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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 flip coil is used to measure magnetic fields. It's a small coil placed with its plane perpendicular to a magnetic field, and then flipped through \(180^{\circ} .\) The coil is connected to an instrument that measures the total charge \(Q\) that flows during this process. If the coil has \(N\) turns, area \(A\), and resistance \(R,\) show that the field strength is \(B=Q R / 2 N A.\)
A circular wire loop of radius \(a\) and resistance \(R\) is pulled with constant speed \(v\) into a uniform magnetic field \(B .\) The loop is perpendicular to the field, and it begins entering the field at time \(t=0 .\) Find an expression for the current in the loop from \(t=0\) until the loop is fully immersed in the field.
A 2000 -turn solenoid is \(2.0 \mathrm{m}\) long and \(15 \mathrm{cm}\) in diameter. The solenoid current is increasing at \(1.0 \mathrm{kA} / \mathrm{s} .\) (a) Find the current in a 10 -cm-diameter wire loop with resistance \(5.0 \Omega\) lying inside the solenoid and perpendicular to the solenoid axis. (b) Repeat for a similarly oriented 25 -cm-diameter loop with the same resistance, lying entirely outside the solenoid.
The table below shows the current in a circuit like that of Fig. \(27.26,\) where a current has been established with the switch in position \(A,\) and then it's thrown to position \(B\) at time \(t=0\) The resistance is \(180 \Omega .\) Determine an appropriate function of current that, when plotted against time, should produce a straight line. Make your plot, determine a best-fit line, and use its slope to find the inductance in the circuit. $$\begin{array}{|l|c|c|c|c|c|c|} \hline \text { Time (ms) } & 0 & 20.0 & 40.0 & 60.0 & 80.0 & 100.0 \\ \hline \text { Current (mA) } & 66.5 & 23.0 & 9.15 & 3.56 & 1.50 & 0.450 \\ \hline \end{array}$$
A generator consists of a rectangular coil \(75 \mathrm{cm}\) by \(1.3 \mathrm{m},\) spinning in a 0.14 -T magnetic field. If it's to produce a \(60-\mathrm{Hz}\) alternating emf with peak value \(6.7 \mathrm{kV},\) how many turns must it have?
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