2 Coax oil A large magnet requires a direct current of 5000 A. The leads are constructed as follows: A solid aluminum rod with a diameter of 5 cm is surrounded by a return lead in the shape of a hollow aluminum cylinder with an inner diameter of 7 cm and an outer diameter of 9 cm. Current flows into the magnet through the inner cylinder and out through the outer shell. (The space between the rods is filled with flowing oil to remove the heat. The presence of the aluminum and the oil do not affect the magnetic field.) The current density is constant over the cross section of each conductor. Use Ampere's Law to calculate and plot the magnitude of the magnetic field as a function of distance from the center of the wire. Start on the central axis and extend to a point 6 cm from the central axis: i.e., plot B(r) for 0srs 6 cm.
2 Coax oil A large magnet requires a direct current of 5000 A. The leads are constructed as follows: A solid aluminum rod with a diameter of 5 cm is surrounded by a return lead in the shape of a hollow aluminum cylinder with an inner diameter of 7 cm and an outer diameter of 9 cm. Current flows into the magnet through the inner cylinder and out through the outer shell. (The space between the rods is filled with flowing oil to remove the heat. The presence of the aluminum and the oil do not affect the magnetic field.) The current density is constant over the cross section of each conductor. Use Ampere's Law to calculate and plot the magnitude of the magnetic field as a function of distance from the center of the wire. Start on the central axis and extend to a point 6 cm from the central axis: i.e., plot B(r) for 0srs 6 cm.
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Concept and Principle:
As per ampere's law, the magnetic field generated by an electric current will be proportional to the size of that electric current with a constant of proportionality equal to the permeability of free space.
Here μ0 is the permeability of free space and Ienc is the total current in the surface.
Total current enclosed can be written in terms of current density as,
Now the given system is,
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