An air-filled toroidal solenoid has a mean radius of 14.5cm and a cross-sectiona

Question

An air-filled toroidal solenoid has a mean radius of 14.5cm and a cross-sectional area of 5.04cm2 (see the figure). The current flowing through it is 12.0A , and it is desired that the energy stored within the solenoid be at least 0.395J .

An air-filled toroidal solenoid has a mean radius of 14.5cm and a cross-sectional area of 5.04cm2 (see the figure). The current flowing through it is 12.0A , and it is desired that the energy stored within the solenoid be at least 0.395J . What is the least number of turns that the winding must have?

Explanation / Answer

Magnetic field of a toroid with N turns of wire, mean radius R, and current I is given by:

B(toroid) = ?NI/2?R

Magnetic energy stored by such a toroid is given by:

E =

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