Why do some appliances have step-down transformers built in?

A rectangular loop of current-carrying wire sits above a long, straight, current-carrying wire. The rectangular loop has a current running clockwise, and the long, straight wire has a current running to the left. (a) Determine the direction of the magnetic force on each of the four sides of the rectangular loop. (b) Determine the direction of the net force on the rectangular loop of wire. Justify your answer.

In the given figure, a long straight wire carries a current i1=30.0 A and a rectangular loop carries current i2=20.0 A. Take a=1.00 cm, b=8.00 cm, and L=30.0 cm. In unitvector notation, what is the net force on the loop due to $i_1$ ?

At what frequency is the reactance of a 20.0 mH inductor equal to 18.8 $\Omega$?

A $0.30 \mu \mathrm{F}$ capacitor is connected across an AC generator that produces a peak voltage of 10 V. What is the peak current to and from the capacitor if the emf frequency is (a) 100 Hz? (b) 100 kHz?

A $20 \mu \mathrm{F}$ capacitor is connected across an AC generator that produces a peak voltage of 6.0 V. The peak current is 0.20 A. What is the oscillation frequency in Hz?

An inductor and capacitor are connected in series across an AC generator, and the voltage across the inductor is higher than across the capacitor. Is the generator frequency above or below resonance?

In a home stereo system, low sound frequencies are handed by large "woofer" speakers, and high frequencies by smaller "tweeter" speakers. For the best sound reproduction, low-frequency currents from the amplifier should not reach the tweeter. One way to do this is to place a capacitor in series with the $8.0 \Omega$ resistance of the tweeter; one then has an $R L C$ circuit with no inductor $L$ (that is, an $R L C$ circuit with $L=0$ ). What value of $C$ should be chosen so that the current through the tweeter at $200 \mathrm{~Hz}$ is half its value at very high frequencies?

Make an order-of-magnitude estimate of the quantity. -The inductance needed for a low-pass filter for the 8-$\Omega$ sub-woofer (very-low-frequency speaker) in a home stereo system.

Some electronic devices such as phones and watches can be charged wirelessly. In the charger, there is a coil that generates a rapidly changing magnetic field. In the device, there is a second, 100-turn rectangular coil with side lengths of $3.0 \mathrm{~cm}$ and $4.0 \mathrm{~cm}$. If the maximum rate of change of the magnetic field in this second coil is $53 \mathrm{~T} / \mathrm{s}$, what is the emf induced in this coil?

Two wires carrying electric current in the same direction are side by side and are attracted to each other. Predict how the force between the wires changes if the current in both wires changes direction.

At a point near the equator, the Earth's magnetic field is horizontal and points to the north. If an electron is moving vertically upward at this point, does the magnetic force acting on it point north, south, east, west, upward, or downward? Explain.

At the equator, the earth's field is essentially horizontal; near the north pole, it is nearly vertical. In between, the angle varies. As you move farther north, the dip angle, the angle of the earth's field below horizontal, steadily increases. Green turtles seem to use this dip angle to determine their latitude. Suppose you are a researcher wanting to test this idea. You have gathered green turtle hatchlings from a beach where the magnetic field strength is $50 \mu \mathrm{T}$ and the dip angle is $56^{\circ}$. You then put the turtles in a $1.2-\mathrm{m}$-diameter circular tank and monitor the direction in which they swim as you vary the magnetic field in the tank. You change the field by passing a current through a 100-turn horizontal coil wrapped around the tank. This creates a field that adds to that of the earth. What current should you pass through the coil, and in what direction, to produce a net field in the center of the tank that has a dip angle of $62^{\circ}$?

Alight-emitting diode (LED) connected to a 3.0 V power supply emits 440 nm blue light. The current in the LED is 10 mA, and the LED is 60% efficient at converting electric power input into light power output. How many photons per second does the LED emit?