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- 5. Consider a coaxial cable which is an (infinitely) long wire of radius a, with given current flowing uniformly up it (so J(t) = I(t)/лa² goes uniformly through the wire). At the outside edge (r=a), there is an infinitesimally thin insulator, and just outside that, an infinitesimally thin sheath that returns all the current, basically a surface current going down the opposite direction carrying a total -I(t) back down. Figure out the B field everywhere in space (direction and magnitude) in terms of givens, and then find the self-inductance per length of this cable. Assume I(t) changes slowly in time, so we can use our usual quasi-static ideas. There are several ways to proceed. You might start from =LI, but this turns out to be tricky here, since the current is not confined to a single path! It is best to think about the total magnetic energy, W, stored by the magnetic field, and use our usual relation between energy and current: WL I²/2.What is the standard quantity3 Charged Closed Wire Consider a thin closed wire with the radius R localized at the origin on the xy-plane, which is charged uniformly with the total charge Q. (i) What is the charge density p in this problem? (ii) Calculate the electric field along the z axis? (Hint: First, consider an infinitessimal piece of the charge.)
- Which of the following is an inexact quantity?(a) the number of people in your chemistry classThe standard factor equation that would answer the questionA particle moves along line segments from the origin to the points (2, 0, 0), (2, 5, 1), (0, 5, 1), and back to the origin under the influence of the force field F(x, y, z) = z2i+ 3xyj + 3y2k. Use Stokes' Theorem to find the work done.