Consider a solenoid with an iron core, which loops back around the outside of the solenoid. When considering the magnetic field OUTSIDE the solenoid, is the magnetic flux higher in the iron core or is it uniform, or zero?
Specifically: please refer to the below diagram:
What are the field strengths at X1, X2, X3? Quantitative comparisons would be good.
Thanks!
Magnetic flux $\phi$ is defined with respect to a non-closed area, since $\phi=\int_A\vec{B}\cdot \mathrm{d}\vec{S}$. If the area $A$, through which you want to define or construct your flux is kept constant, then sure, inside the solenoid $\vec{B}$ is higher, so $\int_A\vec{B}\cdot\mathrm{d}\vec{S}$ is higher than outside. You can understand this by looking at the line of force from the solenoid outside the solenoid, they are much farther apart but within the solenoid they are much more concentrated, hence they will have higher flux within the solenoid for the given area.
