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Magnetism question

2010 · Shift 1 · Q76
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Magnetism question

2010 · Shift 1 · Q76

JEE AdvancedPhysicsMagnetismMCQ+3 / −1
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 Tc(0). An interesting property of superconductors is that their critical temperature becomes smaller than Tc(0), if they are placed in a magnetic field, that is, the critical temperature Tc(B) is a function of the magnetic field strength B. The dependence of Tc(B) on B is shown in the figure. IIT-JEE 2010 Paper 1 Offline Physics - Magnetism Question 15 English ComprehensionA superconductor has Tc(0) = 100 K. When a magnetic field of 7.5 T is applied, its Tc decreases to 75 K. For this material, one can definitely say that when
  1. A
    B = 5 T, Tc(B) = 80 K
  2. B
    B = 5 T, 75 K c (B) < 100 K
  3. C
    B = 10 T, 75 K c < 100 K
  4. D
    B = 10, Tc = 70 K
View written solutionFree

Correct answer: B

  1. Interpret the graph qualitatively

The figure indicates that the critical temperature Tc(B)T_c(B)Tc​(B) decreases monotonically as magnetic field BBB increases.

So:

  • at B=0B=0B=0, Tc(0)=100 KT_c(0)=100\,\text{K}Tc​(0)=100K
  • at larger BBB, Tc(B)<100 KT_c(B)<100\,\text{K}Tc​(B)<100K

We are given one more point: B=7.5 T⇒Tc=75 KB=7.5\,\text{T} \Rightarrow T_c=75\,\text{K}B=7.5T⇒Tc​=75K

Thus the curve passes through: (0,100),(7.5,75)(0,100), \quad (7.5,75)(0,100),(7.5,75)

Since Tc(B)T_c(B)Tc​(B) decreases with BBB:

  • for B<7.5 TB<7.5\,\text{T}B<7.5T, we must have 75 K<Tc(B)<100 K75\,\text{K} < T_c(B) < 100\,\text{K}75K<Tc​(B)<100K
  • for B>7.5 TB>7.5\,\text{T}B>7.5T, we must have Tc(B)<75 KT_c(B) < 75\,\text{K}Tc​(B)<75K
  1. Check each option

Option A: B=5 T,  Tc(B)=80 KB=5\,\text{T},\; T_c(B)=80\,\text{K}B=5T,Tc​(B)=80K

At B=5 T<7.5 TB=5\,\text{T}<7.5\,\text{T}B=5T<7.5T, we can only say: 75<Tc(B)<10075 < T_c(B) < 10075<Tc​(B)<100

The exact value 80 K80\,\text{K}80K is not definite from the given data.

So, A is not definitely true.

Option B: B=5 T,  75 K<Tc(B)<100 KB=5\,\text{T},\; 75\,\text{K}<T_c(B)<100\,\text{K}B=5T,75K<Tc​(B)<100K

Since 5 T<7.5 T5\,\text{T}<7.5\,\text{T}5T<7.5T and Tc(B)T_c(B)Tc​(B) decreases with BBB, Tc(5 T)>Tc(7.5 T)=75 KT_c(5\,\text{T}) > T_c(7.5\,\text{T}) = 75\,\text{K}Tc​(5T)>Tc​(7.5T)=75K Also, Tc(5 T)<Tc(0)=100 KT_c(5\,\text{T}) < T_c(0)=100\,\text{K}Tc​(5T)<Tc​(0)=100K Hence, 75 K<Tc(5 T)<100 K75\,\text{K}<T_c(5\,\text{T})<100\,\text{K}75K<Tc​(5T)<100K

So, B is definitely true.

Option C: B=10 T,  75 K<Tc(B)<100 KB=10\,\text{T},\; 75\,\text{K}<T_c(B)<100\,\text{K}B=10T,75K<Tc​(B)<100K

Since 10 T>7.5 T10\,\text{T}>7.5\,\text{T}10T>7.5T and the function decreases with BBB, Tc(10 T)<Tc(7.5 T)=75 KT_c(10\,\text{T}) < T_c(7.5\,\text{T}) = 75\,\text{K}Tc​(10T)<Tc​(7.5T)=75K So it cannot be between 75 K75\,\text{K}75K and 100 K100\,\text{K}100K.

Therefore, C is false.

Option D: B=10 T,  Tc=70 KB=10\,\text{T},\; T_c=70\,\text{K}B=10T,Tc​=70K

At B=10 TB=10\,\text{T}B=10T, we only know: Tc(B)<75 KT_c(B) < 75\,\text{K}Tc​(B)<75K The exact value 70 K70\,\text{K}70K is not definite.

So, D is not definitely true.

  1. Final conclusion

The only statement that can be said definitely is: B\boxed{\text{B}}B​

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