Answer
a. The new field is $\frac{B}{2}$.
b. No. The magnetic field on the axis changes, but not by the same factor.
Work Step by Step
a. Equation 28.17 gives the magnetic field at the center of a current-carrying coil. We see that if the radius of the loop, a, is doubled to 2a, the magnetic field at the center is reduced to half of its initial value.
b. Equation 28.15 gives the magnetic field at a point along the axis of a current-carrying coil. We see that if the radius of the loop, a, is doubled to 2a, the magnetic field on the axis, at a distance x from the center ($x \ne 0$) is reduced, but not by a simple factor of 2.
