Chapter 2.6, Problem 15E

A magnetic field, B, is given as a function of the distance, r, from the center of a wire as follows:

$B=\{\begin{array}{l}\frac{r}{r_0}{B}_0\text{for}r\le r_0\\ \frac{r_0}{r}{B}_0\text{for}r>r_0.\end{array}$

1. (a) Sketch a graph of B against r. What is the meaning of the constant B₀?
2. (b) Is B continuous at r = r₀? Give reasons.
3. (c) Is B differentiable at r = r₀? Give reasons.