## PHYS208 Fundamentals of Physics II

### Hint for Ch. 31, 50P

The flux linkage per unit length will be the magnetic flux through the area bounded by
the two dotted lines and the wires. Since the wires are symmetric about this area,
you may calculate the flux linked from just one wire and then double. The formula
found for the magnetic field about a long wire should be used here.

The area of linkage can be spanned with the infinitesimal element shown, varying *r*
from *a* to *d-a*. In using these limits of integration, we are staying outside
the wires; the magnetic flux linked inside the wire may also be included, but be sure to use
the correct expression for the magnetic field *inside* the sire.

### Hint for Ch. 31, 77E

a) Use the expression for current in an energizing inductor as a function of time
along with

b) Use the same current in *i*^{2}R.

c) Use the same current in *i* *emf*.

### Hint for Ch. 31, 80P

a) Integrate the power provided by the battery over the time specified,
using the time-dependent current for an energizing inductor.

b) Use *U* = *Li*^{2}/2.

c) Find the difference between the answers for a) and b).

### Hint for Ch. 31, 85E

Equate the two energy densities and solve for E.
Notice the role of the permittivity and permeability in the final expression.

### Hint for Ch. 31, 90P

a) Use the value for the magnetic field in a toroid in the expression for
magnetic energy density.

b) The energy density should be integrated using circular strips of radius *r*,
height *h*, and thickness *dr*, which has an infinitesimal volume of
*2 pi r h dr*.

"http://www.physics.udel.edu/~watson/phys208/exercises/hints/0422.html"

Last updated April 22, 1998.

Copyright George Watson, Univ. of Delaware, 1998.