Question

Match the column:

• A. A: a → p, b → r, c → q, d → q, r
• B. B: a → p, b → r, c → q, d → p, q
• C. C: a → p, b → r, c → q, d → p
• D. D: a → r, b → p, c → q, d → p, r

Answer 1

Answer: (A)

A: a → p, b → r, c → q, d → q, r

Answer 2

The problem asks us to match the given conditions related to magnetic properties with the type of magnetic materials.

Let's analyze each condition:

Understanding the terms:

• x (or χ): Represents magnetic susceptibility. It's a dimensionless quantity that describes how much a material will become magnetized in an applied magnetic field.
• μ: Represents magnetic permeability of the material. It's a measure of the ability of a material to support the formation of a magnetic field within itself.
• μ₀: Represents the permeability of free space (vacuum). Its value is $4\pi \times 10^{-7} \text{ T}\cdot\text{m/A}$.

The relationship between magnetic permeability (μ) and magnetic susceptibility (χ) is given by: $\mu = \mu_0 (1 + \chi)$

Now, let's match the columns:

Column A Analysis:

• (a) -1 ≤ x < 0:

  • For diamagnetic materials, the magnetic susceptibility (χ) is small and negative. This range perfectly describes diamagnetic behavior.
  • Therefore, (a) → (p) Diamagnetic.

• (b) 0 < x < 1:

  • For paramagnetic materials, the magnetic susceptibility (χ) is small and positive. This range indicates paramagnetic behavior.
  • Therefore, (b) → (r) Paramagnetic.

• (c) x >> 1:

  • For ferromagnetic materials, the magnetic susceptibility (χ) is very large and positive (typically in the range of hundreds to hundreds of thousands). This condition signifies ferromagnetic behavior.
  • Therefore, (c) → (q) Ferromagnetic.

• (d) μ > μ₀:

  • Using the relationship $\mu = \mu_0 (1 + \chi)$: If $\mu > \mu_0$, then $\mu_0 (1 + \chi) > \mu_0$. Dividing by $\mu_0$ (which is positive), we get $1 + \chi > 1$. This simplifies to $\chi > 0$.
  • Materials with positive susceptibility (χ > 0) include both paramagnetic materials (where χ is small and positive) and ferromagnetic materials (where χ is very large and positive).
  • Therefore, (d) → (q) Ferromagnetic, (r) Paramagnetic.

Summary of Matches:

• (a) → (p)
• (b) → (r)
• (c) → (q)
• (d) → (q), (r)

Comparing this with the given options, Option A matches our derived solution.