Question

A magnetic field (B) of strength 50000 nT induces a magnetization (M) of magnitude 5 A/m in a rock. Given the magnetic permeability of free space \(\mu_0 = 4\pi \times 10^{-7}\,\text{H/m}\), the susceptibility of the rock is __________ (rounded off to three decimal places).

Hint:

When both \(B\) and \(M\) are given, compute \(H\) from \(H=\dfrac{B}{\mu_0}-M\) (since \(B=\mu_0(H+M)\)). Using \(H=\dfrac{B}{\mu_0}\) alone underestimates \(\chi\) when \(M\) is not negligible.

Answer 1

Step 1: Convert \(B\) to Tesla.
\(B = 50000\,\text{nT} = 5\times10^{-5}\,\text{T}.\) Step 2: Use \(B=\mu_0(H+M)\).
\[ H=\frac{B}{\mu_0}-M =\frac{5\times10^{-5}}{4\pi\times10^{-7}}-5 \approx 39.789-5 =34.789\ \text{A/m}. \] Step 3: Susceptibility.
\[ \chi=\frac{M}{H}=\frac{5}{34.789}\approx 0.14368 \Rightarrow \boxed{0.144}. \]