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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 h is L = μ0N2h/2π ln (R2/R1). R2/R1 = e The described situation is impossible to achieve with an actual solenoid and toroid. R2/R1 = 3 R2/R1 = 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 R1 and R2, respectively, with N number of turns and a height h is L = μ0N2h/2π ln (R2/R1). R2/R1 = e The described situation is impossible to achieve with an actual solenoid and toroid. R2/R1 = 3 R2/R1 = 2

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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 h is L = μ0N2h/2π ln (R2/R1). R2/R1 = e The described situation is impossible to achieve with an actual solenoid and toroid. R2/R1 = 3 R2/R1 = 2

Explanation & Steps

Self-inductance of cylindrical solenoid and rectangular toroid made equal. Use two conditions i.e. (1) Length of the cyndrical solenoid is same average circumeference of rectangular toroid (2) Both have the same cross-sectional area. 

Finally check the validity of the ratio of R1 and R2 whether the calculated ratio is applicable in the given scenario.

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