## 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.