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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An ideal battery (with no internal resistance) supplies \(V_{\mathrm{emf}}\) and is connected to a superconducting (no resistance!) coil of inductance \(L\) at time \(t=0 .\) Find the current in the coil as a function of time, \(i(t) .\) Assume that all connections also have zero resistance.
A wedding ring (of diameter \(2.0 \mathrm{~cm}\) ) is tossed into the air and given a spin, resulting in an angular velocity of 17 rotations per second. The rotation axis is a diameter of the ring. Taking the magnitude of the Earth's magnetic field to be \(4.0 \cdot 10^{-5} \mathrm{~T}\), what is the maximum induced potential difference in the ring?
An 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.
Having just learned that there is energy associated with magnetic fields, an inventor sets out to tap the energy associated with the Earth's magnetic field. What volume of space near Earth's surface contains \(1 \mathrm{~J}\) of energy, assuming the strength of the magnetic field to be \(5.0 \cdot 10^{-5} \mathrm{~T} ?\)
A short coil with radius \(R=10.0 \mathrm{~cm}\) contains \(N=30.0\) turns and surrounds a long solenoid with radius \(r=8.00 \mathrm{~cm}\) containing \(n=60\) turns per centimeter. The current in the short coil is increased at a constant rate from zero to \(i=2.00 \mathrm{~A}\) in a time of \(t=12.0 \mathrm{~s}\). Calculate the induced potential difference in the long solenoid while the current is increasing in the short coil.
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