Magnetic Properties of Matter: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of Magnetic Properties of Matter. Understanding the underlying formula is key to arriving at the correct answer below:

The relationship is \(B = \mu H = \mu_r \mu_0 H\). Given \(B = 12\pi\text{ T}\), \(H = 3 \times 10^3\text{ A m}^{-1}\), and \(\mu_0 = 4\pi \times 10^{-7}\text{ T m A}^{-1}\). Thus, \(12\pi = \mu_r (4\pi \times 10^{-7})(3 \times 10^3)\), which simplifies to \(\mu_r = 10^4\).