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Chapter 10

Q. 10.5

Estimate the size of the induced diamagnetic moment in a typical atom, assuming an orbital radius equal to the Bohr radius and an applied field of 2.0 T. Compare the result with the Bohr magneton \mu_{ B }=e \hbar / 2 m=9.27 \times 10^{-24} J/T, a typical magnetic moment.

Strategy With the numerical values of the orbital radius and magnetic field known, the induced magnetic moment is given by Equation (10.38). Using SI units throughout, the units for change in magnetic moment will be in J/T.

\Delta \mu=\frac{e^{2} r^{2} B}{4 m} (10.38)

Step-by-Step

Verified Solution

Using the numerical values provided along with the electron charge and mass,

 

\begin{aligned}\Delta \mu=\frac{e^{2} r^{2} B}{4 m} &=\frac{\left(1.60 \times 10^{-19} C \right)^{2}\left(5.29 \times 10^{-11} m \right)^{2}(2.0 T )}{4\left(9.11 \times 10^{-31} kg \right)} \\&=3.9 \times 10^{-29} J / T\end{aligned}

 

The change in the magnetic moment is only about 4 \times 10^{-6} as large as the Bohr magneton. This illustrates that diamagnetism is generally a weak effect.