Time Dependent Current in a Wire

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SUMMARY

The discussion focuses on calculating the magnetic flux (Φ) through a conducting loop due to a time-dependent current (I) 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 (B) is calculated using the formula B = μ*I/(2*pi*d), where μ is the permeability of free space and d is the distance from the wire. The user initially struggled with integrating the flux equation but realized the need to apply the integral of 1/x (ln x) to solve the problem correctly.

PREREQUISITES
  • Understanding of electromagnetic theory, specifically magnetic fields generated by current-carrying wires.
  • Familiarity with the concept of magnetic flux and its calculation.
  • Knowledge of calculus, particularly integration techniques.
  • Basic physics principles related to current and its time dependence.
NEXT STEPS
  • Study the derivation and application of the magnetic field equation B = μ*I/(2*pi*d).
  • Learn how to compute magnetic flux using the integral Φ = ∫B*dA.
  • Explore the implications of time-varying currents on magnetic fields and induced electromotive force (EMF).
  • Investigate the properties of logarithmic functions in calculus, particularly their role in integration.
USEFUL FOR

Students and educators in physics, electrical engineers, and anyone involved in electromagnetic theory and applications related to time-varying currents.

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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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