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Chapter 26: Problem 13
Would there be a magnetic force on a piece of iron deep inside a long solenoid? Explain.
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An electron moving with velocity \(\vec{v}\) through a magnetic field \(\vec{B}\) experiences a magnetic force \(\vec{F} .\) Which of the vectors \(\vec{F}, \vec{v}\) and \(\vec{B}\) must be at right angles?
The largest lightning strikes have peak currents of around \(250 \mathrm{kA}\) flowing in essentially cylindrical channels of ionized air. How far from such a flash would the resulting magnetic field be equal to Earth's magnetic field strength, about \(50 \mu \mathrm{T} ?\)
A solid conducting wire of radius \(R\) runs parallel to the \(z\) -axis and
carries a current density given by \(\vec{J}=J_{0}(1-r / R) \hat{k},\) where
\(J_{0}\) is a constant and \(r\) is the distance from the wire axis. Find
expressions for (a) the total current in the wire and (b) the magnetic field
for \(r>R\) and \((\mathrm{c}) r
Find an expression for the magnetic field at the center of a square loop of side \(a\) carrying current \(I\).
You're designing a prosthetic ankle that includes a miniature electric motor containing a 150 -turn circular coil \(15 \mathrm{mm}\) in diameter. The motor needs to develop a maximum torque of \(3.1 \mathrm{mN} \cdot \mathrm{m} .\) The strongest magnets available that will fit in the prosthesis produce a 220 -mT field. What current do you need in your motor's coil?
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