Solenoids produce magnetic fields that are relatively intense for the amount of

Question

Solenoids produce magnetic fields that are relatively intense for the amount of current they carry. To make a direct comparison, consider a solenoid with 53 turns per centimeter, a radius of 1.25 cm, and a current of 0.654 A. Find the magnetic field at the center of the solenoid. Express your answer using two significant figures. 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, 1.25 cm. Express your answer using two significant figures.

Explanation / Answer

Here ,

n = 53 turns/cm = 5300 turns/m

radius , r = 1.25 cm = 0.0125 m

I = 0.654 A

part A)

magnetic field at the centre = u0 * n * I

magnetic field at the centre = 4 pi *10^-7 * 0.654 * 5300

magnetic field at the centre = 4.36 *10^-3 T

the magnetic field at the centre is 4.36 mT

part B)

for the wire ,

let the current in wire is I

B = u0 * I/(2 *pi * d)

4.36 *10^-3 = 4pi *10^-7 * I/(2 * pi * 0.0125)

solving for I

I = 272.5 A

the current in wire needed is 272.5 A

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