Chapter 29: Problem 10
People with pacemakers or other mechanical devices as implants are often warned to stay away from large machinery or motors. Why?
Chapter 29: Problem 10
People with pacemakers or other mechanical devices as implants are often warned to stay away from large machinery or motors. Why?
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Get started for freeAn electromagnetic wave propagating in vacuum has electric and magnetic fields given by \(\vec{E}(\vec{x}, t)=\vec{E}_{0} \cos (\vec{k} \cdot \vec{x}-\omega t)\) and \(\vec{B}(\vec{x}, t)=\vec{B}_{0} \cos (\vec{k} \cdot \vec{x}-\omega t)\) where \(\vec{B}_{0}\) is given by \(\vec{B}_{0}=\vec{k} \times \vec{E}_{0} / \omega\) and the wave vector \(\vec{k}\) is perpendicular to both \(\vec{E}_{0}\) and \(\vec{B}_{0} .\) The magnitude of \(\vec{k}\) and the angular frequency \(\omega\) satisfy the dispersion relation, \(\omega /|\vec{k}|=\left(\mu_{0} \epsilon_{0}\right)^{-1 / 2},\) where \(\mu_{0}\) and \(\epsilon_{0}\) are the permeability and permittivity of free space, respectively. Such a wave transports energy in both its electric and magnetic fields. Calculate the ratio of the energy densities of the magnetic and electric fields, \(u_{B} / u_{E}\), in this wave. Simplify your final answer as much as possible.
A long solenoid with cross-sectional area \(A_{1}\) surrounds another long
solenoid with cross-sectional area \(A_{2}
An elastic circular conducting loop expands at a constant rate over time such that its radius is given by \(r(t)=r_{0}+v t\), where \(r_{0}=0.100 \mathrm{~m}\) and \(v=0.0150 \mathrm{~m} / \mathrm{s} .\) The loop has a constant resistance of \(R=12.0 \Omega\) and is placed in a uniform magnetic field of magnitude \(B_{0}=0.750 \mathrm{~T}\), perpendicular to the plane of the loop, as shown in the figure. Calculate the direction and the magnitude of the induced current, \(i\), at \(t=5.00 \mathrm{~s}\).
Faraday's Law of Induction states a) that a potential difference is induced in a loop when there is a change in the magnetic flux through the loop. b) that the current induced in a loop by a changing magnetic field produces a magnetic field that opposes this change in magnetic field. c) that a changing magnetic field induces an electric field. d) that the inductance of a device is a measure of its opposition to changes in current flowing through it. e) that magnetic flux is the product of the average magnetic field and the area perpendicular to it that it penetrates.
A rectangular conducting loop with dimensions \(a\) and \(b\) and resistance \(R\), is placed in the \(x y\) -plane. A magnetic field of magnitude \(B\) passes through the loop. The magnetic field is in the positive \(z\) -direction and varies in time according to \(B=B_{0}\left(1+c_{1} t^{3}\right),\) where \(c_{1}\) is a constant with units of \(1 / \mathrm{s}^{3}\) What is the direction of the current induced in the loop, and what is its value at \(t=1 \mathrm{~s}\) (in terms of \(a, b, R, B_{0},\) and \(\left.c_{1}\right) ?\)
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