Electric Field Distribution in a Split Conductor with Variable Conductivity

[gruba]

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

$$J=σE$$

The Attempt at a Solution

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

Thanks for replies.

 

[mfb]

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).