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De_Lille_D
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Homework Statement
Given a rectangular loop of length C by length D (C >> D) through which a current I flows, calculate the self-inductance L of the loop (consider only the long sides of the rectangle).
Homework Equations
Self-inductance: [itex]L = \frac{N \cdot \Phi_B}{I}[/itex]
magnetic flux: [itex]\Phi_B = \int{B \cdot dA}[/itex]
magnetic field for a long conductor: [itex]B = \frac{\mu_0 \cdot I}{2\pi r}[/itex]
The Attempt at a Solution
sketch
A single loop: N = 1
C >> D, so we approximate the magnetic field in the loop by one made by 2 long conductors, meaning B is only dependent on the distance from the long sides.
Each of the 2 long sides contributes to the magnetic field constructively:
[itex]\Phi_B = 2 \int{\frac{\mu_0*I}{2\pi y} dx dy} = \frac{2*C*\mu_0*I}{2\pi} \int_0^D{\frac{1}{y}dy}[/itex]
This is where I'm stuck; the integral isn't convergent.