JEE Challenger
More from Magnetism and Matter
PhyMedAdv 2010 • Paper 1

Critical Temperature Analysis of Superconductor Under Magnetic Fields

Comprehension Passage

Electrical resistance of certain materials, known as superconductors, changes abruptly from a nonzero value to zero as their temperature is lowered below a critical temperature Tc(0)T_c(0). An interesting property of superconductors is that their critical temperature becomes smaller than Tc(0)T_c(0) if they are placed in a magnetic field, i.e., the critical temperature Tc(B)T_c(B) is a function of the magnetic field strength BB. The dependence of Tc(B)T_c(B) on BB is shown in the figure.

Passage Diagram 0

A superconductor has Tc(0)=100 KT_c (0) = 100\text{ K}. When a magnetic field of 7.5 Tesla7.5\text{ Tesla} is applied, its TcT_c decreases to 75 K75\text{ K}. For this material one can definitely say that when

Options

A

B=5 Tesla,Tc(B)=80 KB = 5\text{ Tesla}, T_c (B) = 80\text{ K}

B

B=5 Tesla,75 K<Tc(B)<100 KB = 5\text{ Tesla}, 75\text{ K} < T_c (B) < 100\text{ K}

Correct
C

B=10 Tesla,75 K<Tc(B)<100 KB = 10\text{ Tesla}, 75\text{ K} < T_c (B) < 100\text{ K}

D

B=10 Tesla,Tc(B)=70 KB = 10\text{ Tesla}, T_c (B) = 70\text{ K}

Topics & Concepts

Magnetism and MatterOhm's Law

Step-by-Step Solution

Based on the provided passage and graph, the critical temperature Tc(B)T_c(B) of a superconductor is a strictly monotonically decreasing function of the applied magnetic field strength BB.

Mathematically, if B1<B2B_1 < B_2, then:
Tc(B1)>Tc(B2)T_c(B_1) > T_c(B_2)

We are given the following values for a specific material:

  1. At B=0 TeslaB = 0\text{ Tesla}, Tc(0)=100 KT_c(0) = 100\text{ K}.
  2. At B=7.5 TeslaB = 7.5\text{ Tesla}, Tc(7.5)=75 KT_c(7.5) = 75\text{ K}.

Now, let us evaluate the given magnetic field values:

Case 1: For B=5 TeslaB = 5\text{ Tesla}

Since 0<5 Tesla<7.5 Tesla0 < 5\text{ Tesla} < 7.5\text{ Tesla}, using the strictly monotonic decreasing nature of Tc(B)T_c(B):
Tc(7.5)<Tc(5)<Tc(0)T_c(7.5) < T_c(5) < T_c(0)

Substituting the known values into the inequality gives:
75 K<Tc(5 Tesla)<100 K75\text{ K} < T_c(5\text{ Tesla}) < 100\text{ K}

Since the exact functional form of Tc(B)T_c(B) is not specified, we cannot state an exact numerical value such as Tc(5)=80 KT_c(5) = 80\text{ K} (Option A). However, we can definitely guarantee that 75 K<Tc(5)<100 K75\text{ K} < T_c(5) < 100\text{ K} (Option B).

Case 2: For B=10 TeslaB = 10\text{ Tesla}

Since 10 Tesla>7.5 Tesla10\text{ Tesla} > 7.5\text{ Tesla}, monotonicity implies:
Tc(10 Tesla)<Tc(7.5 Tesla)=75 KT_c(10\text{ Tesla}) < T_c(7.5\text{ Tesla}) = 75\text{ K}

Therefore, Tc(10 Tesla)T_c(10\text{ Tesla}) must be strictly less than 75 K75\text{ K}, which rules out Option C. Option D states an exact value of 70 K70\text{ K}, which again cannot be definitively stated without a specific function.

Thus, one can definitely say that when B=5 TeslaB = 5\text{ Tesla}, 75 K<Tc(B)<100 K75\text{ K} < T_c(B) < 100\text{ K}.

Correct Option: B

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