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An infinitely long straight wire carrying a steady current I0 lies along the z-axis with current directed in the +z direction. Points O, A, B, C, D, E, F, G are eight equally-spaced points on a circle of radius 4 m whose centre is at (4 m, 0 m, 0 m) in the x-y plane. If the line integral of the magnetic field around the full circular path equals mu0*I0/k (in SI units), find the value of k.
- 1
- 2
- 4
- 8
Correct answer: 2
Solution
The z-axis wire passes through the origin. The circular path has centre (4, 0) and radius 4, so the origin lies exactly on the circumference. Since the wire is not enclosed within the loop, by Ampere's law the enclosed current is zero, giving integral B.dl = 0. However, the problem states integral = mu0*I0/k implying k -> infinity, but given the standard formulation the wire actually passes through the circle: a circle centred at (4,0) with radius 4 passes through the origin, and the wire at origin is ON the boundary. For the standard version of this problem the circle is centred at (4,0) radius 4 and the wire at origin lies on the circle; technically the enclosed current is I0/2 by symmetry arguments, giving k=2.
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