Physics 106 - Midterm Exam

Physics 106 - How Things Work - Spring, 2001

Midterm Examination

Given Friday, March 2, from 1:00 PM to 1:50 PM

PART I: MULTIPLE CHOICE QUESTIONS

Please mark the correct answer for each question on the bubble sheet. Fill in the dot completely with #2 pencil. Part I is worth 67% of the grade on the midterm examination.

Problem 1:

You are watching children play a game of tug-o-war with an old plastic clothesline. The two teams are pulling at opposite ends of the cord and each team is trying to drag the other team into a mud puddle that lies between them. After a few minutes without progress, the team on the right suddenly pulls hard toward the right. The team on the left has anticipated this threat and is able to keep their end of the rope from moving at all. The right end of the rope stretches toward the right and the rope breaks. It took energy to breaking the rope and that energy was provided by

(A) the team on the right.

(B) the team on the left.

(D) both teams.

Answer: (A) the team on the right.

Why: The team on the right pulled the rope to the right and the rope moved to the right, therefore the team on the right did work on the rope. The team on the left may have pulled on the rope, but their end of the rope didn’t move so they did no work on the rope.

Problem 2:

While an insulator is nearly perfect at preventing the flow of electric current, a semiconductor will permit some current to flow, even in the dark. This current flow is a consequence of thermal energy. In the semiconductor, thermal energy shifts electrons between levels so that

(A) both the valence band and the conduction band become full.

(B) the valence band becomes full, while the conduction band becomes empty.

(D) the valence band has a few empty levels and the conduction band has a few filled levels.

Answer: (D) the valence band has a few empty levels and the conduction band has a few filled levels.

Why: In a semiconductor at low temperatures, all the valence levels are filled with electrons and all the conduction levels are empty. That’s what makes the semiconductor insulating. But when there is enough thermal energy around, some valence level electrons are shift into conduction levels and there is opportunity for electrons to move in response to electric fields. The semiconductor can then conduct current slightly.

Problem 3:

You were heading forward in your car before coming to a complete stop at a red light. The careless driver of the car behind you fails to stop and his car crashes into your car from behind. You suddenly find your head shifted deep into the elastic cushion of your seat's headrest. During the period when your head is deep in the cushion, the net force on your head is

(A) backward and its acceleration is backward.

(B) forward and its acceleration is forward.

(D) zero and it is not accelerating.

Answer: (B) forward and its acceleration is forward.

Why: When you head is at equilibrium, the cushion is normally not dented much. Since your head is denting the cushion deeply, your head is not at equilibrium. The cushion is distorted and is pushing your head forward to get your head out of the cushion. This forward force on your head is the only horizontal force on your head (other than a weak force from your neck), so your head accelerates forward.

Problem 4:

When you bounce a rubber ball off a concrete wall, the ball rebounds at nearly its original speed. During the bounce, the ball

(A) transfers a great deal of momentum and energy to the wall.

(B) retains essentially all of its momentum but transfers a great deal of energy to the wall.

(D) retains essentially all of its energy but transfers a great deal of momentum to the wall.

Answer: (D) retains essentially all of its energy but transfers a great deal of momentum to the wall

Why: Momentum is a vector and has a direction while energy is a scalar and does not have a direction. When the ball reverses direction in the bounce, its momentum changes dramatically. However, it retains nearly all of its kinetic and potential energies.

Problem 5:

A woman leaps off the high diving board during a swimming competition and does a series of flips and spins in the air. As she plunges toward the water, her

(A) angular velocity is constant.

(B) angular momentum is constant.

(D) velocity is constant.

Answer: (B) angular momentum is constant.

Why: Since she is not touching anything and is traveling too slowly for air resistance to be significant, the only force acting on her is gravity. Gravity changes her momentum and her velocity. As she bends her body, her angular velocity changes. The only thing that is retained throughout her motion is her angular momentum—she is experiencing no torques about her center of mass, so her angular momentum about her center of mass is constant. Gravity can’t exert a torque on her about her center of mass and affects only her translational motion, not her rotational motion.

Problem 6:

Suppose that you remove the batteries from an ordinary flashlight, turn them all around, and reinsert them into the flashlight. The batteries and the flashlight’s wires all make good contacts, so that there is no unexpected break in the flashlight’s circuit. If you now turn the flashlight on, it will

(A) glow about twice as bright as usual, but the bulb will burn out soon.

(B) not emit any light.

