Question

1)The differential form of the ampere law for static conditions is:

a)∇xB=o

b)∇xE=0

c)∇xD=pv

d)∇xH=...

2) ∇xB=0 implies for the magnetic field that:

a) is Solenoid

b)is conservative

c) Magnetic load exists

d)all of the above

Answer 1

1) D

d)∇xH=...

2) Question is not very clear so giving some explanation:

In physics it's easiest to think intuitively about divergence by using the divergence theorem which states

∫VdV ∇⋅B=∫∂VB⋅dS
where ∂V is the surface area surrounding the volume V. The magnetic field has zero divergence, which means that

∫∂VB⋅dS=0

We can interpret this by saying there's no net flow of magnetic field across any closed surface. This makes sense because magnetic field lines always come in complete loops, rather than starting or ending at a point.

Put another way, the divergence-free condition is just saying that we don't have magnetic monopoles in Maxwell electromagnetism.