The current density J ! inside a long, solid, cylindrical wire of radius a = 6.4

Question

The current density J! inside a long, solid, cylindrical wire of radius a = 6.4 mm is in the direction of the central axis, and its magnitude varies linearly with radial distance r from the axis according to J = J(naught) r / a , where J(naught) = 620 A/m^2 .

a) Determine the magnitude of the magnetic field at r = 0.

b) Determine the magnitude of the magnetic field at r = a/2.

c) Determine the magnitude of the magnetic field at r = a.

These are my teachers requirements if you could please follow them I would really appreciate it thank you :)

In addition to being neat and clear, and actually answering the question, you must:

1) show the original principle (often in equation form)

2) substitute variables as needed

3) solve it first (before substituting numbers)

4) show every substitution (with units and correct sig figs)

5) present a boxed answer (with units and correct sig figs)

In a Force problem in more than one dimension, you MUST start with a Free Body Diagram.

Explanation / Answer

a)   magnitude of the magnetic field at r = 0 = 0 T

b)   magnitude of the magnetic field at r = a/2    = (4 *3.14*10-7 * 620 * 3.2 * 10-3 * 3.2 * 10-3)/(3 * 6.4 * 10-3)

                                                                           = 4.152 * 10-7 T

c)    the magnitude of the magnetic field at r = a =   (4 *3.14*10-7 * 620 * 6.4 * 10-3)/3

                                                                               = 1.661 * 10-6 T

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