Ampere's Law Problem

1. Apr 13, 2005

Merrank

The question is:

Between two long parallel cylinders of radius "a" and "b" (non-coaxial) and an axal separation of "c", a steady current of "I" flows. (See attachment below) Show that the inner cylinder (radius "a") has a constant magnetic field. Use Ampere's Law. Indicate all steps clearly. [Hint: 0 = 1 + (-1)]

Could someone please show me step by step on how to do this I have no idea where to start.

Thank You

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• Amperes Law Problem.bmp
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2. Apr 13, 2005

learningphysics

Use superposition. I'll let J=current density (I/area between the two cylinders).

The situation you described above is equivalent to a current density of J going through the entire outer cylinder + a current density of -J going through the inner cylinder (so in the area of the inner cylinder: the total current density is J + -J =0)

Find the magnetic field vector a created by the outer cylinder with a current density of J, at an arbitrary point inside the inner cylinder.

Find the magnetic field vector b created by the inner cylinder with a current density of -J, at the same point.

You should find that the vector sum of the two magnetic fields is independent of the point chosen (both magnitude and direction are independent of the point chosen)

Hint: The triangle created by the centers of the inner and outer cylinders, and the point where the magnetic field is calculated.... is "similar" to the triangle formed by the vectors a, b and the sum.

It's kind of tricky. Hope this helps.