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Derive the relation between magnetic field intensity(H) and magnetization(M) for a magnetic material placed in a magnetic field.

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प्रश्न

Derive the relation between magnetic field intensity(H) and magnetization(M) for a magnetic material placed in a magnetic field. 

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उत्तर

  1. Relation between magnetic field intensity(H) and magnetization(M):
    a. Consider a magnetic material (rod) placed in a magnetizing field (solenoid with n turns per unit length and carrying current I).
    b. The magnetic field inside the solenoid is given by,
    B0 = μ0nI  ….(1)
    Where µ0 = permeability of free space.
    c. The magnetic field inside the rod is given as,
    Bm = µ0M ….(2) 
    Where M = magnetization of the material
    d. The net magnetic field inside the rod is expressed as,
    B = B0 + Bm ….(3)
    ∴ B = µ0nI + µ0M
    ∴ B = µ0H + µ0M
    Where H = nI = Magnetic field intensity
    ∴ B = µ0 (H + M) 
    ∴ H = `"B"/mu_0 - "M"`  ….(4)
    e. Equation (4) shows that the magnetic field (B) induced in the material depends on magnetic field intensity (H) and magnetization (M). 
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अध्याय 11: Magnetic materials - Long Answer

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