Question

$B$ is the magnetic flux density and $T_c$ is the critical temperature. The Meissner effect is represented by:

• A. $B = 0$ at $T \leq T_c$
• B. $B = 0$ at $T>T_c$
• C. $B \neq 0$ at $T \leq T_c$
• D. $\nabla B = 0$ at $T = T_c$

Hint:

Always remember: - Zero resistance $\neq$ Meissner effect. - Meissner effect = complete expulsion of magnetic field when $T<T_c$. Thus superconductors are perfect diamagnets.

Answer 1

The Correct Option is A

Step 1: Recall Meissner effect.
The Meissner effect is the phenomenon in which a superconductor expels all magnetic flux lines when cooled below its critical temperature $T_c$. This means that: \[ B = 0 \text{inside the superconductor for } T \leq T_c. \]

Step 2: Important distinction.
- The Meissner effect is not just infinite conductivity (zero resistance). - Even perfect conductors could trap magnetic fields inside. - Superconductors, however, actively expel magnetic fields. This is why $B=0$ in the bulk when $T<T_c$, not just at $T=T_c$.

Step 3: Check options carefully.
- Option (A): Correct — matches the physical principle of superconductivity. - Option (B): Wrong, because when $T>T_c$, the material is normal and magnetic field penetrates freely, so $B \neq 0$. - Option (C): Wrong, opposite of what happens in superconductors. - Option (D): Wrong, $\nabla B = 0$ is not the representation of Meissner effect.

Step 4: Physical significance.
Because $B=0$ inside, superconductors behave as perfect diamagnets. Their magnetic susceptibility $\chi = -1$. Final Answer:
\[ \boxed{B = 0 \;\; \text{at } T \leq T_c} \]