Page 1 1 ELECTRIC FLUX AND GAUSS LAW 2EL-01 1. The three small spheres as shown in figure, carry charges q 1 = 4.0 nC, q 2 = -8.0 nC and q 3 = 2.0 nC. Find the net electric flux through each of the following closed surfaces shown in cross section in the figure. 2. A charge Q is distributed uniformly on a ring of radius r. A sphere of equal radius r is constructed with its centre at the periphery of the ring. Find the flux of the electric field through the surface of the sphere. 3. Figure shows an imaginary cube of edge L/2. A uniformly charged rod of length L moves towards left at a small but constant speed v. At t = 0, the left end just touches the centre of the face of the cube opposite it. Which of the graphs shown in figure represents the flux of the electric field through the cube as the rod goes through it? L/2 L v (a) Flux a b c d time (b) 4. A hemispherical body is placed in a uniform electric field E. What is the flux linked with the curved surface, if field is (a) parallel to base figure (a), (b) perpendicular to base figure (b). R n (A) E R n (B) E (C ) E n R 5. What is the field in the cavity, if a conductor having a cavity is charged ? Does the result depend on the shape and size of cavity or conductor? 6. Figure shows a closed surface which intersects a conducting sphere. If a positive charge is placed at the points P. Find the sign of flux passing through curved surface ‘s’. 7. In which position (A, B, C or D) of second charge the flux of the electric field through the hemisphere remains uncharged. A B C D q Ring A B 0 1 Sphere 0 Page 2 1 ELECTRIC FLUX AND GAUSS LAW 2EL-01 1. The three small spheres as shown in figure, carry charges q 1 = 4.0 nC, q 2 = -8.0 nC and q 3 = 2.0 nC. Find the net electric flux through each of the following closed surfaces shown in cross section in the figure. 2. A charge Q is distributed uniformly on a ring of radius r. A sphere of equal radius r is constructed with its centre at the periphery of the ring. Find the flux of the electric field through the surface of the sphere. 3. Figure shows an imaginary cube of edge L/2. A uniformly charged rod of length L moves towards left at a small but constant speed v. At t = 0, the left end just touches the centre of the face of the cube opposite it. Which of the graphs shown in figure represents the flux of the electric field through the cube as the rod goes through it? L/2 L v (a) Flux a b c d time (b) 4. A hemispherical body is placed in a uniform electric field E. What is the flux linked with the curved surface, if field is (a) parallel to base figure (a), (b) perpendicular to base figure (b). R n (A) E R n (B) E (C ) E n R 5. What is the field in the cavity, if a conductor having a cavity is charged ? Does the result depend on the shape and size of cavity or conductor? 6. Figure shows a closed surface which intersects a conducting sphere. If a positive charge is placed at the points P. Find the sign of flux passing through curved surface ‘s’. 7. In which position (A, B, C or D) of second charge the flux of the electric field through the hemisphere remains uncharged. A B C D q Ring A B 0 1 Sphere 0 2 ELECTRIC FLUX AND GAUSS LAW 2EL-01 8. A charge q is placed at the center of an imaginary hemispherical surface. The flux of the electric field due to the charge through the surface of the hemisphere. q 9. Find the flux of the electric field through each of the five surfaces of the inclined plane as shown in figure. What is the total flux through the entire closed surface? 10. Consider two concentric conducting spheres. The outer sphere is hollow and initially has a charge -7Q on it. The inner sphere is solid and has a charge +2Q on it. (a) How much charge is on the outer surface and inner surface of the outer sphere. (b) If a wire is connected between the inner and outer spheres, after electrostatic equilibrium is established, how much total charge is on the outer sphere? How much charge is on the outer surface and inner surface of outer sphere? Does the electric field at the surface of the inside sphere change when the wire is connected? (c) We return to original condition in (a). We now connect the outer sphere to ground will be on the outer sphere? How much charge will be on the inner surface and outer surface of the outer sphere? 11. A cube of side l has one corner at the origin of coordinates and extends along the positive x, y and z-axes. Suppose the electric field in this region is given by ˆ () E a by j ?? . Determine the charge inside the cube. 12. The electric field in a cubical volume is 00 ˆˆ 1 zz E E i E j aa ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Each edge of the cube measures d and one of the corners lies at the origin of coordinates. Determine the net charge within the cube 13. A point charge is placed at a distance a/2 from the centre of a square of side ‘a’ as shown in the diagram; calculate the electric flux passing through the square. Page 3 1 ELECTRIC FLUX AND GAUSS LAW 2EL-01 1. The three small spheres as shown in figure, carry charges q 1 = 4.0 nC, q 2 = -8.0 nC and q 3 = 2.0 nC. Find the net electric flux through each of the following closed surfaces shown in cross section in the figure. 2. A charge Q is distributed uniformly on a ring of radius r. A sphere of equal radius r is constructed with its centre at the periphery of the ring. Find the flux of the electric field through the surface of the sphere. 