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Chapter 27: Problem 29
Show that the quantity \(B^{2} / 2 \mu_{0}\) has the units of energy density.
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A conducting loop of area \(240 \mathrm{cm}^{2}\) and resistance \(12 \Omega\) is perpendicular to a spatially uniform magnetic field and carries a \(320-\mathrm{mA}\) induced current. At what rate is the magnetic field changing?
A square wire loop of side \(l\) and resistance \(R\) is pulled with constant speed \(v\) from a region of no magnetic field until it's fully inside a region of constant, uniform magnetic field \(\vec{B}\) perpendicular to the loop plane. The boundary of the field region is parallel to one side of the loop. Find an expression for the total work done by whatever is pulling the loop.
A 5 -turn coil \(1.0 \mathrm{~cm}\) in diameter is rotated at \(10 \mathrm{rev} / \mathrm{s}\) about an axis perpendicular to a uniform magnetic field. A voltmeter connected to the coil through rotating contacts reads a peak value \(360 \mu \mathrm{V}\). What's the magnetic-field strength?
A single-turn loop of radius \(R\) carries current \(I .\) How does the magnetic- energy density at the loop center compare with that of a long solenoid of the same radius, carrying the same current, and consisting of \(n\) turns per unit length?
What inductance should you put in series with a \(150-\Omega\) resistor to give a time constant of \(2.2 \mathrm{ms} ?\)
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