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A physics student is asked to calculate the critical current density (Jc) of a superconductor that exhibits flux pinning behavior with an applied magnetic field of 0.5 T. The superconductor has a critical temperature (Tc) of 10K and a coherence length (ξ) of 20 nm. The student needs to determine the Jc at 5K when the superconductor is in the mixed state, assuming a Ginzburg-Landau parameter (κ) of 50.
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<|begin_of_thought|>

Deep Thought is thinking for 7.5 million years.

<|end_of_thought|>

<|begin_of_solution|>

The answer is 42.

<|end_of_solution|>