Question

We're going to prove the following unusual fact regarding a magnetic field due to a wire current. The magnetic field B from a loop of wire is equal to HoJ 4? where ?(f) is a scalar function of space, which equals the solid angle subtended by the loop when viewed from the position r. The sign convention for ? is that it is positive if the unit normal points away from 7, where the direction of the unit normal is determined by the direction of the current flow via the right-hand rule. a) Show that this is true for a dipole. Pick any shape of tiny current loop for this purpose. b) Make a superposition argument to generalize to an arbitrary current loop. c) But wait! How can B be the gradient of a scalar? What about Ampere's law? is the graient of a sealar then its circulation should alway's be zerof How do we resolve this? en its cirulation shou

Answer 1

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