Time Dependent Current in a Wire

AI Thread Summary
The discussion revolves around calculating the magnetic flux through a conducting loop due to a time-varying current in an infinite straight wire. The current increases to a maximum of 5.2 A at 15 seconds, remains constant, and then decreases to -5.2 A by 26 seconds. The magnetic field is determined using the formula B = μ*I/(2*pi*d), where d is the distance from the wire. The user initially struggles with integrating the flux equation and realizes a mistake related to the integration of 1/x. The correct approach involves properly applying the magnetic flux equation to find the desired value at the specified time.
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Homework Statement


An infinite straight wire carries a current I that varies with time as shown above. It increases from 0 at t = 0 to a maximum value I1 = 5.2 A at t = t1 = 15 s, remains constant at this value until t = t2 when it decreases linearly to a value I4 = -5.2 A at t = t4 = 26 s, passing through zero at t = t3 = 23 s. A conducting loop with sides W = 27 cm and L = 50 cm is fixed in the x-y plane at a distance d = 57 cm from the wire as shown.What is the magnitude of the magnetic flux Φ through the loop at time t = t1 = 15 s?

Homework Equations



B = μ*I/(2*pi*d)

I = 5.2 A

Φ = ∫B*dA

The Attempt at a Solution



I know I need to use the magnetic flux equation in this somehow. I tried integrating the flux equation above to get something like Φ = ∫B*dA = B*A = ((μ*I)/(2*pi*(((d+L)^2) - (d^2)) * (W*L). (?)

However, when I plugged in the values and typed in what I got into the computer, it didn't like what I had. I tried doing everything I could, & I feel like this is a relatively simple problem. What am I doing wrong?
 

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Ignore. I just forgot the integral of 1/x. (ln x)
 
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