Really Quick Maxwell Eqns Question

[bon]

Homework Statement

Consider a magnetic flux density of the form:

Bx=A1 y
By=A2 x
Bz = 0

where A1 and A2 are constants. SHow that the field is fully compatible with maxwell's equations if and only if A1 = A2

Homework Equations

The Attempt at a Solution

SO i guess i just have to show divB = 0, which it does regardless of A1 and A2 being equal and curl B = mu0 (Jc + Jd). But what do i use for Jc and Jd here? Is it possible for them both to equal 0? I.e. for there not to be any electric field at all and just a pure B field? in which case curl B = 0 which leads to A1=A2. Is this possible?

 

[bon]

I ask because i know that in free space Jc = 0 but we still count Jd i.e. epsillon 0 dE/dt right?

 

[bon]

anyone able to help with this? seems like an easy question...

 

[eczeno]

yes, there can be an electric field, but if is static, i.e. not changing in time, then the curl of B must be zero (if Jc=0 too, of course).