, at the same instant, a proton is released from the +ve plate. (a)how do their (i) velocity (ii) Energy compare, when they strike the opposite plates. (b) How far from the positive plate will they pass each other? 20. A charge +Q fixed on the Y axis at a distance of 1m from the origin and another charge +2Q is fixed on the X axis at a distance of 2 m from the origin. A third charge Q is placed at the origin. What is the angle at which it moves? 21. What is an equivalent capacitance of the arrangement the shown below

10 1.. Discuss briefly the behavior of conductors in electrostatic field. 2. Two capacitors with capacitances C1 and C2 are charged to potentials V1 and V2 respectively and then connected in parallel. Calculate the common potential across the combination, the charge on each capacitor, the electrostatic energy stored in the system and the change in electrostatic energy from its initial value. 3. Briefly explain the principle of a capacitor. Derive an expression for the capacitance of a parallel plate capacitor, whose plates are separated by a dielectric medium. 4. Derive the expression for the electric potential due to an electric dipole. Mention the contrasting features of electric potential of a dipole at a point as compared to that due to a single charge. 5. Find an expression for the capacitance of a parallel plate capacitor when a dielectric slab of dielectric constant K and thickness t = d but of same area on the plates is inserted between the 2 capacitor plate. 6. State Gauss s theorem in electrostatics and express it mathematically. Using it derive an expression for electric field at a point near a thin infinite plane sheet of electric charge. How does this electric field change for a uniformly thick sheet of charge. 7. Explain the principle on which Van-de Graff generator operates. Draw a labeled schematic sketch and write briefly it s working. 8. Obtain the expression for the capacitance of a parallel plate capacitor. Three capacitors of capacitances C1, C2 and C3 are connected in parallel. Derive an expression for the equivalent capacitance. 9. i) Using Gauss s theorem derive the expression for the electric field intensity at a point outside a uniformly charged thin spherical shell of radius R and surface charge density σc/m 2. Ii) Use Gauss s theorem to find the value of electric field intensity at a point inside this shell ( or hollow charged conducting sphere)? 9. Apply Gauss theorem to obtain the expression for the electric fielda) At a point due to an infinitely long, thin, uniformly charged straight wire of linear charge density cm- 1 b) Near an infinite plane sheet of charge. Designed by Md. Wasim Iqbal (Physics Faculty, GOVIND VIDYALAYA TAMULIA)

11 LONG TYPE (5 MARKS) 1.. Discuss briefly the behavior of conductors in electrostatic field. 2. Two capacitors with capacitances C1 and C2 are charged to potentials V1 and V2 respectively and then connected in parallel. Calculate the common potential across the combination, the charge on each capacitor, the electrostatic energy stored in the system and the change in electrostatic energy from its initial value. 3. Briefly explain the principle of a capacitor. Derive an expression for the capacitance of a parallel plate capacitor, whose plates are separated by a dielectric medium. 4. Derive the expression for the electric potential due to an electric dipole. Mention the contrasting features of electric potential of a dipole at a point as compared to that due to a single charge.

12 5. Find an expression for the capacitance of a parallel plate capacitor when a dielectric slab of dielectric constant K and thickness t = d but of same area on the plates is inserted between the 2 capacitor plate. 6. State Gauss s theorem in electrostatics and express it mathematically. Using it derive an expression for electric field at a point near a thin infinite plane sheet of electric charge. How does this electric field change for a uniformly thick sheet of charge. 7. Explain the principle on which Van-de Graff generator operates. Draw a labeled schematic sketch and write briefly it s working. 8. Obtain the expression for the capacitance of a parallel plate capacitor. Three capacitors of capacitances C1, C2 and C3 are connected in parallel. Derive an expression for the equivalent capacitance. 9. i) Using Gauss s theorem derive the expression for the electric field intensity at a point outside a uniformly charged thin spherical shell of radius R and surface charge density σc/m 2. Ii) Use Gauss s theorem to find the value of electric field intensity at a point inside this shell ( or hollow charged conducting sphere)? 9. Apply Gauss theorem to obtain the expression for the electric fielda) At a point due to an infinitely long, thin, uniformly charged straight wire of linear charge density cm- 1 b) Near an infinite plane sheet of charge.

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