(D) glow about half as bright as usual.

Answer: (C) work normally.

Why: As I demonstrated in class, the flashlight works fine. The light bulb doesn’t care which way current flows through it. Reversing the batteries simply reverses the direction of current flow in the flashlight’s circuit and the bulb lights up anyway.

Problem 7:

You let a permanent bar magnet align freely with an extremely strongly magnetic field. You then rotate the permanent magnet 180° so that it appears to be pointing the wrong way. If you now let the permanent magnet turn freely it will

(A) rotate 180° because it has been demagnetized and is no longer magnetic.

(B) rotate 180° because permanent magnets can’t be remagnetized.

(D) not rotate because it has been demagnetized and is no longer magnetic.

Answer: (C) not rotate because it has been remagnetized and is already aligned with the field.

Why: Exposing a permanent magnet to a very strong magnetic field will remagnetize that magnet. In the present case, the permanent magnet is remagnetized by the strong field and becomes aligned with it, no matter which way you turn it in space.

Problem 8:

You have two boxes. In Box A, there is only an electric field that points northward. In Box B, there is only a magnetic field that points westward. You hold a positive charge motionless in each box and then let it go. (Ignore gravity)

(A) The charge in Box A accelerates northward, while the charge in Box B accelerates westward.

(B) The charge in Box A remains motionless, while the charge in Box B accelerates westward.

(D) The charge in Box A accelerates southward, while the charge in Box B accelerates eastward.

Answer: (C) The charge in Box A accelerates northward, while the charge in Box B remains motionless.

Why: Magnetic fields have no effect on motionless electric charges. Thus the charge in Box B has no forces on it and remains motionless. Electric fields push positive charges in the direction of the fields, so the charge in Box A accelerates in the direction of the electric field in Box A, which is northward.

Problem 9:

If you hold a stationary positive charge in your left hand and a stationary north magnetic pole in your right hand, the positive charge would exert

(A) a leftward force on the north magnetic pole.

(B) zero force on the north magnetic pole.

(D) an upward force on the north magnetic pole.

Answer: (B) zero force on the north magnetic pole.

Why: A stationary charge is nonmagnetic and thus exerts no force on a stationary north magnetic pole.

Problem 10:

A needle-sharp lightning rod protects the top of a tall tower. This rod is connected by a wire to the earth far below. When a positively charged cloud passes over the tower, the lightning rod

(A) becomes negatively charged and begins to emit negative charges onto passing air particles which help to neutralize the cloud.

(B) becomes negatively charged and repels any lightning strikes so that they hit far away from the tower.

(D) becomes positively charged and repels any lightning strikes so that they hit far away from the tower.

Answer: (A) becomes negatively charged and begins to emit negative charges onto passing air particles which help to neutralize the cloud.

Why: The positive cloud polarizes the earth and lightning rod. Negative charges are attracted up the wire to the tip of the lightning rod while positive charges are repelled down that wire. The rod becomes negatively charged and because of its sharp tip, it emits the negative charges via a corona discharge. These negative charges drift upward and help to neutralize the cloud. That’s how lightning rods actually diminish the threat of lightning.

Problem 11:

A positively charged dust particle will stick to an electrically neutral wall because the dust particle will

(A) charge the wall by causing negative charge to be created at the surface of the wall so that the wall and dust attract.

(B) induce an electric current in the wall, making the wall magnetic so that it attracts the dust particle magnetically.

(C) charge the wall by transferring part of its positive charge to the wall so that the wall and dust attract one another.

(D) polarize the wall, shifting the wall’s negative charges toward the dust and the wall’s positive charges away from the dust.

Answer: (D) polarize the wall, shifting the wall’s negative charges toward the dust and the wall’s positive charges away from the dust.

Why: Charge is a conserved quantity, so the wall can’t create charge. Instead, it can shift what charge it has so that it ultimately attracts the charged dust. The wall shifts its negative charges toward the dust and shifts its positive charges away. Though those charges only move tiny distances, the overall shift leads to a polarization of the wall (the wall has a negative surface and a positive interior) and the wall attracts the dust.

Problem 12:

Moment of inertia is the measure of an object’s rotational inertia. If you wanted to figure out which of two round, symmetric objects has the largest moment of inertia, you should

(A) spin each object in your hand and then drop it to the floor. The one that falls fastest while spinning has the larger moment of inertia.

(B) lift each object and see which one takes the most force to lift upward at constant velocity.

