## PHYS208 Fundamentals of Physics II

### Hint for Ch. 30, 55E

Use the result for **B** of a solenoid and the relationship between multiple circular turns
and the total length of wire.

### Hint for Ch. 30, 64E

Use *HRW* Eq. 30-28 with *z* = *R*/2; superimpose result
of two coils.

### Hint for Ch. 30, 72P

*Preparation for Lab Exercise 9. This is a calculationally-intensive problem; I would
recommend the use of Maple or other symbolic processor if you are so-inclined.*

Use *HRW* Eq. 30-28 with an arbitrary distance between coils *s*;
superimpose result of two coils.
Generalize to a distance *x* on-axis away from the point in the center.
This will correspond to setting
*z* = *x* for one coil
and
*z* = *s-x* for the other coil.

Now evaluate the derivative of *B* with respect to *x* and demonstrate that
at the midpoint, *x* = *s*/2, the derivative is zero.

Evaluate the second derivative of *B* with respect to *x*.
Show that at *x* = *s*/2, the second derivative is also zero
if *s* = *R*.

### Hint for Ch. 30, special problem

Go to a point *P* located a distance *x* away from the center;
choose infinitesimally thin bands of the solenoid and treat as circular current loops.
Span the solenoid with bands from *z* = -(*L*+*x*)
to +*L*-*x* and thereby integrate
the contributions to *B* at a distance *z*
away from the center of each infinitesimal current ring.

"http://www.physics.udel.edu/~watson/phys208/exercises/hints/0413.html"

Last updated Apr. 13, 1998.

Copyright George Watson, Univ. of Delaware, 1997.