Electromagnetism, Auxiliary field

[michael2020]

Homework Statement

I only need help with part C and D

Homework Equations

Curl of B = mu0 J
J = J free + J bound
H = B/mu0 - M

The Attempt at a Solution

For C i, I said they're the same because free current is the same at both points. My argument is that because curl of B (at L) = mu0 Jfree, and @R because Jb = 0, (curl of M = 0) thus , curl of B(at R) = mu0Jfree, thus B field is the same.
for ii, because M is different at the two points, using H = B/mu0 - M, H must be different.
for d, I think they are supposed to equal to each other to have uniform B field. but I'm not exactly sure. Can someone check my solutions above?

 

[anathema]

Your solutions for part C and D seem to be correct. In part C, since the free current is the same at both points, the curl of B will also be the same, resulting in the same B field. In part D, for a uniform B field, both H and M should be constant at all points, so their values will be the same at both L and R. This will result in the same B field at both points.