A paramagnetic sample has a relative permeability of 1.0006 at an absolute temperature of 300 K . What will be its relative permeability at 200 K ?

Step-by-step solution

The relative permeability ( _r ) of a magnetic material is related to its magnetic susceptibility ( ) by the relation: _r = 1 + At T₁ = 300 K , the initial susceptibility is: ₁ = _ r1 - 1 = 1.0006 - 1 = 0.0006 According to Curie's law for paramagnetic materials, susceptibility is inversely proportional to absolute temperature ( 1 T ). Therefore, the ratio of susceptibilities is: ₂ ₁ = T₁ T₂ ₂ = ₁ T₁ T₂ = 0.0006 300 200 ₂ = 0.0006 1.5 = 0.0009 The new relative permeability at T₂ = 200 K is: _ r2 = 1 + ₂ = 1 + 0.0009