Question

A long, hollow wire has inner radius R1 and outer radius R2. The wire carries current I uniformly distributed across the area of the wire.

a) Use Ampere's law to find an expression for the magnetic field strength in the region 0 Express your answer in terms of the variables R1, R2, r, I, and appropriate constants.
b) Use Ampere's law to find an expression for the magnetic field strength in the region R1 Express your answer in terms of the variables R1, R2, r, I, and appropriate constants.
c) Use Ampere's law to find an expression for the magnetic field strength in the region R2 Express your answer in terms of the variables R1, R2, r, I, and appropriate constants.
Just info given, no diagrams.
Obviously, the answer to A is 0, since no magnetic field exists in the center of the hollow wire, but I don't have a clue on where to begin for the equations to B and C.

Answer 1

a) The magnetic field strength in the region 0 < r < R1 is 0 T. b) The magnetic field strength in the region R1 < r < R2 is μοI/π(R₂² - R₁²). c) The magnetic field strength in the region r > R2 is μοI/2πr.

Step-by-step explanation:

According to Ampere's law, the magnetic field strength in the region outside the wire (0 < r < R1) can be found by drawing a circular path with radius r and current I encircled by it. Since the current I enclosed by the path is zero, the expression for the magnetic field strength is 0 T.

In the region between the inner and outer radii of the wire (R1 < r < R2), Ampere's law can be applied by drawing a circular path with radius r and current I encircled by it. The enclosed current I is given by the area between the inner and outer radii, so the expression for the magnetic field strength is μοI/π(R₂² - R₁²).

In the region outside the wire (r > R2), Ampere's law can be applied by drawing a circular path with radius r and current I encircled by it. Since the enclosed current I is equal to the total current I flowing through the wire, the expression for the magnetic field strength is μοI/2πr.