Current density inside superconductors

[rheajain]

Homework Statement

consider an infinite superconducting slab of thickness 2d (-d<=z<=d), outside of which there is a given constant magnetic field parallel to the suface. H_x =H_z=0 h_y= H₀ (some value for z<d and z>-d) , with E vector= D vector=0 everywhere. compute H vector < J vector inside the slab, assuming surface currents and charges absent.

Homework Equations

consider Maxwell's equations in Gaussian units:
divergence D vector= 4∏ρ
divergence of B vector = 0
curl of E vector= -(1/c) partial differential of B with respect to time.
curl of H vector= (1/c) partial differential of D with respect to time + (4∏/c)J vector
with D=E+4∏Pvector
B vector = H vector + 4∏M vector
now inside superconductor
current density obeys following equation:
c * curl(λJ)= -B , partial differential of (λJ) with respect to time= E
λ is a constant

The Attempt at a Solution

 

[member 553083]

now as E vector and D vector are 0 so curl of E vector=0 and divergence of B vector=0. thus we get equation for J vector:curl(λJ)= -B as H vector is known outside the slab so we can calculate B vector also. we know that J vector is constant inside the slab, so we can integrate:lambda*integral(J)dxdy dz=-integral(B)dxdy dz on solving this equation we can get J vector inside the slab.