A paramagnetic salt contains 2.0×10²⁴ atomic dipoles, each of moment 1.5×10⁻²³ J/T. At B=0.84 T and T=4.2 K, magnetic saturation is 15%. Using Curie's law, estimate the total dipole moment at B=0.98 T and T=2.8 K.
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Question

A paramagnetic salt contains 2.0×10²⁴ atomic dipoles, each of moment 1.5×10⁻²³ J/T. At B=0.84 T and T=4.2 K, magnetic saturation is 15%. Using Curie's law, estimate the total dipole moment at B=0.98 T and T=2.8 K.

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G1 Physics · Accepted Answer

Curie's law gives magnetic moment proportional to B/T in the unsaturated regime. Initial total saturation moment is Nμ=30 J/T, so actual moment=0.15×30=4.5 J/T. Scaling gives 4.5×(0.98/2.8)/(0.84/4.2)=7.9 J/T. Hence A.