3. Figure shows an imaginary cube of edge L/2. A uniformly charged rod of length L moves towards left at a small but constant speed v. At t = 0, the left end just touches the centre of the face of the cube opposite it. Which of the graphs shown in figure represents the flux of the electric field through the cube as the rod goes through it? L/2 L v (a) Flux a b c d time (b) 4. A hemispherical body is placed in a uniform electric field E. What is the flux linked with the curved surface, if field is (a) parallel to base figure (a), (b) perpendicular to base figure (b). R n (A) E R n (B) E (C ) E n R 5. What is the field in the cavity, if a conductor having a cavity is charged ? Does the result depend on the shape and size of cavity or conductor? 6. Figure shows a closed surface which intersects a conducting sphere. If a positive charge is placed at the points P. Find the sign of flux passing through curved surface ‘s’. 7. In which position (A, B, C or D) of second charge the flux of the electric field through the hemisphere remains uncharged. A B C D q Ring A B 0 1 Sphere 0 2 ELECTRIC FLUX AND GAUSS LAW 2EL-01 8. A charge q is placed at the center of an imaginary hemispherical surface. The flux of the electric field due to the charge through the surface of the hemisphere. q 9. Find the flux of the electric field through each of the five surfaces of the inclined plane as shown in figure. What is the total flux through the entire closed surface? 10. Consider two concentric conducting spheres. The outer sphere is hollow and initially has a charge -7Q on it. The inner sphere is solid and has a charge +2Q on it. (a) How much charge is on the outer surface and inner surface of the outer sphere. (b) If a wire is connected between the inner and outer spheres, after electrostatic equilibrium is established, how much total charge is on the outer sphere? How much charge is on the outer surface and inner surface of outer sphere? Does the electric field at the surface of the inside sphere change when the wire is connected? (c) We return to original condition in (a). We now connect the outer sphere to ground will be on the outer sphere? How much charge will be on the inner surface and outer surface of the outer sphere? 11. A cube of side l has one corner at the origin of coordinates and extends along the positive x, y and z-axes. Suppose the electric field in this region is given by ˆ () E a by j ?? . Determine the charge inside the cube. 12. The electric field in a cubical volume is 00 ˆˆ 1 zz E E i E j aa ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Each edge of the cube measures d and one of the corners lies at the origin of coordinates. Determine the net charge within the cube 13. A point charge is placed at a distance a/2 from the centre of a square of side ‘a’ as shown in the diagram; calculate the electric flux passing through the square. 3 ELECTRIC FLUX AND GAUSS LAW 2EL-01 14. In figure shown a charge q is placed at a distance ? =0 near one of the edges of a cube of edge l on a line of symmetry along diagonal. (a) What is flux through each of the sides containing the point a. (b) What is the flux through the other three faces? 15. Find the electric flux through cylindrical surface in a uniform electric field E 16. What is the flux if the cylinder of previous problem were vertical ? 17. Two identical metal plates each having surface area ‘A’, having charge ‘q 1 ’ and ‘q 2 ’ are placed facing each other at a separation ‘d’. Find the charge appearing on surface (1), (2), (3) and (4). Assume the size of the plate is much longer than the separation between the plates. 18. A point charge q is placed on the apex of a cone of semi-vertex angle ?. Find the electric flux through the base of the cone. 19. The cube as shown in figure has sides of length L = 10.0 cm. The electric field is uniform, has a magnitude E = 4.00 × 10 3 N/C, and is parallel to the xy-plane at an angle of 37° measured from the +x axis toward the +y-axis. What is the electric flux through each of the six cube faces S 1 , S 2 , S 3 , S 4 , S 5 and S 6 ? (b) What is the total electric flux through all faces of the cube? 20. A cube has sides of length L = 0.300 m. It is placed with one corner at the origin as shown in the above figure. The electric field is not uniform, but is given by ? ˆ . 5.00 / . ) (3.00 N/C ) . E N C m xi m zk ? ? ? Find the electric flux through each of the six cube faces S 1 , S 2 , S 3 , S 4 , S 5 and S 6 and find the total electric charge inside the cube. Page 4 1 ELECTRIC FLUX AND GAUSS LAW 2EL-01 1. The three small spheres as shown in figure, carry charges q 1 = 4.0 nC, q 2 = -8.0 nC and q 3 = 2.0 nC. Find the net electric flux through each of the following closed surfaces shown in cross section in the figure. 2. A charge Q is distributed uniformly on a ring of radius r. A sphere of equal radius r is constructed with its centre at the periphery of the ring. Find the flux of the electric field through the surface of the sphere. 3. Figure shows an imaginary cube of edge L/2. A uniformly charged rod of length L moves towards left at a small but constant speed v. At t = 0, the left end just touches the centre of the face of the cube opposite it. Which of the graphs shown in figure represents the flux of the electric field through the cube as the rod goes through it? L/2 L v (a) Flux a b c d time (b) 4. A hemispherical body is placed in a uniform electric field E. What is the flux linked with the curved surface, if field is (a) parallel to base figure (a), (b) perpendicular to base figure (b). R n (A) E R n (B) E (C ) E n R 5. What is the field in the cavity, if a conductor having a cavity is charged ? Does the result depend on the shape and size of cavity or conductor? 