Diamagnetism — Question 1

Question 1

Weak diamagnetism reduces the field by a small signed fraction

A long cylinder parallel to an applied field has negligible demagnetization and susceptibility $\chi=-2.0\times10^{-5}$. The applied vacuum field is $B_a=0.80$ T. Use $\mu_0=4\pi\times10^{-7}$ H/m.

1. Find its magnetization and the change B-Ba inside the material.

2. If the cylinder volume is $3.0\times10^{-6}$ cubic meters, find its total dipole moment and state its direction.

Question 1 - Solution

Weak diamagnetism reduces the field by a small signed fraction

(a) Method and calculation

$$H=B_a/\mu_0,\quad M=\chi B_a/\mu_0=\boxed{-12.73\,\mathrm{A/m}}.$$$$\boxed{B-B_a=\mu_0M=\chi B_a=-1.60\times10^{-5}\,\mathrm T}.$$

(b) Interpretation and further calculation

$$m=MV=(-12.7324)(3.0\times10^{-6})\,\mathrm{A\,m^2}.$$$$\boxed{m=-3.820\times10^{-5}\,\mathrm{A\,m^2}}\quad\text{along the signed field axis}.$$

Physical check

The negative sign means the induced moment opposes the applied field, while the total field remains in its original direction.