Fundamentals of Materials Science and Engineering, Binder Ready Version: An Integrated Approach
Fundamentals of Materials Science and Engineering, Binder Ready Version: An Integrated Approach
5th Edition
ISBN: 9781119175483
Author: William D. Callister Jr., David G. Rethwisch
Publisher: WILEY
Question
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Chapter 18.12, Problem 1QP

(a)

To determine

The magnitude of the magnetic field strength.

(a)

Expert Solution
Check Mark

Answer to Problem 1QP

The magnitude of the magnetic field strength is 24,000A-turns/m_ .

Explanation of Solution

Given:

The length of coil, l=0.25m

The number of turns in the coil, N=400turns .

The current passed through wire, I=15A

Explanation:

Write the equation of magnetic field strength.

H=NIl (I)

Conclusion:

Substitute 400turns for N, 15 A for I, and 0.25 m for l in Equation (I).

H=(400turns)15A0.25mH=24,000A-turns/m

Thus, the magnitude of the magnetic field strength is 24,000A-turns/m_ .

(b)

To determine

The flux density B.

(b)

Expert Solution
Check Mark

Answer to Problem 1QP

The flux density B is 3.0168×102tesla_ .

Explanation of Solution

Write the equation of flux density in vacuum.

B=μ0H (II)

Here, the permeability of a vacuum is μ0 .

Conclusion:

Substitute 1.257×106H/m for μ0 and 24,000A-turns/m for H in Equation (II). B=(1.257×106H/m)24,000A-turns/m=3.0168×102tesla

Thus, the flux density B is 3.0168×102tesla_ .

(c)

To determine

The flux density inside the bar of chromium.

(c)

Expert Solution
Check Mark

Answer to Problem 1QP

The flux density inside the bar of chromium is 3.0177×102tesla_ .

Explanation of Solution

Write the equation of flux density in vacuum.

B=μ0H+μ0M=μ0H+μχmH=μ0H(1+χm) (III)

Here, the magnetic susceptibility is χm .

Conclusion:

Refer to Table 20.2, the value of χm is 3.13×104 .

Substitute 1.257×106H/m for μ0 , 24,000A-turns/m for H, and 3.13×104 for χm in Equation (III).

B=(1.257×106H/m)(24,000A-turns/m)(1+3.13×104)=3.0177×102tesla

Thus, the flux density inside the bar of chromium is 3.0177×102tesla_ .

(d)

To determine

The magnitude of magnetization.

(d)

Expert Solution
Check Mark

Answer to Problem 1QP

The magnitude of magnetization is 7.51A/m_ .

Explanation of Solution

Write the magnitude of magnetization.

M=χmH (IV)

Conclusion:

Substitute 24,000A-turns/m for H and 3.13×104 for χm in Equation (IV).

M=(3.13×104)24,000A-turns/m=7.51A/m

Thus, the magnitude of magnetization is 7.51A/m_ .

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