You have a spool of copper wire 4.90 mm in diameter and a power supply. You deci

Question

You have a spool of copper wire 4.90 mm in diameter and a power supply. You decide to wrap the wire tightly around a soda can that is 12.0 cm long and has a diameter of 6.50 cm, forming a coil, and then slide the wire coil off the can to form a solenoid. The power supply can produce a maximum current of 240 A in the coil.

This solenoid is wrapped into a donut to form a toroid. The solenoid (12.0 cm long) is wrapped as tightly as possible, so that the inner circumference of the toroid is the same as the length of the solenoid. What is the range of magnetic fields inside the toroid when the maximum current of 240 A is sent through the wire? (Enter the magnitudes.)

(smallest value)

(largest value)

(smallest value)

(largest value)

Explanation / Answer

N = 12 / (4.90 x 10^-3) = 2449 turns

B = u0 (N/L) I = (4pi x 10^-7) (2449/0.12) (240) = 6.15 T .... For solenoid.

FOr Toroid:

field , B = u0 N I / (2 pi r)

2 pi Rin = 12 cm = 0.12 m

Rin = 1.91 cm

Rout = (1.91 + 6.50) = 8.41 cm = 0.0841 m

2 pi Rout = 0.53 m

B_smallest = u0 N I / (2 pi Rout) = (4pi x 10^-7) (2449) (240) / (0.53)

= 1.39 T ...........Ans

B_largest = u0 N I / (2 pi Rin) = (4pi x 10^-7)(2449)(240) / (0.12)

= 6.16 T ......Ans

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