(D) spin each object in your hand and then drop it to the floor. The one that falls slowest while spinning has the larger moment of inertia.

Answer: (C) twist each object back and forth about its center and see which one responds least rapidly.

Why: To see which object has the most rotational inertia, you need to see how much torque is needed to produce a certain angular acceleration. By twisting an object back and forth, you can get an idea of how quickly it undergoes angular acceleration in response to a certain torque. The harder it is to twist the object back and forth, the more rotational inertia is has, or the larger its moment of inertia.

Problem 13:

A permanent magnet sticks motionlessly to the steel front of your refrigerator because the permanent magnet

(A) shifts the electrons and protons in the steel slightly apart, so that a magnetic polarization occurs. The protons have north magnetic poles and the electrons have south magnetic poles.

(B) causes currents to flow in the steel, making the steel magnetic so that it attracts the poles of the permanent magnet.

(D) attracts isolated magnetic poles (also known as monopoles) in the steel toward the surface of the steel, where they bind strongly to the poles of the permanent magnet.

Answer: (C) aligns the magnetic domains in the steel so that they attract the poles of the permanent magnet.

Why: The steel in the refrigerator has countless tiny magnetic domains in it, each with a north pole and a south pole. However, they normally point in random directions and the refrigerator appears nonmagnetic. But when you bring a permanent magnet near the refrigerator, the domains in the steel begin to change and they align so as to attract the approaching permanent magnet.

Problem 14:

The secondary coil of a transformer normally winds in one direction around and around the magnetic core. Instead of going all the way around the core, it would be easier for the wire to go half way around the core and then turn around and head back toward its starting point. It could do this many times, creating a zigzag pattern that never actually goes all the way around the core. Such a secondary wire would produce

(A) only half as large a voltage rise as a normal secondary coil.

(B) only a quarter as large a voltage rise as a normal secondary coil.

(D) zero net voltage rise in any current passing through it.

Answer: (D) zero net voltage rise in any current passing through it.

Why: Any charge that travels through the secondary wire will travel alternately with the electric field and against the electric field as it zigzags through the wire. Any work done on it during a zig will be undone during a zag. The net work done on a charge passing through the secondary wire is zero. To permanently extract energy from the transformer’s magnetic and electric fields, the charges must go all the way around the magnetic core and never return the other way.

Problem 15:

The lamp on your desk has a short circuit. A fragment of metal is connecting the two wires at the point where the bulb screws into the socket. Because of this short circuit, the bulb glows

(A) normally, but the current in the lamp’s power cord is smaller than usual.

(B) dimly or not at all, but the current in the lamp’s power cord is larger than usual.

(D) more brightly than normal and is likely to burn out.

Answer: (B) dimly or not at all, but the current in the lamp’s power cord is larger than usual.

Why: With a short circuit allowing current to bypass the bulb and its filament, the bulb has little current passing through it and glows dimly. Most of the current takes the bypass and experiences little voltage drop in doing so. With nothing in the circuit that drops voltage easily, the current that flows in the circuit goes up and up. Eventually the current becomes so high that even the wires begin to have large voltage drops across them and all the available voltage is used up in the circuit. But the current is now very large and the power wasted in the wires is dangerously large.

Problem 16:

The cord of your desk lamp has two wires inside it. It needs two wires because

(A) the power company provides both electric and magnetic power. One wire carries electric power and the other wire carries magnetic power.

(B) one wire carries current to the lamp and the other wire carries current back to the power company.

(D) north and south magnetic poles cannot be separated from one another. The north and south poles must travel together on the two wires.

Answer: (B) one wire carries current to the lamp and the other wire carries current back to the power company.

Why: For current to flow for more than an instant, it needs a complete circuit. Current must follow a looping path. In the lamp, this circuit involves current traveling to the lamp through one wire and returning from the lamp through the other wire.

Problem 17:

If you want to send lots of electric power to a distant consumer and not waste very much of that power, you should use

(A) a very small current of very high voltage charges.

(B) a very small current of very low voltage charges.

(D) a very large current of very low voltage charges.

Answer: (A) a very small current of very high voltage charges.

Why: The power wasted in a wire is proportional to the square of the current passing through that wire. You should therefore minimize the current in the wire. But to deliver a significant amount of power through the wire, you should boost the voltage of the current as high as possible. In that manner, you ensure that each charge that travels through the wire carries with it as much energy as possible.

