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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.

          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.

2. Find the total magnetic flux through a circular toroid with a rectangular cross section.
This toroid, carrying a current of I0, 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 μ.
3. Find the resultant magnetic flux density at the origin of the coordinate system due to
four wire segments carrying currents I1 = I0, I2 = 2I0, I3 = 3I0 and I4 = 4I0. The
locations of the segments 1, 2, 3 and 4 are defined by the following relations:
1: r = 2a, (π)/(2) < ϕ < π, z = 0 (current is in increasing ϕ direction),
2: r = 4a, (π)/(2) < ϕ < π, z = 0 (current is in increasing ϕ direction),
3: r = 3a, (π)/(2) < ϕ < (3π)/(2), z = 0 (current is in decreasing ϕ direction)
4: 2a < r < 7a, ϕ = 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 2I0 which creates a magnetic flux density
of magnitude of B0. 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.

Added by Veronica B.

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