2. Find the total magnetic flux through a circular toroid with a rectangular cross section.
This toroid, carrying a current of $I_0$, has total number of turns of N, inner radius of 2a,
outer radius of 5b, and height of 3h. Core of the toroid is made up of a material with
the permeability of $\mu$.
3. Find the resultant magnetic flux density at the origin of the coordinate system due to
four wire segments carrying currents $I_1 = I_0$, $I_2 = 2I_0$, $I_3 = 3I_0$ and $I_4 = 4I_0$. The
locations of the segments 1, 2, 3 and 4 are defined by the following relations:
1: $r = 2a$, $\frac{\pi}{2} < \phi < \pi$, $z = 0$ (current is in increasing $\phi$ direction),
2: $r = 4a$, $\frac{\pi}{2} < \phi < \pi$, $z = 0$ (current is in increasing $\phi$ direction),
3: $r = 3a$, $\frac{\pi}{2} < \phi < \frac{3\pi}{2}$, $z = 0$ (current is in decreasing $\phi$ direction)
4: $2a < r < 7a$, $\phi = 0$, $z = 0$ (current is in increasing r direction).
4. Consider two coaxial solenoids with free space cores. Solenoid A is placed inside
Solenoid B and solenoid B carries a current of $2I_0$ which creates a magnetic flux density
of magnitude of $B_0$. If the cross-sectional area, length and number of turns per length of
Solenoid A are S, 4h and n respectively, calculate the mutual inductance between
Solenoid A and Solenoid B.