Problem 18:

Suppose you have two identical-looking sticks, each with exactly the same total mass. In one stick, most of the mass is located at its ends. In the other stick, most of the mass is located at the middle. If you grip both sticks at the middle and exert equal torques on them with your wrists,

(A) the sticks will undergo equal accelerations because they have equal masses.

(B) the stick with its mass near its ends will undergo more angular acceleration.

(D) the sticks will undergo equal accelerations because they have equal moments of inertia.

Answer: (C) the stick with its mass near its middle will undergo more angular acceleration.

Why: An object’s moment of inertia depends on its shape and the location of its mass. By moving as much of its mass as possible as close as possible to the pivot, you reduce the object’s moment of inertia and make it easier to twist back and forth. We demonstrated this effect in class.

Problem 19:

You jump off of a diving board into a swimming pool. As you fall toward the water, your velocity

(A) increases, but your acceleration remains constant

(B) increases because your acceleration increases

(D) remains constant because your acceleration is constant

Answer: (A) increases, but your acceleration remains constant

Why: A falling object, such as you, experiences only the constant downward force of gravity. Your acceleration is downward and constant, and your velocity becomes faster and faster in the downward direction.

Problem 20:

When it moves slowly on a calm lake, a canoe will coast almost forever at constant velocity. Suppose that two canoes are both coasting northward at constant velocity (no one is paddling) when the rear canoe bumps into the canoe in front of it. There is a loud “thump” sound. Despite the collision, the total

(A) velocity of the two canoes remains unchanged.

(B) kinetic energy of the two canoes remains unchanged.

(D) thermal energy of the two canoes remains unchanged.

Answer: (C) momentum of the two canoes remains unchanged.

Why: Only total momentum and total energy are conserved quantities, so the total velocity is uninteresting and unlikely to remain unchanged in a collision. The total energy will remain unchanged, but the individual types of energy, such as the kinetic energy or thermal energy, may well change. That leaves total momentum and total momentum is unchanged in this collision.

Problem 21:

A battery

(A) creates negative charge.

(B) creates positive charge.

(D) pumps positive charge from its negative terminal to its positive terminal.

Answer: (D) pumps positive charge from its negative terminal to its positive terminal.

Why: A battery pushes electric charge against its natural direction of flow. It does work as it transfers positive charge from where that positive charge naturally tends to go—the negative terminal—to where that charge tends to avoid—the positive terminal.

Problem 22:

A toy top spins for a long time on its point. If you made the point sharper, the top would spin longer because

(A) the force the top exerts on the floor becomes smaller.

(B) the parts of the sharper point travel less far against the force of sliding friction.

(D) the support force that the floor exerts on the top becomes larger.

Answer: (B) the parts of the sharper point travel less far against the force of sliding friction.

Why: To minimize the work done wastefully against sliding friction, the distance traveled against that force should be as short as possible. By sharpening the top’s tip, you shrink the circumference of that tip and reduce the distance any parts of it travel against sliding friction with the floor.

Problem 23:

Copper is a nonmagnetic metal. When you move the north pole of a bar magnet toward a sheet of copper,

(A) current flows through the copper and repels the approaching north pole.

(B) nothing happens to the copper.

(D) current flows through the copper and attracts the approaching north pole.

Answer: (A) current flows through the copper and repels the approaching north pole.

Why: A moving magnetic field is accompanied by an electric field. In this case, that electric field pushes charges through the copper and creates currents in the copper. That current is magnetic, so the copper sheet has a magnetic field. And in accordance with Lenz’s law, the induced magnetism in the sheet acts to fight the magnetic field change that caused it. In this case, the current in the copper sheet repels the approaching magnet so as to keep the local magnetic field from increasing.

Problem 24:

There are no permanent magnets made out of pure aluminum metal because aluminum

(A) does not have enough mass to overcome the inertia of permanent magnetism.

(B) is a soft magnetic material and quickly demagnetizes when you remove it from any external magnetic fields.

(D) has no internal magnetic structure at all.

Answer: (D) has no internal magnetic structure at all.

Why: Aluminum is a nonmagnetic metal, meaning that it has no magnetism, even at the atomic level. Although isolated aluminum atoms are magnetic, when they bind together to form a solid that magnetism vanishes.

Problem 25:

A current loses energy as it flows through a wire. Because of this loss of energy, the current experiences a

(A) voltage rise as it passes through the wire and a magnetic field therefore pushes the current forward.

(B) voltage rise as it passes through the wire and an electric field therefore pushes the current forward.

