Question

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

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 $$=X={\displaystyle \frac{M}{H}}$$
 lies in the region $$-1⩽X<0$$ (Where M is magnetization and H is magnetic field strength)
Using the relation between X and $${\mu }_r$$
 $$\Rightarrow X={\mu }_r-1$$
 $$\Rightarrow {\mu }_r=X+1$$
 $$-1⩽X<0$$ adding 1 to all three
 $$\Rightarrow 0⩽{\mu }_r<1$$

Therefore, the answer is option D.

Note: One often does not add $$⩽$$ 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 $$=M={\displaystyle \frac{m_{net}}{V}}$$ 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 $$=H={\displaystyle \frac{B}{{\mu }_o}}-M$$
Where B is the net magnetic field inside a body.
B has the same unit as that of M.