Two long wires carrying current

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SUMMARY

The discussion focuses on calculating the line integrals of magnetic field (∫B⋅ds) and electric field (∫E⋅ds) for two long wires carrying currents I1 and I2 in opposite directions. Using Ampere's Law, the value of ∫B⋅ds is determined to be zero when I1 equals I2, and μ0 when I1 is 1A and I2 is 0A. The challenge remains in calculating ∫E⋅ds, where Faraday's Law indicates that the integral depends on the rate of change of magnetic flux (ΦB) over time. The participants emphasize that the constancy of the currents does not affect the calculation of ΦB.

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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?

physexam1q5.png


Homework Equations


Ampere's Law: ∫B⋅ds=μ0I
Faraday's Law: ∫E⋅ds=-dΦB/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.
 
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What about the righthand side if you knw the currents are constant ?
 
scrubber said:
Faraday's Law: ∫E⋅ds=-dΦB/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.
 

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