6. Figure shows a closed surface which intersects a conducting sphere. If a positive charge is placed at the points P. Find the sign of flux passing through curved surface ‘s’. 7. In which position (A, B, C or D) of second charge the flux of the electric field through the hemisphere remains uncharged. A B C D q Ring A B 0 1 Sphere 0 2 ELECTRIC FLUX AND GAUSS LAW 2EL-01 8. A charge q is placed at the center of an imaginary hemispherical surface. The flux of the electric field due to the charge through the surface of the hemisphere. q 9. Find the flux of the electric field through each of the five surfaces of the inclined plane as shown in figure. What is the total flux through the entire closed surface? 10. Consider two concentric conducting spheres. The outer sphere is hollow and initially has a charge -7Q on it. The inner sphere is solid and has a charge +2Q on it. (a) How much charge is on the outer surface and inner surface of the outer sphere. (b) If a wire is connected between the inner and outer spheres, after electrostatic equilibrium is established, how much total charge is on the outer sphere? How much charge is on the outer surface and inner surface of outer sphere? Does the electric field at the surface of the inside sphere change when the wire is connected? (c) We return to original condition in (a). We now connect the outer sphere to ground will be on the outer sphere? How much charge will be on the inner surface and outer surface of the outer sphere? 11. A cube of side l has one corner at the origin of coordinates and extends along the positive x, y and z-axes. Suppose the electric field in this region is given by ˆ () E a by j ?? . Determine the charge inside the cube. 12. The electric field in a cubical volume is 00 ˆˆ 1 zz E E i E j aa ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Each edge of the cube measures d and one of the corners lies at the origin of coordinates. Determine the net charge within the cube 13. A point charge is placed at a distance a/2 from the centre of a square of side ‘a’ as shown in the diagram; calculate the electric flux passing through the square. 3 ELECTRIC FLUX AND GAUSS LAW 2EL-01 14. In figure shown a charge q is placed at a distance ? =0 near one of the edges of a cube of edge l on a line of symmetry along diagonal. (a) What is flux through each of the sides containing the point a. (b) What is the flux through the other three faces? 15. Find the electric flux through cylindrical surface in a uniform electric field E 16. What is the flux if the cylinder of previous problem were vertical ? 17. Two identical metal plates each having surface area ‘A’, having charge ‘q 1 ’ and ‘q 2 ’ are placed facing each other at a separation ‘d’. Find the charge appearing on surface (1), (2), (3) and (4). Assume the size of the plate is much longer than the separation between the plates. 18. A point charge q is placed on the apex of a cone of semi-vertex angle ?. Find the electric flux through the base of the cone. 19. The cube as shown in figure has sides of length L = 10.0 cm. The electric field is uniform, has a magnitude E = 4.00 × 10 3 N/C, and is parallel to the xy-plane at an angle of 37° measured from the +x axis toward the +y-axis. What is the electric flux through each of the six cube faces S 1 , S 2 , S 3 , S 4 , S 5 and S 6 ? (b) What is the total electric flux through all faces of the cube? 20. A cube has sides of length L = 0.300 m. It is placed with one corner at the origin as shown in the above figure. The electric field is not uniform, but is given by ? ˆ . 5.00 / . ) (3.00 N/C ) . E N C m xi m zk ? ? ? Find the electric flux through each of the six cube faces S 1 , S 2 , S 3 , S 4 , S 5 and S 6 and find the total electric charge inside the cube. 4 ELECTRIC FLUX AND GAUSS LAW 2EL-01 21. A cube of side a is placed such that the nearest face which is parallel to the y-z plane is at a distance ‘a’ from the origin. The electric field component are E x = ax 1/2 , E y = E z = 0. Calculate y z x (a) the flux f E through the cube (b) the charge within the cube 22. A very long uniformly charged wire oriented along the axis of a circle of radius R rests on its center with one of the ends (as shown in figure). The linear charge density on the wire is l. Evaluate the flux of vector E across the circle area. + ? R 23. Find the electric flux crossing the wire frame ABCD of length l width b and whose center is at a distance OP = d from an infinite line of charge with linear charge density ?. Consider that the plane of frame is perpendicular to the line OP. A B C D O b d ? P 24. Two point charges q and -q separated by the distance 2a. Evaluate the flux of electric field strength vector across a circle of radius R. a a -q +q R 25. A solid spherical region having a spherical cavity whose diameter ‘R’ is equal to the radius of the spherical region, has a total charge ‘Q’. Find the electric field at a point P as shown. P R x 26. An insulating sphere of radius R has a spherical hole of radius a located within its volume and centered a distance b from the center of the sphere, where a < b < R (a cross section of the sphere is shown in figure). The solid part of the sphere has a uniform volume charge density ?. Find the magnitude and direction of the electric field E inside the hole, and show that E is uniform over the entire hole.Read More

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