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A long cylindrical capacitor. Q=- AL =-o 2ar, L E E-0 E-0 Q=+AL +o 2ar, L, Figure 1: 1. Two long, coaxial cylindrical conductors are separated by vacuum (Fig. 24.6). The inner cylinder has radius ra and linear charge density A. The outer cylinder has inner radius r, and linear charge density -A. (a) The capacitance per unit length for this capacitor. AL 55.6 x 10-12 F/m In "h AL 2neoL C' 2neo C (True, False) %3D %3D Va - V, S Edr Sra 2nor dr ই In ra In "h Ta In h. ra L. (b) The potential difference V = Va - V, is: V = Va - V, = Edr = -dr 3= In ra (True, False) ra 2nEor 2neo (c) If (b) is true then A = 2*p(Va-V) and therefore V, - Va = ["a Edr = A In ra = In "h ra In ra "l -A (d) The potential Va relative to infinity is Va - Voo = Edr = Edr + E dr = dr = In = Va - V, ra 2neor Ta it follows that if the potential at infinity is set to zero then V, = 0 and hence Va = V and therefore if (c) is true V, = V+ In , In La (True,False) (e) If the potential at infinity is set to zero then the potential V, = V + , In "a is the potential relative to infinity In (True,False) 65.0p/mL (f) If part (a) is true ra = rhe Hence if the capacitance of meter length of a cable is 70pf the ratio of inner to outer radius is 0.45 but if the cable is 7pF the ratio is .00036! (True,False) A spherical capacitor. Inner shell, charge +0 Gaussian surface Outer shell, charge -Q E E=0 +Q E=0

A long cylindrical capacitor. Q=- AL =-o 2ar, L E E-0 E-0 Q=+AL +o 2ar, L, Figure 1: 1. Two long, coaxial cylindrical conductors are separated by vacuum (Fig. 24.6). The inner cylinder has radius ra and linear charge density A. The outer cylinder has inner radius r, and linear charge density -A. (a) The capacitance per unit length for this capacitor. AL 55.6 x 10-12 F/m In "h AL 2neoL C' 2neo C (True, False) %3D %3D Va - V, S Edr Sra 2nor dr ই In ra In "h Ta In h. ra L. (b) The potential difference V = Va - V, is: V = Va - V, = Edr = -dr 3= In ra (True, False) ra 2nEor 2neo (c) If (b) is true then A = 2*p(Va-V) and therefore V, - Va = ["a Edr = A In ra = In "h ra In ra "l -A (d) The potential Va relative to infinity is Va - Voo = Edr = Edr + E dr = dr = In = Va - V, ra 2neor Ta it follows that if the potential at infinity is set to zero then V, = 0 and hence Va = V and therefore if (c) is true V, = V+ In , In La (True,False) (e) If the potential at infinity is set to zero then the potential V, = V + , In "a is the potential relative to infinity In (True,False) 65.0p/mL (f) If part (a) is true ra = rhe Hence if the capacitance of meter length of a cable is 70pf the ratio of inner to outer radius is 0.45 but if the cable is 7pF the ratio is .00036! (True,False) A spherical capacitor. Inner shell, charge +0 Gaussian surface Outer shell, charge -Q E E=0 +Q E=0

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A long cylindrical capacitor. Q=- AL = -o 2nr, L E=0 E=0 Q=+ÀL = +o 2ar,L Figure 1: 1. Two long, coaxial cylindrical conductors are separated by vacuum (Fig. 24.6). The inner cylinder has radius ra and linear charge density A. The outer cylinder has inner radius r, and linear charge density -A. (a) The capacitance per unit length for this capacitor. AL 55.6 x 10-12 F/m In "h Q AL C = %3D (True, False) Va - Vb Sra Edr dr Σπερ A In "h In "h ra In ra ra (b) The potential difference V = Va - V is: V = Va - V = Edr = dr 3= In 2TEO (True, False) 2neor ra (c) If (b) is true then A = 2*En(Va-Vh) and therefore Vr - Va = S"a Edr = A- In "a = Va – V, In a In ra In ra (d) The potential Va relative to infinity is Va - Vo = | = Va - V, Edr = Edr + E dr = dr = In 2neor ra - In ra it follows that if the potential at infinity is set to zero then V, = 0 and hence Va = V and therefore if (c) is true V, = V+ In ra (True, False) (e) If the potential at infinity is set to zero then the potential V, = V + , In a is the potential relative to infinity (True,False) In "h 55.6pf/mL (f) If part (a) is true ra = rhe Hence if the capacitance of meter length of a cable is 70pf the ratio of inner to outer radius is 0.45 but if the cable is 7pF the ratio is .00036! (True,False) A spherical capacitor. Inner shell, charge +0 Gaussian surface Outer shell, charge -0 E E=0 +Q E=0
Transcribed Image Text:A long cylindrical capacitor. Q=- AL = -o 2nr, L E=0 E=0 Q=+ÀL = +o 2ar,L Figure 1: 1. Two long, coaxial cylindrical conductors are separated by vacuum (Fig. 24.6). The inner cylinder has radius ra and linear charge density A. The outer cylinder has inner radius r, and linear charge density -A. (a) The capacitance per unit length for this capacitor. AL 55.6 x 10-12 F/m In "h Q AL C = %3D (True, False) Va - Vb Sra Edr dr Σπερ A In "h In "h ra In ra ra (b) The potential difference V = Va - V is: V = Va - V = Edr = dr 3= In 2TEO (True, False) 2neor ra (c) If (b) is true then A = 2*En(Va-Vh) and therefore Vr - Va = S"a Edr = A- In "a = Va – V, In a In ra In ra (d) The potential Va relative to infinity is Va - Vo = | = Va - V, Edr = Edr + E dr = dr = In 2neor ra - In ra it follows that if the potential at infinity is set to zero then V, = 0 and hence Va = V and therefore if (c) is true V, = V+ In ra (True, False) (e) If the potential at infinity is set to zero then the potential V, = V + , In a is the potential relative to infinity (True,False) In "h 55.6pf/mL (f) If part (a) is true ra = rhe Hence if the capacitance of meter length of a cable is 70pf the ratio of inner to outer radius is 0.45 but if the cable is 7pF the ratio is .00036! (True,False) A spherical capacitor. Inner shell, charge +0 Gaussian surface Outer shell, charge -0 E E=0 +Q E=0
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