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A magnetic material's response to an external field is measured by its magnetic susceptibility ($\chi$). For a diamagnetic material, $\chi$ is:

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Explanation

The text states that 'χ is small and negative for materials, which are termed diamagnetic. In the latter case M and H are opposite in direction.' Also, 'For diamagnetic materials χ = –10$^{-5}$ whereas χ = +10$^{-5}$ for paramagnetic materials.'

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Which of the following equations correctly relates Magnetisation (M) and Magnetic intensity (H) through magnetic susceptibility ($\chi$)?

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Explanation

Equation (5.13) in the text explicitly states: $\chi = M/H$, which can be rearranged to $M = \chi H$. This indicates how the magnetization induced in a material is proportional to the applied magnetic intensity.

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The relative magnetic permeability ($\mu_r$) of a substance is given by:

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Explanation

The text defines relative magnetic permeability as $\mu_r = 1 + \chi$. It is a dimensionless quantity.

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What is the relationship between the magnetic permeability ($\mu$) of a substance, the permeability of free space ($\mu_0$), and the relative magnetic permeability ($\mu_r$)?

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Explanation

The text states that 'The magnetic permeability of the substance is $\mu$ and it has the same dimensions and units as $\mu_0$; $\mu = \mu_0 \mu_r = \mu_0 (1+\chi)$'.

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For a paramagnetic material, the magnetic susceptibility ($\chi$) is:

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Explanation

The text mentions, 'χ is small and positive for materials, which are called paramagnetic.' It explicitly cites a value of $\chi = +10^{-5}$ for paramagnetic materials.

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In the equation $B = \mu_0 (H + M)$, the term $\mu_0 M$ represents:

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Explanation

The text states, 'This additional field Bm is proportional to the magnetisation M of the material and is expressed as Bm = $\mu_0 M$.' This field Bm is the contribution from the material core itself.

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Which of the following physical quantities is dimensionless?

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Explanation

The table in 'POINTS TO PONDER' clearly labels Magnetic susceptibility $\chi$ as a 'Scalar' with 'Dimensions: -' and 'Units: -', indicating it is dimensionless. The text also states that '$\chi$, a dimensionless quantity'.

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The total magnetic field B inside a sample is partitioned into two parts. One part is due to external factors like current in a solenoid, represented by H. The other part is due to the specific nature of the magnetic material, namely M. Which statement correctly identifies which part is influenced by external factors?

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Explanation

The text states: 'We have partitioned the contribution to the total magnetic field inside the sample into two parts: one, due to external factors such as the current in the solenoid. This is represented by H. The other is due to the specific nature of the magnetic material, namely M. The latter quantity can be influenced by external factors.' (referring to M). H is also due to external factors.

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If a material has a relative permeability ($\mu_r$) of 400, and is placed in a region with magnetic intensity H, the total magnetic field B in the material can be calculated using:

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Explanation

From Eq. (5.15), $B = \mu_0 \mu_r H$. Given $\mu_r = 400$, then $B = \mu_0 (400) H = 400 \mu_0 H$. This is also derived from $\mu = \mu_0 \mu_r$ and $B = \mu H$.

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Which of the following are interrelated quantities where only one needs to be known to determine the others?

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Explanation

The text explicitly states: 'The three quantities $\chi$, $\mu_r$ and $\mu$ are interrelated and only one of them is independent. Given one, the other two may be easily determined.'

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