Two long wires carrying current

[scrubber]

Homework Statement

Two long wires carrying current I1 and I2 in opposite directions pass through a closed path S as shown in the picture.
What are the values of ∫B⋅ds and ∫E⋅ds if:
i) I1=I2=1A
ii) I1=1A and I2=0A?

Homework Equations

Ampere's Law: ∫B⋅ds=μ₀I
Faraday's Law: ∫E⋅ds=-dΦ_B/dt

The Attempt at a Solution

For i, ∫B⋅ds=μ₀(I1-I2)=μ₀(0)=0
For ii, ∫B⋅ds=μ₀(I1)=μ₀(1)=μ₀

Is these correct? But I have no idea of finding ∫E⋅ds

Please help.

 

[BvU]

What about the righthand side if you knw the currents are constant ?

 

[rude man]

Faraday's Law: ∫E⋅ds=-dΦ_B/dt

The Attempt at a Solution

But I have no idea of finding ∫E⋅ds
Please help.

What is Φ for your situation? Hint: it doesn't matter whether the currents are constant or time-varying.