Question

The range of magnetic susceptibility and relative magnetic permeability for diamagnetic substances are:
(A) \[ - 1 \geqslant X > 0,0 \leqslant {\mu _r} < 1\]
(B) \[ - 1 \leqslant X > 0,0 \geqslant {\mu _r} < 1\]
(C) \[ - 1 \geqslant X > 0,0 \leqslant {\mu _r} < 1\]
(D) \[ - 1 \leqslant X < 0,0 \leqslant {\mu _r} < 1\]

Answer 1

Hint: We know that diamagnetic materials are such which get weakly repelled by a magnetic field. The electron pairs in the material are placed opposite to each other, so the magnetic moment from each electron cancels out.

Complete step-by-step solution

Diamagnetic materials have electrons present in them in such a way that each cancels the other’s magnetic moment.
As these materials are weakly repelled by a magnetic field
Therefore, susceptibility \[ = X = \dfrac{M}{H}\]
 lies in the region \[ - 1 \leqslant X < 0\] (Where M is magnetization and H is magnetic field strength)
Using the relation between X and \[{\mu _r}\]
 \[ \Rightarrow X = {\mu _r} - 1\]
 \[ \Rightarrow {\mu _r} = X + 1\]
 \[ - 1 \leqslant X < 0\] adding 1 to all three
 \[ \Rightarrow 0 \leqslant {\mu _r} < 1\]

Therefore, the answer is option D.

Note: One often does not add \[ \leqslant \] and just use < which is not the correct way. One also gets confused in magnetization and magnetic field strength. Both represent different quantities but the unit is the same.

Additional information
The magnetization \[ = M = \dfrac{{{m_{net}}}}{V}\] that is magnetic moment per unit volume.
M is a vector with dimensions \[{L^{ - 1}}A\] and is measured in a unit of \[A{m^{ - 1}}\] .
The magnetic field strength is \[ = H = \dfrac{B}{{{\mu _o}}} - M\]
Where B is the net magnetic field inside a body.
B has the same unit as that of M.