Chapter 30: Electromagnetic Induction

An FM radio station broadcasts at a frequency of 100 MHz. What inductance should be paired with a 10 pF capacitor to build a receiver circuit for this station?

3. I A 10-cm-long wire is pulled along a U-shaped conducting rail in a perpendicular magnetic field. The total resistance of the wire and rail is$0.20\Omega$ . Pulling the wire at a steady speed of$4.0\text{m}/\text{s}$ causes $4.0\text{W}$of power to be dissipated in the circuit.

a. How big is the pulling force?

b. What is the strength of the magnetic field?

A vertical, rectangular loop of copper wire is half in and half out of the horizontal magnetic field in FIGURE (The field is zero beneath the dashed line.) The loop is released and starts to fall. Is there a net magnetic force on the loop? If so, in which direction? Explain

A 2.0 mH inductor is connected in parallel with a variable capacitor. The capacitor can be varied from 100 pF to 200 pF. What is the range of oscillation frequencies for this circuit?

An MRI machine needs to detect signals that oscillate at very high frequencies. It does so with an LC circuit containing a 15 mH coil. To what value should the capacitance be set to detect a 450 MHz signal?

An LC circuit has a 10 mH inductor. The current has its maximum value of 0.60 A at t = 0 s. A short time later the capacitor reaches its maximum potential difference of 60 V. What is the value of the capacitance?

The switch in FIGURE EX30.33 has been in position 1 for a long time. It is changed to position 2 at t = 0 s. a. What is the maximum current through the inductor? b. What is the first time at which the current is maximum?

What value of resistor$\mathrm{R}$gives the circuit in FIGURE $\mathrm{EX}30.34$a time constant of$25\mathrm{\mu s}$$?$

At , the current in the$\mathrm{t}=0\mathrm{s}$circuit in FIGURE $\mathrm{EX}30.35$is ${\mathrm{I}}_0$. At what time is the current $\frac{1}{2}{\mathrm{I}}_0$

The switch in FIGURE $\mathrm{EX}30.36$has been open for a long time. It is closed at $\mathrm{t}=0\mathrm{s}$.

a. What is the current through the battery immediately after the switch is closed$?$

b. What is the current through the battery after the switch has been closed a long time$?$