Explain the difference between the following substances with the help of examples:
(i) Paramagnetic
(ii) Diamagnetic
(iii) Ferromagnetic
i. Paramagnetic Substances
Step 1: Paramagnetic materials have unpaired electrons in their atomic structure, which cause weak attraction to external magnetic fields.
Step 2: They have a small and positive magnetic susceptibility and align weakly with the applied magnetic field. Examples: Aluminum, Platinum, Oxygen. \[ \boxed{\text{Weak attraction, e.g., Aluminum}} \]
ii. Diamagnetic Substances
Step 1: Diamagnetic materials have all paired electrons, causing them to create an induced magnetic field in the opposite direction to the applied field.
Step 2: They have a small and negative magnetic susceptibility and are weakly repelled by the applied magnetic field.
Examples: Copper, Gold, Bismuth. \[ \boxed{\text{Weak repulsion, e.g., Copper}} \]
iii. Ferromagnetic Substances
Step 1: Ferromagnetic materials have domains of atoms that align strongly with an external magnetic field, creating a strong attraction.
Step 2: They have high positive susceptibility and retain magnetization even after removing the external field.
Examples: Iron, Nickel, Cobalt. \[ \boxed{\text{Strong attraction, e.g., Iron}} \]
Find the values of \( x, y, z \) if the matrix \( A \) satisfies the equation \( A^T A = I \), where
\[ A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix} \]
(b) Order of the differential equation: $ 5x^3 \frac{d^3y}{dx^3} - 3\left(\frac{dy}{dx}\right)^2 + \left(\frac{d^2y}{dx^2}\right)^4 + y = 0 $