A toroid has a mean radius `R` equal to `20/pi` cm, and a total of 400 turns of wire carrying a current of `2.0 A`. An aluminium ring at temperature `280 K` inside the toroid provides the core. (a) If the magnetization `I` is `4.8 xx 10^(-2) A m^(-1)`, find the susceptibility of aluminium at `280 K`. (b) If the temperature of the aluminium ring is raised to `320 K`, what will be the magnetization?

Explanation

To solve the problem step by step, we'll break it into two parts as per the question.

### Part (a): Finding the susceptibility of aluminium at 280 K

1. **Calculate the number of turns per unit length (n)**:
- The total number of turns \( N = 400 \).
- The mean radius \( R = \frac{20}{\pi} \) cm = \( \frac{20}{\pi} \times 10^{-2} \) m.
- The circumference of the toroid \( C = 2\pi R = 2\pi \left(\frac{20}{\pi} \times 10^{-2}\right) = 0.4 \) m.
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