Question

A rectangular toroid and a cylindrical solenoid have equal cross-sectional areas, equal inductances, the same number of total turns, and the length of the solenoid is the same as the average circumference of the toroid. What is the ratio of the outer radius to the inner radius of the toroid? Hint: the inductance of a rectangular toroid with outer and inner radii 𝑅1R1 and 𝑅2R2, respectively, with 𝑁N number of turns and a height ℎh is 𝐿=𝜇0𝑁2ℎ2𝜋ln(𝑅2𝑅1)L=μ0N2h2πln(R2R1). Select answer from the options below 𝑅2𝑅1=3R2R1=3 𝑅2𝑅1=𝑒R2R1=e The described situation is impossble to achieve with an actual solenoid and toroid. 𝑅2𝑅1=2

          A rectangular toroid and a cylindrical solenoid have equal cross-sectional areas, equal inductances, the same number of total turns, and the length of the solenoid is the same as the average circumference of the toroid. What is the ratio of the outer radius to the inner radius of the toroid? Hint: the inductance of a rectangular toroid with outer and inner radii 𝑅1R1 and 𝑅2R2, respectively, with 𝑁N number of turns and a height ℎh is 𝐿=𝜇0𝑁2ℎ2𝜋ln(𝑅2𝑅1)L=μ0N2h2πln(R2R1). 
Select answer from the options below
𝑅2𝑅1=3R2R1=3
𝑅2𝑅1=𝑒R2R1=e
The described situation is impossble to achieve with an actual solenoid and toroid.
𝑅2𝑅1=2

Added by Stephanie H.

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