What is the Meissner effect?

Complete expulsion of magnetic flux from a material cooled below Tc in a weak field

Drop of resistance to zero when a current flows

Trapping of the existing flux when a perfect conductor is cooled

Increase of Tc with applied field

Inside a superconductor showing the Meissner effect, which set of results holds?

B = 0, M = -H, susceptibility = -1

B = mu0 H, M = 0, susceptibility = 0

B = 0, M = +H, susceptibility = +1

B = mu0 M, H = 0, susceptibility = -1 only above Tc

How do the two types respond as the field rises?

Type-I stays fully diamagnetic up to Hc then turns normal suddenly; type-II has a mixed state between Hc1 and Hc2

Type-I has a mixed state between Hc1 and Hc2; type-II turns normal suddenly at Hc

Both turn normal suddenly, but type-II at a higher field

Type-I has two critical fields and type-II has one

Which statement correctly compares the two types?

Type-II has high Jc with flux pinning and is used for MRI and accelerator magnets; type-I has low Jc

Type-I has high Jc and is used for MRI magnets

Both have equally low Jc and low Hc

Type-II has reversible magnetization and type-I shows hysteresis

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Meissner effect; type I vs type II superconductors

Short answer

The Meissner effect is the complete expulsion of magnetic flux from a superconductor below Tc, making it a perfect diamagnet (B=0). Type-I superconductors show complete flux expulsion up to a single Hc then suddenly become normal; type-II have complete expulsion only up to Hc1, then flux partially enters as vortices in a mixed state up to Hc2.

What is Meissner effect? Explain the difference between type-I and type-II superconductor.

Meissner effect

Meissner effect is the complete expulsion of magnetic flux from the interior of a material when it is cooled below its critical temperature $T_c$ in a weak magnetic field ( $H < H_c$ ). The superconductor becomes a perfect diamagnet.

Inside the superconductor:

\begin{aligned} B &= \mu_0 (H + M) = 0 \\ \Rightarrow M &= -H, \quad \chi_m = \frac{M}{H} = -1 \end{aligned}

Screening currents flow in a thin surface layer (the London penetration depth, $\lambda_L \approx 10$ to $100$ nm) and create a field that exactly cancels the applied field inside.

   T > Tc (normal)        T < Tc (superconducting)
   | | | | | | |           \ \         / /
   | |+-----+| |            \ \ +---+ / /
   | ||     || |   cool      ) )|   |( (
   | ||     || |   ---->    / / +---+ \ \
   | |+-----+| |           / /         \ \
   | | | | | | |      flux lines bend around it

The effect is independent of history: whether the field is applied before or after cooling, the flux is expelled. This shows a superconductor is not just a perfect conductor (a perfect conductor would trap the flux present at cooling).

Type-I and type-II superconductors

Superconductors are classified by how they respond to a rising magnetic field.

Type-I: the material stays a perfect diamagnet (full flux expulsion) until the field reaches $H_c$ , then it suddenly becomes fully normal and flux enters completely.
Type-II: below $H_{c1}$ flux is fully expelled. Between $H_{c1}$ and $H_{c2}$ flux enters as thin quantized tubes called vortices (each carries $\Phi_0 = h/2e = 2.07\times10^{-15}$ Wb). The material around them stays superconducting (mixed state). Above $H_{c2}$ it becomes normal.

 -M                         -M
  |    /|                    |   /\
  |   / |                    |  /  \
  |  /  |                    | /    \_
  | /   |                    |/       \__
  |/    |____ H              +----|------|--- H
  0    Hc                    0   Hc1    Hc2
   Type-I                     Type-II

Point	Type-I (soft)	Type-II (hard)
Critical field	Single $H_c$	Two: $H_{c1}$ and $H_{c2}$
Meissner effect	Complete up to $H_c$	Complete only up to $H_{c1}$
Transition	Sharp, normal at $H_c$	Gradual; mixed (vortex) state between $H_{c1}$ and $H_{c2}$
Value of field	Low, about 0.01 to 0.2 T	$H_{c2}$ very high, up to 20 to 100 T
Current capacity	Low $J_c$	High $J_c$ (with flux pinning)
Magnetization	Reversible	Irreversible, hysteresis
Materials	Pure metals: Pb, Hg, Sn, Al, In	Alloys, compounds: NbTi, Nb $_3$ Sn, V $_3$ Ga, YBCO
Uses	Limited (research, SQUID parts)	Magnets for MRI, accelerators, maglev

✓ Answer checked by Claude Opus 5.5 (high effort)

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