PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Tensors and differential geometry · Topology and global structure
Invariance, Ch Integrating forms: Stokes's theorem, holes and Maxwell's equations
Problem
A straight wire carries a steady current I=5.0A. A closed loop lies entirely outside the wire and winds twice round it in the sense that gives a positive winding number, before closing up. Treat B outside the wire as the closed one-form (μ0I/2π)dϕ, with μ0=4π×10−7TmA−1.
((a)) State why B has zero curl everywhere on the loop's path yet a nonzero circulation is expected.
((b)) Compute ∮B⋅dl round this loop.