An air-filled toroidal solenoid has a mean radius of 15.0 c m and a cross-sectio

Question

An air-filled toroidal solenoid has a mean radius of 15.0cmand a cross-sectional area of 4.96cm2 (see the figure). The current flowing through it is 12.5A , and it is desired that the energy stored within the solenoid be at least 0.388J.  What is the least number of turns that the winding must have?

An air-filled toroidal solenoid has a mean radius of 15.0cmand a cross-sectional area of 4.96 cm2 (see the figure). The current flowing through it is 12.5A , and it is desired that the energy stored within the solenoid be at least 0.388J. What is the least number of turns that the winding must have?

Explanation / Answer

inductance of the solonoid is L = u0N^2A/l

abd energy U =0.5 Li^2

so L = 2U/i^2 = 2* 0.388/12.5^2

L = 0.0049664 H

so now 0.0049664 = u0N^2A

N^2 = 0.0049664 * 2*3.14 * 0.15/(4pi*10^-7 * 4.96*10^-4)

N^2 = 7509677.419

No. of turns N = 2740 turns

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