Math Problem Statement
Problem 5B: Consider two wires both aligned with the 𝑧-axis at positions 𝑦 = ±𝑦0 with 𝑦0 = 6[cm]. The wires have radius 𝑟0 = 5[mm] and they are carrying equal and opposite current ±𝐼0 = ±1 [mA]. If we assume the current is uniformly distributed around the surface of the wire and that 𝑦0 ≫ 𝑟0, verify that the inductance per unit length of this structure is L^'=μ_r μ_0 (cosh^(-1) (〖y_0/r〗_0 ))/π
Solution
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Math Problem Analysis
Mathematical Concepts
Electromagnetism
Inductance
Mutual Inductance
Hyperbolic Functions
Formulas
L' = (μ_r μ_0 / π) cosh^(-1) (y0 / r0)
cosh^(-1)(x) = ln(x + sqrt(x^2 - 1))
Theorems
Mutual Inductance Theorem
Hyperbolic Cosine Inverse Theorem
Suitable Grade Level
Undergraduate (Physics/Engineering)
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