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# The magnetic field created by a dipole has a strength of

ISBN: 9780201380279 40

## Solution for problem 34P Chapter 4

An Introduction to Thermal Physics | 1st Edition

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Problem 34P

PROBLEM 35P

The magnetic field created by a dipole has a strength of approximately (μ0/4π)(μ/r3), where r is the distance from the dipole and μ0 is the “permeability of free space,” equal to exactly 4π × 10–7 in SI units. (In the formula I’m neglecting the variation of field strength with angle, which is at most a factor of 2.) Consider a paramagnetic salt like iron ammonium alum, in which the magnetic moment μ of each dipole is approximately one Bohr magneton (9 × 10–24 J/T), with the dipoles separated by a distance of 1 nm. Assume that the dipoles interact only via ordinary magnetic forces.

a) Estimate the strength of the magnetic field at the location of a dipole, due to its neighbouring dipoles. This is the effective field strength even when there is no externally applied field.

b)  If a magnetic cooling experiment using this material begins with an external field strength of 1 T, by about what factor will the temperature decrease when the external field is turned off?

c) Estimate the temperature at which the entropy of this material rises most steeply as a function of temperature, in the absence of an externally applied field.

d)  If the final temperature in a cooling experiment is significantly less than the temperature you found in part (c), the material ends up in a state where ∂S/∂T is very small and therefore its heat capacity is very small. Explain why it would be impractical to try to reach such a low temperature with this material.

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##### ISBN: 9780201380279

Since the solution to 34P from 4 chapter was answered, more than 283 students have viewed the full step-by-step answer. An Introduction to Thermal Physics was written by and is associated to the ISBN: 9780201380279. The full step-by-step solution to problem: 34P from chapter: 4 was answered by , our top Physics solution expert on 07/05/17, 04:29AM. The answer to “The magnetic field created by a dipole has a strength of approximately (?0/4?)(?/r3), where r is the distance from the dipole and ?0 is the “permeability of free space,” equal to exactly 4? × 10–7 in SI units. (In the formula I’m neglecting the variation of field strength with angle, which is at most a factor of 2.) Consider a paramagnetic salt like iron ammonium alum, in which the magnetic moment ? of each dipole is approximately one Bohr magneton (9 × 10–24 J/T), with the dipoles separated by a distance of 1 nm. Assume that the dipoles interact only via ordinary magnetic forces.a) Estimate the strength of the magnetic field at the location of a dipole, due to its neighbouring dipoles. This is the effective field strength even when there is no externally applied field.________________b) If a magnetic cooling experiment using this material begins with an external field strength of 1 T, by about what factor will the temperature decrease when the external field is turned off?________________c) Estimate the temperature at which the entropy of this material rises most steeply as a function of temperature, in the absence of an externally applied field.________________d) If the final temperature in a cooling experiment is significantly less than the temperature you found in part (c), the material ends up in a state where ?S/?T is very small and therefore its heat capacity is very small. Explain why it would be impractical to try to reach such a low temperature with this material.” is broken down into a number of easy to follow steps, and 250 words. This full solution covers the following key subjects: Field, temperature, magnetic, Strength, dipole. This expansive textbook survival guide covers 10 chapters, and 454 solutions. This textbook survival guide was created for the textbook: An Introduction to Thermal Physics , edition: 1.

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