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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?
(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?
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