   Chapter 19, Problem 60P

Chapter
Section
Textbook Problem

A certain superconducting magnet in the form of a solenoid of length 0.50 m can generate a magnetic field of 9.0 T in its core when its coils carry a current of 75 A. The windings, made of a niobium-titanium alloy, must be cooled to 4.2 K. Find the number of turns in the solenoid.

To determine
The number of turns in the solenoid.

Explanation

Given info: The coils in the solenoid carry a current of 75A . The length of the solenoid is 0.50m . The magnetic field at the center of the solenoid is 9.0T . The windings made of niobium-titanium alloy must be cooled to 4.2K .

Explanation:

The magnetic field inside a solenoid is given by,

B=μ0nI       (1)

• μ0 is the permeability of free space
• I is the current
• n is the number of turns per unit length

The number of turns per unit length can be written as,

n=Nl       (2)

• N is the total number of turns
• l is the length of the solenoid

From (1) and (2),

B=μ0(Nl)I

On re-arrangement,

N=Blμ0I

Substitute 4π

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