Physics

Problem

Two identical coaxial circular coils, each of radius

R

and having

N

turns, are separated by a distance equal to the radius

R

. The same current

I

flows through both coils in the same sense. a. (i) Derive an expression for the magnetic field

B_{\text{mid}}

at the midpoint of the common axis between the two coils. b. (ii) Show that the first derivative of the axial magnetic field with respect to

x

vanishes at this midpoint, indicating a region of nearly uniform magnetic field. c. (iii) Evaluate

B_{\text{mid}}

numerically for

R = 0.30\,\text{m}

N = 120

and

I = 2.5\,\text{A}

. Express your answer in millitesla

(\text{mT})