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Distance of a point inside a superconductor from the surface, at which the magnetic field is two-third of its value at the surface, in terms of London penetration depth (λ) is
  • a)
    0.405 λ
  • b)
    1.098 λ
  • c)
    0.810 λ
  • d)
    1.215 λ
Correct answer is option 'A'. Can you explain this answer?
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Distance of a point inside a superconductor from the surface, at which...
Bz (x) = Bz = (0)e -x/λ, λ is London penetration depth.
Given that at some depth x.
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Distance of a point inside a superconductor from the surface, at which...
The distance of a point inside a superconductor from the surface, at which the magnetic field is two-thirds of its value at the surface, can be expressed in terms of the London penetration depth (λ).

The London penetration depth is a characteristic length scale that describes how far a magnetic field can penetrate into a superconductor. It is denoted by the symbol λ and is typically measured in meters.

Let's assume that the magnetic field at the surface of the superconductor is denoted by B0. According to the given condition, the magnetic field at a distance x from the surface is (2/3)B0.

The relationship between the magnetic field and the distance from the surface in a superconductor is given by:

B(x) = B0 * exp(-x/λ)

Substituting (2/3)B0 for B(x), we get:

(2/3)B0 = B0 * exp(-x/λ)

Dividing both sides of the equation by B0, we have:

(2/3) = exp(-x/λ)

Taking the natural logarithm (ln) of both sides of the equation, we get:

ln(2/3) = -x/λ

Multiplying both sides of the equation by -λ, we have:

-x = λ * ln(2/3)

Finally, multiplying both sides of the equation by -1, we get:

x = -λ * ln(2/3)

Therefore, the distance of a point inside a superconductor from the surface, at which the magnetic field is two-thirds of its value at the surface, is given by x = -λ * ln(2/3).
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Distance of a point inside a superconductor from the surface, at which the magnetic field is two-third of its valueat the surface, in terms of London penetration depth (λ) isa)0.405 λb)1.098 λc)0.810 λd)1.215 λCorrect answer is option 'A'. Can you explain this answer?
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