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    Magnetic field due to a current carrying conductor

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    1. A long hollow, cylindrical conductor (inner radius 2.4 mm, outer radius 4.1mm) carries a current of 49 A distributed uniformly across its cross section. A long thin wire that is coaxial with the cylinder carries a current of 36A in the opposite direction. What is the magnitude of the magnetic field (in mT) (a) 1.3mm (b) 2.5mm (c) 4.9 mm from the central axis of the wire and cylinder?

    2. A long straight wire carries a current of 69.6A. An electron, traveling at 8.61 x 10^7 m/s, is 5.14 cm from the wire. What is the magnitude of the magnetic force on the electron if the electron velocity is directed (a) toward the wire, (B) parallel to the wire in the direction of the current, and (c) perpendicular to the two directions defined by (a) and (b)?

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    Solution Preview

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    Cross sectional area of the hollow cylinder A = ПRo^2 - ПRi^2 where Ro and Ri are the outer and internal radii of the hollow cylinder (in m). Substituting values we get:
    A = П [(4.1 x 10^-3)^2 - (2.4 x 10^-3)^2] = 34.7 x 10^-6 m^2
    Total current distributed uniformly over the cross section of the cylinder = I_1 = 49 A
    Current density ρ = I_1/A = 49/34.7 x 10^-6 = 1.41 x 10^6 A/m^2
    Ampere's circuital law: Line integral of the magnetic field vector around a closed path (Amperean loop) is equal to μ_o times the net current threaded by the closed path.
    ∫B.dl = μ_o I .......(1)
    a) Magnetic field at 1.3 mm from central ...

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