Two parallel, infinitely long, z- axis oriented conducting cylinders of radius "a" are a distance "b" apart. "b" is much, much, greater than "a". Both cylinders carry a current, "I", of the same magnitude but opposite direction. The current is flowing uniformly through the cross-section of the conductors. Find the approximate B field at y = 103 “b"

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## Magnetic Field Between Two Parallel Conductors

**Problem Statement:**

Two parallel, infinitely long, z-axis oriented conducting cylinders of radius “a” are a distance “b” apart. “b” is much, much, greater than “a”. Both cylinders carry a current, “I”, of the same magnitude but in opposite directions. The current is flowing uniformly through the cross-section of the conductors.

**Question:**

Find the approximate B field at \( y = 10^3 \cdot b \).

**Options:**

- \(\mathbf{A.} \frac{\mu_0}{2\pi} \ln \left( \frac{b}{a} \right) \mathbf{a_{\phi}}\)
- \(\mathbf{B.} \frac{\mu_0}{\pi} \ln \left( \frac{b}{a} \right) \mathbf{a_{\phi}}\)
- \(\mathbf{C.} \frac{\mu_0}{\pi} \ln \left( b \right) \mathbf{a_{\phi}}\)
- \(\mathbf{D.} \pi \mu_0 \ln \left( \frac{b}{a} \right) \mathbf{a_{\phi}}\)
- \(\mathbf{E.} \mathbf{0 a_{\phi}}\)
- \(\mathbf{F.} \pi \mu_0 \ln \left( \frac{a}{b} \right) \mathbf{a_{\phi}}\)
- \(\mathbf{G.} \text{None of these}\)
Transcribed Image Text:## Magnetic Field Between Two Parallel Conductors **Problem Statement:** Two parallel, infinitely long, z-axis oriented conducting cylinders of radius “a” are a distance “b” apart. “b” is much, much, greater than “a”. Both cylinders carry a current, “I”, of the same magnitude but in opposite directions. The current is flowing uniformly through the cross-section of the conductors. **Question:** Find the approximate B field at \( y = 10^3 \cdot b \). **Options:** - \(\mathbf{A.} \frac{\mu_0}{2\pi} \ln \left( \frac{b}{a} \right) \mathbf{a_{\phi}}\) - \(\mathbf{B.} \frac{\mu_0}{\pi} \ln \left( \frac{b}{a} \right) \mathbf{a_{\phi}}\) - \(\mathbf{C.} \frac{\mu_0}{\pi} \ln \left( b \right) \mathbf{a_{\phi}}\) - \(\mathbf{D.} \pi \mu_0 \ln \left( \frac{b}{a} \right) \mathbf{a_{\phi}}\) - \(\mathbf{E.} \mathbf{0 a_{\phi}}\) - \(\mathbf{F.} \pi \mu_0 \ln \left( \frac{a}{b} \right) \mathbf{a_{\phi}}\) - \(\mathbf{G.} \text{None of these}\)
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