Question

If the image is hard to see, just zoom in on your screen. Been having trouble with this question and tried so many times. I am not sure if I am just inputting my values incorrectly or what, but please explain in full detail on your work.

An air-filled toroidal solenoid has a mean radius of 15.2 cm and a cross-sectional area of 4.98 cm^2 as shown in (Figure 1). Picture this as the toroidal core around which the windings are wrapped to form the toroidal solenoid. The current flowing through it is 11.8 A, and it is desired that the energy stored within the solenoid be at least 0.387 J. What is the least number of turns that the winding must have? Express your answer numerically, as a whole number, to three significant figures.

Answer 1

Inductance of toroidal solenoid is given by

L = u*N^2*A/(2*pi*r)

E = 0.5*L*i^2

E = u*N^2*A*i^2/(4*pi*r)

N = sqrt [4*pi*r*E/(u*A*i^2)]

N = sqrt [4*pi*0.152*0.387/(4*pi*10^-7*4.98*10^-4*11.8^2)]

N = 2912.59 turns