Chapter 12, Problem 2ICA

An inductor is an electrical device that can store energy in the form of a magnetic field. In the simplest form, an inductor is a cylindrical coil of wire, and its inductance (L), measured in henrys [H), can be calculated by

$L=\frac{\mu 0n^{2}A}{l}$

Where

µ0 =.permeability of free space=4π × 10^-7 [newtons per ampere squared, N/ A²]

n = number of turns of wire [dimensionless]

A = cross-sectional area of coil [square meters, m²]

l = length of coil [meters, m]

L = inductance [henrys, H] = [J /A²]

Several inductors were fabricated with the same number of turns of wire (n) and the same length (ℓ), but with different diameters, thus different cross-sectional areas (A). The inductances were measured and plotted as a function of cross-sectional area, and a mathematical model was developed to describe the relationship, as shown on the following graph.

1. a. What are the units of the slope (9.66)?
2. b. For an inductor fabricated as described above, what is its diameter if its inductance is 0.4 henrys?

   Give your answer in centimeters.

3. c. If the length of the coil (ℓ) equals 0.2 meter, how many turns of wire (n) are in the inductor?