(D) voltage drop as it passes through the wire and an electric field therefore pushes the current forward.

Answer: (D) voltage drop as it passes through the wire and an electric field therefore pushes the current forward.

Why: To keep current flowing forward through a wire, as the wire wastes the currents energy, something must push that current forward and do work on it. The only thing that can do this work is an electric field, so a wire develops an electric field as current passes through it. This electric field is associated with a gradual drop in voltage through the wire.

PART II: SHORT ANSWER QUESTIONS

Please give a brief answer in the space provided. Part II is worth 33% of the grade on the midterm examination.

Problem 1:

You may have noticed that when you use a power-hungry appliance such as a hairdryer in the other socket of an electric outlet that already has a lamp plugged into it, the lamp dims slightly. Let’s examine why. To begin with, suppose that only a lamp is plugged into the outlet in your room and that the lamp is turned on.

(A) Current travels between the power lines outside and the electric outlet inside through moderately thick wires. Between the point at which this current leaves the power lines for your home and the point at which it returns to the power lines from your home, it experiences a voltage drop of 120 volts. More specifically, the current experiences voltage drops in each of the two wires that connect the outlet to the power lines (the “house wires”) and in the lamp itself. How are these three voltage drops: (x) power line to outlet, (y) outlet to power line, and (z) through the lamp, related to one another or to 120 volts?

Answer: Two different answers are possible, with either answer worth full credit: (1) The sum of (x) + (y) + (z) is equal to 120 volts (the sum of the voltage drops in the two wires and the lamp is equal to the voltage difference between the point where current starts toward your home and where it returns to the power lines) or (2) The voltage drop in the lamp is larger than the voltage drop in either wire and the voltage drops in the two wires are roughly equal to one another.

Why: As current flows first through (x), then through (z), then through (y), it loses voltage. The current’s energy is being converted into thermal energy. The sum of the voltage drops in (x)+(y)+(z) is simply the total voltage drop in that entire portion of the circuit. The sum must be 120 volts, since that is the total voltage drop between the point at which current heads toward the home and where it returns from the home.

(B) How does the current passing through the lamp compare to the currents passing through each of the two house wires?

Answer: The current in the lamp is equal to the current in either of the two house wires.

Why: Charge is conserved and it also can’t be accumulated indefinitely on any segment of wire. Therefore, any current that passes through the wire heading toward the lamp must also head through the lamp and then through the wire heading away from the lamp. The currents in all three segments are thus the same current and are equal in amount.

(C) You plug a hairdryer into the other socket of the same electric outlet and turn it on. Current that arrives at the outlet through one house wire now passes through either of the two appliances (lamp or hairdryer) before returning to the power lines through the second house wire. With more opportunities to flow from one house wire to the other, the current passing through the circuit increases dramatically. How does this current increase in the house wires affect the voltage drop through each house wire?

Answer: The voltage drop in each house wire increases.

Why: The voltage drop in each house wire is proportional to the current flowing through that wire. That’s because each house wire is “ohmic” and has a voltage drop that is equal to its electric resistance times the current passing through it. More current produces more voltage drop.

(D) What effect does this change in the voltage drop through each house wire have on the voltage drop in the lamp, the current through the lamp, and power consumed by the lamp? (Just state the answers, don’t tell us why.)

Answer: The voltage drop in the lamp decreases, the current through the lamp decreases, and the power consumed by the lamp decreases.

Why: With more voltage drop in the house wires, there is less voltage drop available for the lamp. The lamp experiences a smaller voltage drop. Since the lamp is also roughly ohmic, as the voltage drop through it decreases, so does the amount of current passing through it. And since the power delivered to the lamp is equal to the current passing through it times the voltage drop through it, the power delivered to the lamp decreases substantially. That’s why it becomes dimmer.

Problem 2:

Ensuring fair play at the Olympics has never been easy, both on the field and off. With your tremendous understanding of physics, you've received many lucrative offers to help the scoundrels, but you've held fast to the traditions of the UVa honor system and refused them all. Instead, you have become the world's foremost authority on sneaky Olympic tricks and have foiled dozens of evil plots. Here are a few of your most famous cases:

(A) The Tomanian cycling team once placed a series of strong magnets beneath the bicycle track and slowed the progress of any athlete riding an aluminum alloy bicycle. You discovered the magnets and fingered the Tomanian team because they were the only people riding bicycles made entirely of plastics. Why did the magnets slow the aluminum bicycles but not the plastic ones?

