I The component of the total spin in the direction of H

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The total spin component in the direction of an external magnetic field H is defined as M_s = 1/2(N_up - N_down). This formula arises because N_up particles contribute +1/2 to the magnetization, while N_down particles contribute -1/2. The difference between the number of up and down spins directly influences the overall magnetization. Understanding this relationship is crucial for analyzing magnetic properties in various materials. The discussion emphasizes the significance of spin orientation in determining magnetization.
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Why The component of the total spin in the direction of H is ##M_s = \frac{1}{2}(N_{up}-N_{down})##
 

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Another said:
Why The component of the total spin in the direction of H is ##M_s = \frac{1}{2}(N_{up}-N_{down})##
Because ##N_{\uparrow}## particles contribute ##+1/2## and ##N_{\downarrow}## particles contribute ##-1/2## to the total magnetisation.
 
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