- #1

quasar987

Science Advisor

Homework Helper

Gold Member

- 4,780

- 12

__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].

(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?

Last edited: