General Physics 2, Lec 5, By/ T.A. Eleyan 1 Additional Questions (Gauss’s Law)

General Physics 2, Lec 5, By/ T.A. Eleyan 2 [1] A solid conducting sphere of radius a has a net charge +2Q. A conducting spherical shell of inner radius b and outer radius c is concentric with the solid sphere and has a net charge –Q as shown in figure. Using Gauss’s law find the electric field in the regions labeled 1, 2, 3, 4 and find the charge distribution on the spherical shell.

General Physics 2, Lec 5, By/ T.A. Eleyan 3 [2] A long straight wire is surrounded by a hollow cylinder whose axis coincides with that wire as shown in figure. The solid wire has a charge per unit length of +λ, and the hollow cylinder has a net charge per unit length of +2λ. Use Gauss law to find (a) the charge per unit length on the inner and outer surfaces of the hollow cylinder and (b) the electric field outside the hollow cylinder, a distance r from the axis.

General Physics 2, Lec 5, By/ T.A. Eleyan 4 [3] Consider a long cylindrical charge distribution of radius R with a uniform charge density ρ. Find the electric field at distance r from the axis where r < R. [4] Two large non-conducting sheets of +ve charge face each other as shown in figure. What is E at points (i) to the left of the sheets (ii) between them and (iii) to the right of the sheets?

General Physics 2, Lec 5, By/ T.A. Eleyan 5 [5] Two large metal plates face each other and carry charges with surface density +σ and -σ respectively, on their inner surfaces as shown in figure What is E at points (i) to the left of the sheets (ii) between them and (iii) to the right of the sheets? [6] A square plate of copper of sides 50cm is placed in an extended electric field of 8*10 4 N/C directed perpendicular to the plate. Find (a) the charge density of each face of the plate

General Physics 2, Lec 5, By/ T.A. Eleyan 6 [7] An electric field of intensity 3.5*10 3 N/C is applied the x axis. Calculate the electric flux through a rectangular plane 0.35m wide and 0.70m long if (a) the plane is parallel to the yz plane, (b) the plane is parallel to the xy plane, and (c) the plane contains the y axis and its normal makes an angle of 40 o with the x axis. [8] A point charge of +5mC is located at the center of a sphere with a radius of 12cm. What is the electric flux through the surface of this sphere? [10] (a) Two charges of 8mC and -5mC are inside a cube of sides 0.45m. What is the total electric flux through the cube? (b) Repeat (a) if the same two charges are inside a spherical shell of radius m.

General Physics 2, Lec 5, By/ T.A. Eleyan 7 [11] A long, straight metal rod has a radius of 5cm and a charge per unit length of 30nC/m. Find the electric field at the following distances from the axis of the rod: (a) 3cm, (b) 10cm, (c) 100cm. [12] The electric field everywhere on the surface of a conducting hollow sphere of radius 0.75m is measured to be equal to 8.90*10 2 N/C and points radially toward the center of the sphere. What is the net charge within the surface?

General Physics 2, Lec 5, By/ T.A. Eleyan 8 [13] A closed surface encloses a net charge of 2.50 x 10-6 C. What is the net electric flux through the surface? In what direction is this net flux? Ans: 2.82 x 105 N m2/C; outward [14] What is the charge per unit area, in coulombs per square meter, of an infinite sheet of charge if the electric field produced by the sheet of charge has a magnitude of 4.50 N/C ? Ans 7.97 x C/m2 [15] The electric field in the region between a pair of oppositely charges plane parallel conducting plates, each 100 cm2 in area, is 7.20 x 103 N/C. What is the charge on each plate? Neglect edge effects. Ans 6.37 x C

General Physics 2, Lec 5, By/ T.A. Eleyan 9 [16] A conducting sphere carrying a charge ‘q’ has a radius ‘a’. It is inside a concentric hollow conducting sphere of inner radius ‘b’ and outer radius ‘c’. The hollow sphere has no net charge. Calculate the electric field for: a) r c; e) What is the charge on the inner surface of the hollow sphere? f) What is the charge on the outer surface? [17] A small sphere whose mass is 0.60 g carries a charge of 3.0 x C and is attached to one end of a silk fiber 8.00 cm long. The other end of the fiber is attached to a large vertical conducting plate, which has a surface charge of 25.0 x 10-6 C/m2 on each side. Find the angle the fiber makes with the vertical plate when the sphere is in equilibrium.

General Physics 2, Lec 5, By/ T.A. Eleyan 10 [18] A conducting sphere is enclosed by a conducting shell as shown in Fig. The electric field at point Q, which is 2m from the center of the sphere, is 2,000 V/m pointing away from the sphere. The electric field at point P, which is 1m from the center of the sphere, is 1,000 V/m pointing away from the sphere. What is the net charge on the conducting shell? A.1 micro Coulomb B.2 micro Coulomb C.4 micro Coulomb D.8 micro Coulomb E.9 micro Coulomb

General Physics 2, Lec 5, By/ T.A. Eleyan 11 [19] A conducting shell encloses a conducting sphere as shown in Fig. 5. If the charge on the sphere is 3C and the charge on the outer surface of the conducting shell is -2C, what is the charge on the inner surface of the conducting shell? A.-3 C B.-1 C C.1 C D.2 C E.5 C

General Physics 2, Lec 5, By/ T.A. Eleyan 12 [20] Consider a long cylindrical charge distribution of radius R with a uniform charge density ρ 0 C/m3, of which a segment is shown below. Find the electric field at a distance r from the axis of the cylinder in the case where r < R. Keep in mind that (a) this is a solid cylinder, not a shell, (b) it is an insulator, not a conductor, and (c) the charge density is given in terms of volume, not the just the length of the cylinder

General Physics 2, Lec 5, By/ T.A. Eleyan 13 [21] A solid, insulating sphere of radius a has a uniform charge density and total charge Q. Concentric with this sphere is a hollow, uncharged, conducting sphere whose inner and outer radii are b and c, as shown below. Compute the electric field in the regions (a) r c. You may write your answers in terms or or Q, whichever you prefer.

General Physics 2, Lec 5, By/ T.A. Eleyan 14 [22] A solid, non-conducting sphere with a net charge of -12µC is located at the origin. Assume this charge is uniformly spread throughout the 10 cm radius volume of the sphere. A hollow conducting spherical shell is located concentric with the non-conducting sphere. The inner radius of the shell is 30 cm and the outer radius is 50 cm (thus it is 20 cm thick). There is 15 µC of charge on the conducting spherical shell. a) Determine the electric field at a distance of 5 cm from the origin. b) Determine the electric eld at a distance of 35 cm from the origin. c) Determine the electric eld at a distance of 70 cm from the origin.

General Physics 2, Lec 5, By/ T.A. Eleyan 15 [23] At the center of a large insulating sphere of 3 m radius is a 0.5 m radius solid spherical conductor. The conductor has a charge of 2 µC and the insulator carries a uniform charge density of -3 µC/m a) Determine the electric field at a distance of 0.25 m from the center of the two spheres. b) Determine the electric field at a distance of 1.5 m from the center of the two spheres. (Hint: The charged insulating material does not extend all the way to the center!)

General Physics 2, Lec 5, By/ T.A. Eleyan 16