Chapter 8: Problem 8
Two conducting strips, having infinite length in the \(z\) direction, lie in the
\(x z\) plane. One occupies the region \(d / 2
Chapter 8: Problem 8
Two conducting strips, having infinite length in the \(z\) direction, lie in the
\(x z\) plane. One occupies the region \(d / 2
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Get started for freeAssume that an electron is describing a circular orbit of radius \(a\) about a positively charged nucleus. (a) By selecting an appropriate current and area, show that the equivalent orbital dipole moment is \(e a^{2} \omega / 2\), where \(\omega\) is the electron's angular velocity. \((b)\) Show that the torque produced by a magnetic field parallel to the plane of the orbit is \(e a^{2} \omega B / 2 .(c)\) By equating the Coulomb and centrifugal forces, show that \(\omega\) is \(\left(4 \pi \epsilon_{0} m_{e} a^{3} / e^{2}\right)^{-1 / 2}\), where \(m_{e}\) is the electron mass. \((d)\) Find values for the angular velocity, torque, and the orbital magnetic moment for a hydrogen atom, where \(a\) is about \(6 \times 10^{-11} \mathrm{~m} ;\) let \(B=0.5 \mathrm{~T}\).
A coaxial cable has conductor radii \(a\) and \(b\), where \(a
Calculate values for \(H_{\phi}, B_{\phi}\), and \(M_{\phi}\) at \(\rho=c\) for a coaxial cable with \(a=2.5 \mathrm{~mm}\) and \(b=6 \mathrm{~mm}\) if it carries a current \(I=12 \mathrm{~A}\) in the center conductor, and \(\mu=3 \mu \mathrm{H} / \mathrm{m}\) for \(2.5 \mathrm{~mm}<\rho<3.5 \mathrm{~mm}, \mu=5 \mu \mathrm{H} / \mathrm{m}\) for \(3.5 \mathrm{~mm}<\rho<4.5 \mathrm{~mm}\), and \(\mu=10 \mu \mathrm{H} / \mathrm{m}\) for \(4.5 \mathrm{~mm}<\rho<6 \mathrm{~mm}\). Use \(c=:(a) 3 \mathrm{~mm} ;(b) 4 \mathrm{~mm} ;(c) 5 \mathrm{~mm} .\)
Show that the external inductance per unit length of a two-wire transmission line carrying equal and opposite currents is approximately \((\mu / \pi) \ln (d / a)\) \(\mathrm{H} / \mathrm{m}\), where \(a\) is the radius of each wire and \(d\) is the center-to-center wire spacing. On what basis is the approximation valid?
A point charge for which \(Q=2 \times 10^{-16} \mathrm{C}\) and \(m=5 \times 10^{-26} \mathrm{~kg}\) is moving in the combined fields \(\mathbf{E}=100 \mathbf{a}_{x}-200 \mathbf{a}_{y}+300 \mathbf{a}_{z} \mathrm{~V} / \mathrm{m}\) and \(\mathbf{B}=-3 \mathbf{a}_{x}+\) \(2 \mathbf{a}_{y}-\mathbf{a}_{z} \mathrm{mT}\). If the charge velocity at \(t=0\) is \(\mathbf{v}(0)=\left(2 \mathbf{a}_{x}-3 \mathbf{a}_{y}-\right.\) \(\left.4 \mathrm{a}_{z}\right) 10^{5} \mathrm{~m} / \mathrm{s}(a)\) give the unit vector showing the direction in which the charge is accelerating at \(t=0 ;(b)\) find the kinetic energy of the charge at \(t=0 .\)
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