- #1

bobred

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## Homework Statement

Cylinder of radius [itex]a[/itex] and a cylindrical hole [itex]b < a[/itex] is displaced a distance [itex]d[/itex] in x-direction. Current density [itex]\textbf{J}=J_z\textbf{e}_z[/itex]. Show that a uniform magnetic field inside the hole is

[itex]\textbf{B}=\frac{\mu_0}{2}J_zd\textbf{e}_y[/itex]

## Homework Equations

Using previous result of whole cylinder

[itex]\textbf{B}=\frac{\mu_0}{2}J_z(-y\textbf{e}_x + x\textbf{e}_y)[/itex]

and that the cylindrical hole can be modeled as a charge density of [itex]-J_z\textbf{e}_z[/itex].

## The Attempt at a Solution

I tried superposition of fields so

[itex]\textbf{B}_1=\frac{\mu_0}{2}J_z(-y\textbf{e}_x + x\textbf{e}_y)[/itex]

[itex]\textbf{B}_2=-\frac{\mu_0}{2}J_z(-y\textbf{e}_x + (x + d)\textbf{e}_y)[/itex]

[itex]\textbf{B}= \textbf{B}_1 + \textbf{B}_2[/itex] to which I get

[itex]\textbf{B}=-\frac{\mu_0}{2}J_zd\textbf{e}_y[/itex]

Any ideas, is this the right approach?