The problem: In the regions of space where [itex]\vec{J_f} = 0[/itex], the curl of [itex]\vec{H}[/itex] vanishes, and hence we can define a scalar potential [itex]V_m[/itex].(adsbygoogle = window.adsbygoogle || []).push({});

(a) Show that [itex]V_m[/itex] must be continuous at the boundary of material.- Done

(b) Consider a very long cylinder of radius a made out of a linear magnetic material of relative permeability [itex]\mu_r[/itex]. The axis of the cylinder is oriented along [itex]\hat{z}[/itex] and the cylinder is emerged in a field [itex]\vec{H}[/itex] that is worth [itex]H_0 \hat{x}[/itex] very far from it. From symetrical considerations, [itex]V_m[/itex] must be of the form

[tex]V_{m_1}=(As+B/s)cos\phi[/tex]

[tex]V_{m_2}=Cscos\phi[/tex]

Where [itex]V_{m1}[/itex] is the potential outside the cylinder and [itex]V_{m2}[/itex] the one inside. Find the value of the constant A, B and C in terms of the other parameters.

My solution: I used the condition of continuity to find B in terms of C, and I used the condition at infinity to find A = -H_0.

What is the 3rd condition on V that'll let me find the value of the third constant?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Magnetic field in matter.

**Physics Forums | Science Articles, Homework Help, Discussion**