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

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.