Problem 22.97 Solenoids produce magnetic fields that are relatively intense for

Question

Problem 22.97

Solenoids produce magnetic fields that are relatively intense for the amount of current they carry. To make a direct comparison, consider a solenoid with 50 turns per centimeter, a radius of 1.20 cm , and a current of 0.664 A .

Part A

Find the magnetic field at the center of the solenoid.

Express your answer using two significant figures.

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Part B

What current must a long, straight wire carry to have the same magnetic field as that found in part A? Let the distance from the wire be the same as the radius of the solenoid, 1.20 cm .

Express your answer using two significant figures.

Explanation / Answer

Part A.

B = u0*n*I where  u0 = 4*pi*10-7   n = turns per metre = 50 per cm = 5000 per metre and I = 0.664 A

B = 41699.2 * 10-7 T = 4.16992 * 10-3 T = 4.17 mT

Part B.

B = (u0/2pi) * (I/a) where a = distance from wire = 1.2 cm = 1.2*10-2 m and given B = 4.17 mT = 4.17 * 10-3 T and u0 = 4*pi*10-7

This gives required current, I = 2.502*10+2 A = 250.2 A.

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