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A spherical shell with inner radius ra and outer radius rb is formed from a material of resistivity ρ. It carries current radially, with uniform density in all directions. Show that its resistance is
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Chapter 27 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
- A cylindrical conducting wire which is 342.57cm long, 85.39mm thick and resistivity of 3.13Ω.m, (a) has the resistance of R = ? If current I = 12.9A is generated by flowing of 217 electrons/m3 via a conductor, Then the electrons through this conductor (b) have a density J = ?and (c) are drifting at a speed of VD = ?arrow_forwardA high voltage transmission line of diameter 2.55 cm and length 3.42167 km carries a steady current of 2 x103 A. If the conductor is copper with a free charge density of 7 x 1028 electrons/m3, how long (in seconds ) does it take one electron to travel the full length of the cable? (e = 1.6 x 10−19 C).For this problem use scientific/exponential notation to represent your answer.arrow_forwardSuppose you have a rod of pure silicon with a diameter of 2.79cm and a length of 20.6cm. These rods are often used in experiments, such as the Large Hadron Collider in France/Switzerland to detect high-energy particles, and they have a very high resistivity of 2300Ω⋅m. What current, in amperes, flows through the rod when a potential difference of 1.23* 10^3 V is applied between its ends ?arrow_forward
- At room temperature, what is the strength of the electric field in a 12 gauge copper wire (diameter 2.05 mm) that is needed to cause a 3.90 A current to flow? Use the resistivity at room temperature for copper ρ = 1.72×10−8 Ω⋅m. Express your answer with the appropriate units. What field would be needed if the wire were made of silver instead? Use the resistivity at room temperature for silver ρ = 1.47×10−8 Ω⋅m. Express your answer with the appropriate units.arrow_forwardA high voltage transmission line of diameter 3.73 cm and length 3.76189 km carries a steady current of 1.9 x10³ A. If the conductor is copper with a free charge density of 6 x 1028 electrons/m³, how long (in seconds ) does it take one electron to travel the full length of the cable? (e = 1.6 x 10-19 C).For this problem use scientific/exponential notation to represent your %3D answer. Eg., -0.0001 can be written as 1.0e-4 or as 1.0E-4. Spaces are not allowed.arrow_forwardDetermine the drift speed if given a cylindrical conductor of radius 1.50 mm with current density 2.50 A/m2 and free-electron density of 8.00×1028 m−3.arrow_forward
- Consider a resistor of resistivity 3.96 × 10-8 Ω • m. If an electric field of 12 V/m is applied across the resistor and the electron volume concetration in the conductor is 5.16 × 1028 per m3, determine the drift velocity, in mm/s, of the free electron constituting the current.arrow_forwardThe quantity of charge through a conductor is modeled as: q(t)=at4+bt+c --> I(t) = 4 a t^3 + b If a = 5.02C/s4, and b = -4.36C/s, and c = 1.75μC, then what is the current, in amperes, at t=1.45s?arrow_forwardA straight, cylindrical wire lying along the x axis has a length of 0.616 m and a diameter of 0.6 mm. It is made of a material described by Ohm's law with a resistivity of ρ = 4.72 ✕ 10−8Ω· m. Assume a potential of 4.85 V is maintained at the left end of the wire at x = 0. Also assume V = 0 at x = 0.616 m. Find the current density (in A/m2) in the wire.arrow_forward
- An infinite non-uniform cylindrical conductor is made up of different materials that causes the conductor to have different current densities depending on the radius. The overall radius of the conductor is 17.26 meters. For the region where the radius ρ less than 2.63 meters, the current density is 13.43 amperes per square meter. For the region where the radius ρ from 2.63 meters to 6.39 meters, the current density is -27.63 amperes per square meter. Finally, for the region in the conductor where radius ρ is greater than 6.39 meters, the current density is 39.19 amperes per square meter. Find the magnetic field intensity, in ampere-turns per meter, at a distance 13.86 meters from the axis of the conductor.arrow_forwardA straight, cylindrical wire lying along the x axis has a length of 0.376 m and a diameter of 0.68 mm. It is made of a material described by Ohm's law with a resistivity of ρ = 4.86 ✕ 10−8Ω· m. Assume a potential of 4.143 V is maintained at the left end of the wire at x = 0. Also assume V = 0 at x = 0.376 m. Find the current density (in A/m2) in the wire. Use scientific/exponential notation to represent your answer to this problem. Eg., -0.0001 can be written as 1.0e-4 or as 1.0E-4. Spaces are not allowed.arrow_forwardCalculate the drift velocity (in ×10-6 m/s) of electrons in a silver cylindrical conductor with a diameter of 2.0 cm carrying 5.0 A current, given there is one free electron per silver atom. ρsilver = 10490 kg/m3 atomic mass of silver = 107.9 g/mol Avogadro's number = 6.02×1023 atoms/molarrow_forward
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