Magnetic Susceptibility Basics
Magnetic susceptibility, denoted by the Greek letter $\chi$, quantifies how a material responds to an external magnetic field. The question states the susceptibility is temperature independent and constant, represented as $\chi = C$. We need to determine the material type based on the sign of $C$.
Classifying Magnetic Materials
- Diamagnetic Materials: Exhibit a small, negative magnetic susceptibility ($\chi < 0$) that is independent of temperature. They are weakly repelled by magnetic fields.
- Paramagnetic Materials: Have a small, positive magnetic susceptibility ($\chi > 0$). Typically, susceptibility is temperature dependent (following Curie's law, $\chi \propto 1/T$). They are weakly attracted to magnetic fields.
- Ferromagnetic Materials: Possess a large, positive magnetic susceptibility ($\chi \gg 0$). This property is strongly dependent on temperature, decreasing significantly above the Curie temperature ($T_C$). They are strongly attracted to magnetic fields and can retain magnetization.
Superconductors and Magnetic Fields
Type I superconductors exhibit a phenomenon called the Meissner effect below their critical temperature ($T_c$) and critical magnetic field ($H_c$). This effect involves the expulsion of all magnetic fields from the interior of the superconductor, resulting in perfect diamagnetism.
- For a perfect diamagnet, the magnetic susceptibility is $\chi = -1$.
- This value ($\chi = -1$) is negative and independent of temperature (as long as the material remains superconducting).
Analyzing the Options
We are given $\chi = C$, where $C$ is a constant. Let's evaluate the options:
- Option 1: If $C$ is positive, the material is a diamagnet. Incorrect. Diamagnets have negative susceptibility ($C < 0$).
- Option 2: If $C$ is positive, the material is a ferromagnet. Incorrect. While ferromagnets have positive susceptibility, it is strongly temperature-dependent, contradicting $\chi = C$.
- Option 3: If $C$ is negative, the material could be a type I superconductor. Correct. Type I superconductors have $\chi = -1$, which is negative and temperature independent. A negative $C$ is consistent with this.
- Option 4: If $C$ is positive, the material could be a type I superconductor. Incorrect. Superconductors require negative susceptibility ($\chi = -1$).
Conclusion
A material with a temperature-independent magnetic susceptibility $\chi = C$ could be a Type I superconductor if $C$ is negative, specifically if $C = -1$, due to the Meissner effect.
Important Questions from Superconductivity Meissner Effect BCS Theory
Consider a metal-superconductor junction connected to a dc voltage $V$. At $T < T_c$, where $T_c$ is the superconductor's transition temperature, the current $I$ versus $V$ behavior of this junction is shown schematically in the figure below. If the superconducting energy gap is $D \text{ meV}$. The value of $D$ (rounded off to one decimal place) is _____
- Which of the following option(s) is/are correct for a Type I superconductor?
The figure schematically shows the $M$ (magnetization) - $H$ (magnetic field) plots for certain types of materials. Here $M$ and $H$ are plotted in the same scale and units. Which one of the following is the most appropriate combination?
- A material behaves as a superconductor below a critical temperature $T_c$ and as a normal conductor above $T_c$. A magnetic field $\vec{B} = B\hat{z}$ is applied when $T > T_c$. The material is then cooled below $T_c$ in the presence of $\vec{B}$. Which of the following figure represent the correct configuration of magnetic field lines?
- Amongst electrical resistivity ($\rho$), thermal conductivity ($\kappa$), specific heat ($C$), Young's modulus ($Y$), and magnetic susceptibility ($\chi$), which quantities show a sharp change at the superconducting transition temperature?
