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 R₁ and R₂, respectively, with N number of turns and a height his HoNh L (R₁). 2n R₂ R₁ -In R₁ R₂ R₁ 2 O The described situation is impossble to achieve with an actual solenoid and toroid. R₂ 3

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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 R₁ and R₂, respectively, with N number of turns and a height his
¹ (R₁).
L =
Mo N²h.
2π
R₂
R₁
- In
= 2
O The described situation is impossble to achieve with an actual solenoid and toroid.
R₂
R₁
R₂
R₁
= e
= 3
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Transcribed Image Text: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 R₁ and R₂, respectively, with N number of turns and a height his ¹ (R₁). L = Mo N²h. 2π R₂ R₁ - In = 2 O The described situation is impossble to achieve with an actual solenoid and toroid. R₂ R₁ R₂ R₁ = e = 3 Save for Later Submit Answer
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