# Time Dependent Current in a Wire

**1. The problem statement, all variables and given/known data**

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?

**2. Relevant equations**

B = μ*I/(2*pi*d)

I = 5.2 A

Φ = ∫B*dA

**3. 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?

**1. The problem statement, all variables and given/known data**

**2. Relevant equations**

**3. The attempt at a solution**

**1. The problem statement, all variables and given/known data**

**2. Relevant equations**

**3. The attempt at a solution**

**1. The problem statement, all variables and given/known data**

**2. Relevant equations**

**3. The attempt at a solution**

**1. The problem statement, all variables and given/known data**

**2. Relevant equations**

**3. The attempt at a solution**

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