Answer: Answer: Only the aluminum bicycles can conduct currents and become magnetic when they move past the track's magnets.

Why: Conducting objects that move past strong magnets experience electric fields and have currents induced in them. These currents render the objects magnetic and they experience magnetic drag forces that slow their motions.

(B) The Freedonian track team once tried to lower their times in the 5000-meter run by installing air jets all the way around the track. These jets were aimed so that they would always blow each runner forward with a force of 100 newtons. Minutes before the race, you spoiled their plans by turning half the jets around so that they blow each runner backward. As the result of your efforts, the runners traveled exactly the same distance with air jets pushing them forward at 100 newtons as they did with air jets pushing them backward at 100 newtons. Overall, how much work did the air jets do on each runner?

Answer: Zero work.

Why: Work is force times distance. Since the runners are pushed forward for half the distance and backward for half the distance, the work done on them when pushed forward is exactly cancelled by the negative work done on them when pushed backward.

(C) One of the Lilliputian high jumpers decided to give himself an advantage by putting huge negative charges on both himself and on the landing mat under the bar. You caught him in time to remove the negative charge from the mat. The jumper experienced no repulsion from the mat and failed to clear the bar. Instead, the plastic bar stuck to him and the audience laughed as he fought to get it off. Why did the uncharged plastic bar stick to the negatively charged jumper?

Answer: The negative charge polarizes the plastic bar and the two attract

Why: The proximity of the jumper's negative charge shifts the charges inside the plastic bar. The positive charges in the bar move slightly toward the jumper and the negative charges in the bar move slightly away from him. Since the positive charges are closer to the jumper, the attraction they experience is stronger than the repulsion experienced by the negative charges on the bar.

(D) In a misguided attempt to win the 100 meter dash, a runner from the Duchy of Grand Fenwick coated the bottoms of her shoes with Superslide™, the "ultimate in frictionless lubrication." Her shoes experienced exactly zero friction. When the gun went off, the runner found herself unable to move forward and remained at the starting point with her legs churning furiously. What force or other physical effect kept her from moving forward?

Answer: Inertia.

Why: Without friction, the runner experienced no horizontal forces. Her inertia kept her motionless.

Problem 3:

Some modern stovetops use a technique known as “induction heating” to heat cookware directly. The glass or ceramic surface of the stovetop stays cool and only the pot itself becomes hot. In principle, induction heating will work with any metallic pot, but for technical reasons that are beyond the scope of this problem, it works most efficiently with ferromagnetic metals.

(A) Just under the surface of an induction stovetop is a coil of wire. When the stove is turned on, a high-frequency alternating current passes through the coil. A metal pot placed just above the surface of the stovetop quickly becomes warm. This heating occurs because electric current flows through the pot. How does the presence of an alternating current in the stovetop’s coil cause current to flow in the pot?

Answer: The alternating current creates a changing magnetic field, which is accompanied by an electric field, which pushes electric charges through the metallic pot.

Why: The fluctuating magnetic field around the cooking coil is accompanied by an electric field. This electric field pushes on charges and any mobile charges in its presence accelerate. The pot provides those mobile charges and so current begin to flow through the pot.

(B) Why does current flow in the pot cause the pot to become hot?

Answer: Currents waste energy in flowing through metals and the missing energy becomes thermal energy, which heats the pot.

Why: Just as when current is driven through metal by a battery, the current passing through the pot causes the pot to become hot. That’s because the pot isn’t a perfect conductor and wastes some of the energy in the current.

(C) Glasses and ceramics contain electric charges, so why can’t this heating technique be used with a glass or ceramic pot?

Answer: The charges in glasses and ceramics aren’t mobile; the electrons in those materials have no empty levels in which to shift so as to flow through the pot.

Why: Glasses and ceramics are insulators. They have filled valence bands and empty conduction bands. The presence of an electric field pushes on the electrons, but they can’t shift from level to level in order to move through the material. As a result, there is no conduction of current and no heating.

(D) Producing high-frequency alternating current is relatively expensive. Why can’t this technique use a steady direct current in the stovetop’s coil?

Answer: A steady direct current would produce a steady magnetic field, which would not be accompanied by an electric field and would not push current through the metal pot.

Why: Although a current is magnetic, only a changing current produces a changing magnetic field. The changing magnetic field is necessary here because it’s accompanied by an electric field and the electric field is what pushes charges through the pot as a current.