PHY II, CH 22

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22.01 A nonuniform electric field is directed along the x-axis at all points in space. This magnitude of the field varies with x, but not with respect to y or z. The axis of a cylindrical surface, 0.80 m long and 0.20 m in diameter, is aligned parallel to the x-axis, as shown in the figure. The electric fields E 1 and E 2, at the ends of the cylindrical surface, have magnitudes of 6000 N/C and 1000 N/C respectively, and are directed as shown. What is the net electric flux passing through the cylindrical surface?

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22.03 If a rectangular area is rotated in a uniform electric field from the position where the maximum electric flux goes through it to an orientation where only half the flux goes through it, what has been the angle of rotation?

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22.04 A charge q = 2.00 μC is placed at the origin in a region where there is already a uniform electric field E⃗ = (100 N/C) iˆ . Calculate the flux of the net electric field through a Gaussian sphere of radius R = 10.0 cm centered at the origin. (ε 0 = 8.85 × 10-12 C2/N · m2)

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22.06 A charge of 1.0 × 10-6 μC is located inside a sphere, 1.25 cm from its center. What is the electric flux through the sphere due to this charge? (ε0 = 8.85 × 10-12 C2/N · m2)

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22.07 Four dipoles, each consisting of a +10-µC charge and a -10-µC charge, are located in the xy-plane with their centers 1.0 mm from the origin, as shown. A sphere passes through the dipoles, as shown in the figure. What is the electric flux through the sphere due to these dipoles? (ε0 = 8.85 × 10-12 C2/N · m2)

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22.08 A nonuniform electric field is directed along the x-axis at all points in space. This magnitude of the field varies with x, but not with respect to y or z. The axis of a cylindrical surface, 0.80 m long and 0.20 m in diameter, is aligned parallel to the x-axis, as shown in the figure. The electric fields E 1 and E 2, at the ends of the cylindrical surface, have magnitudes of 7000 N/C and 2000 N/C respectively, and are directed as shown. (ε 0 = 8.85 × 10-12 C2/N · m2) The charge enclosed by the cylindrical surface is closest to

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22.09 Two concentric spheres are shown in the figure. The inner sphere is a solid nonconductor and carries a charge of +5.00 µC uniformly distributed over its outer surface. The outer sphere is a conducting shell that carries a net charge of -8.00 µC. No other charges are present. The radii shown in the figure have the values R 1 = 10.0 cm, R 2 = 20.0 cm, and R 3 = 30.0 cm. (k = 1/4π ε0 = 8.99 × 109 N · m2/C2) (a) Find the total excess charge on the inner surfaces of the conducting sphere (b) Find the total excess charge on the outer surfaces of the conducting sphere. (c) Find the magnitude of the electric field at the distance r = 9.5 cm from the center of the inner sphere. (d) Find the direction of the electric field at the distance r = 9.5 cm from the center of the inner sphere. (e) Find the magnitude of the electric field at the distance r = 15 cm from the center of the inner sphere. (g) Find the magnitude of the electric field at the distance r = 27 cm from the center of the inner sphere. (h) Find the direction of the electric field at the distance r = 27 cm from the center of the inner sphere. (i) Find the magnitude of the electric field at the distance r = 35 cm from the center of the inner sphere. (j) Find the direction of the electric field at the distance r = 35 cm from the center of the inner sphere

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22.11 A solid nonconducting sphere of radius R carries a uniform charge density throughout its volume. At a radial distance r1 = R/4 from the center, the electric field has a magnitude E0. What is the magnitude of the electric field at a radial distance r2 = 2R?

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22.12 A solid nonconducting sphere of radius R carries a charge Q distributed uniformly throughout its volume. At a certain distance r1 (r1 < R) from the center of the sphere, the electric field has magnitude E. If the same charge Q were distributed uniformly throughout a sphere of radius 2R, the magnitude of the electric field at the same distance r1 from the center would be equal to

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22.13 A spherical, non-conducting shell of inner radius r 1 = 20 cm and outer radius r 2= 25 cm carries a total charge Q = 25 μC distributed uniformly throughout the volume of the shell. What is the magnitude of the electric field at a distance r = 22 cm from the center of the shell? (k = 1/4πε 0 = 8.99 × 109 N · m2/C2)

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22.14 A non-conducting sphere of radius R = 5.0 cm carries a charge Q = 3.0 mC distributed uniformly throughout its volume. At what distance, measured from the center of the sphere, does the electric field reach a value equal to half its maximum value?

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22.15 Electric charge is uniformly distributed inside a nonconducting sphere of radius 0.30 m. The electric field at a point P, which is 0.50 m from the center of the sphere, is 15,000 N/C and is directed radially outward. At what distance from the center of the sphere does the electric field have the same magnitude as it has at P?

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22.18 An infinitely long nonconducting cylinder of radius R = 2.00 cm carries a uniform volume charge density of 18.0 μC/ m3. Calculate the electric field at distance r = 1.00 cm from the axis of the cylinder. (ε0 = 8.85 × 10-12 C2/N · m2)

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22.19 The cross section of a long coaxial cable is shown in the figure, with radii as given. The linear charge density on the inner conductor is -40 nC/m and the linear charge density on the outer conductor is -60 nC/m. The inner and outer cylindrical surfaces are respectively denoted by A, B, C, and D, as shown. (ε 0 = 8.85 × 10-12 C2/N · m2) The radial component of the electric field at a point that 32 mm from the axis is closest to

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22.22 A very large sheet of a conductor carries a uniform charge density of 4.00 pC/mm2 on its surfaces. What is the electric field strength 3.00 mm outside the surface of the conductor? (ε0 = 8.85 × 10-12 C2/N · m2)

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22.23 A huge (essentially infinite) horizontal nonconducting sheet 10.0 cm thick has charge uniformly spread over both faces. The upper face carries +95.0 nC/m2 while the lower face carries -25.0 nC/ m2. What is the magnitude of the electric field at a point within the sheet 2.00 cm below the upper face? (ε0 = 8.85 × 10-12 C2/N · m2)

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22.26 Consider two closely spaced and oppositely charged parallel metal plates. The plates are square with sides of length L and carry charges Q and -Q on their facing surfaces. What is the magnitude of the electric field in the region between the plates?

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22.28 A hollow conducting spherical shell has radii of 0.80 m and 1.20 m, as shown in the figure. The sphere carries an excess charge of -500 nC. A point charge of +300 nC is present at the center. The surface charge density on the inner spherical surface is closest to

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22.30 A hollow conducting spherical shell has radii of 0.80 m and 1.20 m, as shown in the figure. The sphere carries a net excess charge of -500 nC. A point charge of +300 nC is present at the center. (k = 1/4π ε0 = 8.99 × 109 N · m2/C) The radial component of the electric field at a point that is 1.50 m from the center is closest to