Answer
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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.
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.
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