Chapter 30, Problem 73E

(a)

To determine

To show: The magnetic flux through a cross section of the toroid is ${\Phi }_B=\frac{{\mu }_{0}Nih}{2\pi }\ln \left(\frac{b}{a}\right)$.

(b)

To determine

To show: The inductance of the toroidal solenoid is given by $L=\frac{{\mu }_0{N}^{2}h}{2\pi }\ln \left(\frac{b}{a}\right)$.

(c)

To determine

To show: The inductance of the toroidal solenoid is given by $L=\frac{{\mu }_0{N}^{2}h\left(b-a\right)}{2\pi a}$ when $\left(b-a\right)<<a$.