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Electrical resistance of certain materials, known as superconductors, changes abruptly from a non-zero value to zero as their temperature is lowered below a critical temperature $T_C(0)$. An interesting property of superconductors is that their critical temperature becomes smaller than $T_C(0)$ if they are placed in a magnetic field i.e., the critical temperature $T_C(B)$ is a function of the magnetic field strength $B$. The dependence of $T_C(B)$ on $B$ is shown in the figure.
Question:
A superconductor has $T_C(0)=100 \mathrm{~K}$. When a magnetic field of $7.5$ Tesla is applied, its $T_C$ decreases to $75 \mathrm{~K}$. For this material one can definitely say that when (Note : $\mathrm{T}$ = Tesla)
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Electrical resistance of certain materials, known as superconductors, changes abruptly from a non-zero value to zero as their temperature is lowered below a critical temperature $T_C(0)$. An interesting property of superconductors is that their critical temperature becomes smaller than $T_C(0)$ if they are placed in a magnetic field i.e., the critical temperature $T_C(B)$ is a function of the magnetic field strength $B$. The dependence of $T_C(B)$ on $B$ is shown in the figure.
Question:
A superconductor has $T_C(0)=100 \mathrm{~K}$. When a magnetic field of $7.5$ Tesla is applied, its $T_C$ decreases to $75 \mathrm{~K}$. For this material one can definitely say that when (Note : $\mathrm{T}$ = Tesla)
Solution:
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Verified Answer
The correct answer is:
$B=5 \mathrm{~T}, 75 \mathrm{~K} < T_C(B) < 100 \mathrm{~K}$
$B=5 \mathrm{~T}, 75 \mathrm{~K} < T_C(B) < 100 \mathrm{~K}$
With increase in temperature, $T_C$ is decreasing.
$$
\begin{aligned}
T_C(0) & =100 \mathrm{~K} \\
T_C & =75 \mathrm{~K} \text { at } B=7.5 \mathrm{~T}
\end{aligned}
$$
Hence, at $B=5 \mathrm{~T}, \quad T_C$ should lie between $75 \mathrm{~K}$ and $100 \mathrm{~K}$. Hence, the correct option should be (b).
$$
\begin{aligned}
T_C(0) & =100 \mathrm{~K} \\
T_C & =75 \mathrm{~K} \text { at } B=7.5 \mathrm{~T}
\end{aligned}
$$
Hence, at $B=5 \mathrm{~T}, \quad T_C$ should lie between $75 \mathrm{~K}$ and $100 \mathrm{~K}$. Hence, the correct option should be (b).
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