4-21. Consider a lattice of M equivalent noninteracting magnetic dipoles, u (associated, say, with electron or nuclear spins). When placed in a magnetic field H, each dipole can orient itself either in the same direction, ↑, or opposed to,t, the field. The energy of a dipole is -µH if oriented with the field, and + µH if oriented against the field. Let N be the number of 4 states and M – N the number of ↑ states. For a given value of N, the total energy is μΗΝ- μΗ(M-) - (2Ν -M)μΗ The total magnetic moment I is I= (M-2N)µ where N'is the average value of N for a given M, H, and T. The work necessary to increase H by dH is – IdH. Find the specific heat C and the total magnetic moment for this system
4-21. Consider a lattice of M equivalent noninteracting magnetic dipoles, u (associated, say, with electron or nuclear spins). When placed in a magnetic field H, each dipole can orient itself either in the same direction, ↑, or opposed to,t, the field. The energy of a dipole is -µH if oriented with the field, and + µH if oriented against the field. Let N be the number of 4 states and M – N the number of ↑ states. For a given value of N, the total energy is μΗΝ- μΗ(M-) - (2Ν -M)μΗ The total magnetic moment I is I= (M-2N)µ where N'is the average value of N for a given M, H, and T. The work necessary to increase H by dH is – IdH. Find the specific heat C and the total magnetic moment for this system
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![4-21. Consider a lattice of M equivalent noninteracting magnetic dipoles, u (associated,
say, with electron or nuclear spins). When placed in a magnetic field H, each dipole can orient
itself either in the same direction, ↑, or opposed to, t, the field. The energy of a dipole is -µH
if oriented with the field, and +µH if oriented against the field. Let N be the number of !
states and M – N the number of ↑ states. For a given value of N, the total energy is
µHN – µH(M – N)=(2N – M)µH
The total magnetic moment I is
I=(M -- 2N)µ
where Nis the average value of N for a given M, H, and T. The work necessary to increase H
by dH is -IdH. Find the specific heat C and the total magnetic moment for this system](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fddaece62-c748-41a0-80d0-fafdb1836a11%2F3885c537-f930-474f-af6e-b74ca6c5ed53%2Fnottuhm_processed.png&w=3840&q=75)
Transcribed Image Text:4-21. Consider a lattice of M equivalent noninteracting magnetic dipoles, u (associated,
say, with electron or nuclear spins). When placed in a magnetic field H, each dipole can orient
itself either in the same direction, ↑, or opposed to, t, the field. The energy of a dipole is -µH
if oriented with the field, and +µH if oriented against the field. Let N be the number of !
states and M – N the number of ↑ states. For a given value of N, the total energy is
µHN – µH(M – N)=(2N – M)µH
The total magnetic moment I is
I=(M -- 2N)µ
where Nis the average value of N for a given M, H, and T. The work necessary to increase H
by dH is -IdH. Find the specific heat C and the total magnetic moment for this system
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