Chapter 7: Problem 3
Two semi-infinite filaments on the \(z\) axis lie in the regions \(-\infty
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Chapter 7: Problem 3
Two semi-infinite filaments on the \(z\) axis lie in the regions \(-\infty
These are the key concepts you need to understand to accurately answer the question.
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Get started for freeA filamentary conductor carrying current \(I\) in the \(\mathbf{a}_{z}\) direction extends along the entire negative \(z\) axis. At \(z=0\) it connects to a copper sheet that fills the \(x>0, y>0\) quadrant of the \(x y\) plane. \((a)\) Set up the Biot-Savart law and find \(\mathrm{H}\) everywhere on the \(z\) axis; \((b)\) repeat part \((a)\), but with the copper sheet occupying the entire \(x y\) plane (Hint: express \(\mathbf{a}_{\phi}\) in terms of \(\mathbf{a}_{x}\) and \(\mathbf{a}_{y}\) and angle \(\phi\) in the integral).
A filamentary conductor on the \(z\) axis carries a current of \(16 \mathrm{~A}\)
in the \(\mathbf{a}_{z}\) direction, a conducting shell at \(\rho=6\) carries a
total current of \(12 \mathrm{~A}\) in the \(-\mathbf{a}_{z}\) direction, and
another shell at \(\rho=10\) carries a total current of \(4 \mathrm{~A}\) in the
\(-\mathbf{a}_{z}\) direction. \((a)\) Find \(\mathbf{H}\) for \(0<\rho<12
.\left(\right.\) b) Plot \(H_{\phi}\) versus \(\rho\).
(c) Find the total flux \(\Phi\) crossing the surface \(1<\rho<7,0
A disk of radius \(a\) lies in the \(x y\) plane, with the \(z\) axis through its center. Surface charge of uniform density \(\rho_{s}\) lies on the disk, which rotates about the \(z\) axis at angular velocity \(\Omega \mathrm{rad} / \mathrm{s}\). Find \(\mathbf{H}\) at any point on the \(z\) axis.
A current filament carrying \(I\) in the \(-\mathbf{a}_{z}\) direction lies along the entire positive \(z\) axis. At the origin, it connects to a conducting sheet that forms the \(x y\) plane. (a) Find \(\mathbf{K}\) in the conducting sheet. \((b)\) Use Ampere's circuital law to find \(\mathbf{H}\) everywhere for \(z>0 ;(c)\) find \(\mathbf{H}\) for \(z<0\).
Assume that there is a region with cylindrical symmetry in which the conductivity is given by \(\sigma=1.5 e^{-150 \rho} \mathrm{kS} / \mathrm{m}\). An electric field of \(30 \mathbf{a}_{z} \mathrm{~V} / \mathrm{m}\) is present. ( \(a\) ) Find \(\mathbf{J}\). \((b)\) Find the total current crossing the surface \(\rho<\rho_{0}\), \(z=0\), all \(\phi\). ( \(c\) ) Make use of Ampère's circuital law to find \(\mathbf{H}\).
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