What is relative magnetic permeability of superconductors?

Options

A. Zero
B. 1
C. `-1`
D. `0.5`

Answer

To determine the relative magnetic permeability of superconductors, we can follow these steps:

### Step 1: Understand the concept of magnetic permeability
Magnetic permeability (μ) is a measure of how easily a material can become magnetized or how well it can conduct magnetic lines of force. Relative magnetic permeability (μ_r) is the ratio of the permeability of the material (μ) to the permeability of free space (μ₀).

### Step 2: Identify the behavior of superconductors in a magnetic field
Superconductors exhibit a unique property called the Meissner effect, where they expel all magnetic fields from their interior when cooled below a critical temperature. This means that the magnetic field (B) inside a superconductor is zero.

### Step 3: Relate magnetic field to permeability
From the relationship between magnetic field (B), magnetic permeability (μ), and magnetic field intensity (H), we have:
\[ B = μH \]
In superconductors, since B = 0, we can infer that:
\[ μH = 0 \]
This implies that the permeability of the superconductor must be such that it leads to zero magnetic field.

### Step 4: Determine relative magnetic permeability
Since the magnetic field inside a superconductor is zero, we can express the relative magnetic permeability (μ_r) as:
\[ μ_r = \frac{μ}{μ₀} \]
For superconductors, μ is effectively zero, leading to:
\[ μ_r = 0 \]

### Step 5: Calculate magnetic susceptibility
Magnetic susceptibility (χ) is related to relative permeability by the equation:
\[ χ = μ_r - 1 \]
Substituting μ_r = 0, we get:
\[ χ = 0 - 1 = -1 \]

### Conclusion
Thus, the relative magnetic permeability of superconductors is:
\[ μ_r = 0 \]