Electric Field Distribution in a Split Conductor with Variable Conductivity

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SUMMARY

The discussion focuses on calculating the electric field distribution in a split conductor with variable conductivity, specifically two segments with conductivities σ1 and σ2. When connected to a constant voltage U, the electric fields in each segment are defined by the equations E_1 = (2σ2U) / (l(σ1 + σ2)) and E_2 = (2σ1U) / (l(σ1 + σ2)). The participants emphasize the importance of understanding current flow per area and suggest introducing a cross-section A to facilitate calculations of total resistance and current flow.

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gruba
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Homework Statement


Wire conductor of length l consists of two part with equal length in series, and of specific conductivity σ1 and σ2. When conductor is connected to constant voltage U, what are electric fields in parts of this conductor?

Homework Equations


[tex]J=σE[/tex]

The Attempt at a Solution


Electric fields should be [tex]E_1=\frac{2σ_2U}{l(σ_1+σ_2)}[/tex]
[tex]E_2=\frac{2σ_1U}{l(σ_1+σ_2)}[/tex]
I don't know how to derive these equations.
Could someone give a hint?

Thanks for replies.
 
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What do you know about the current flow per area?
You can introduce a cross-section A if that helps (that allows to calculate the total resistance and total current flow, the area will drop out later).
 

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