Due Monday, February 26, In Class
Please Answer Each Question As Briefly As Possible
You May Work Together, But Write Up Your Answers Separately
Question 1: A nerve cell is an electrostatic device that operates very differently from a wire. It's a fluid-filled tube that's surrounded by another fluid. Both fluids contain ions (electrically charged atoms) of sodium, potassium, and chlorine. Each sodium or potassium ion has one elementary unit of positive charge while each chlorine ions has one elementary unit of negative charge. The wall of the nerve cell normally prevents these ions from passing through it.
a. When the nerve is in its resting state, the fluid outside it has slightly more sodium plus potassium ions than chlorine ions. The fluid inside it has slightly more chlorine ions than sodium plus potassium ions. What are the net electric charges of these two fluids?
Answer: Outside the nerve, the net charge is positive; inside the nerve the net charge is negative.
Why: Outside the nerve, the positively charged particles outnumber the negatively charged ones. That gives the region a net positive charge. The situation inside the nerve is reversed.
b. Explain why the resting nerve has electrostatic potential energy.
Answer: The positive charges outside the cell could do work if they were allowed to move toward the inside of the cell. They thus contain stored energy.
Why: There are many ways to show that the resting nerve has electrostatic potential energy. In general, a separation of charge-positive on one side and negative on the other-contains electrostatic potential energy because it takes work to produce.
c. To produce its electrostatic potential energy, the nerve pumps sodium ions out of the nerve cell. Show that the nerve must do work on the sodium ions during this transfer.
Answer: To move a sodium ion out of the cell, the nerve must push that sodium ion outward and it must move outward; force times distance in the same direction. The nerve must push the positively charge ion outward because it's repelled by the positive charges already there.
Why: Creating a charge separation takes work because each new charge you transfer experiences an attraction toward where it came from and a repulsion from where it's going to. You have to push it the whole way as it moves in the direction of your push, so you do work on it.
d. Which part of the nerve has a positive voltage? which part has a negative voltage?
Answer: The outside of the cell has a positive voltage while the inside has a negative voltage.
Why: To determine the voltage of a particular location, you can see how much work it takes to bring one tiny positive charge to that region from very far away. Bringing a positive charge to the outside of the nerve requires work because the new positive charge is repelled by the ones already there. Thus the voltage outside the nerve is positive (positive work done; positive electrostatic potential energy in the new positive charge). Bringing a positive charge to the inside of the nerve does work because the new positive charge is attracted by negative charges already there. Thus the voltage inside the nerve is negative (negative work done; negative electrostatic potential in the new positive charge).
e. When the nerve cell "fires," it abruptly begins to allow sodium ions to pass through its walls. Which way do the sodium ions move and what happens to the voltages of the various parts of the cell?
Answer: The sodium ions flow into the nerve and the voltages inside and out approach zero.
Why: The sodium ions are attracted toward the negative charge inside the nerve and repelled by the positive charge outside. They accelerate toward the inside of the cell. As they flow, they neutralize both the inside and outside of the cell. With no net charge inside or out, the cell's voltages drop to zero.
Question 2: Your local market has an electric eye that rings a bell as you walk in door. Your passage through a light beam is what activates the bell. The light beam is emitted at the left side of the door and normally strikes a small photoconductor on the right side of the door.
a. When the light beam is turned off, no light strikes the photoconductor. A battery pumps negative charges onto one side of the photoconductor and positive charges onto the other. These opposite charges exert attractive forces on one another so why don't they move together?
Answer: In the dark, the photoconductor is an insulator. The charges can't move through it.
Why: With no light to transfer electrons from the filled valence levels to the empty conduction levels, the photoconductor can't respond to electric fields. No electric current can flow through the photoconductor.
b. Because the photoconductor is in the dark, the battery soon stops sending charges to it. What makes it stop?
Answer: The charges accumulate on the wires leading up to the photoconductor and repel any further like charges.
Why: One wire leading to the photoconductor becomes positively charged and the other becomes negatively charged. The charges on these two wires eventually repel any additional charges enough that the battery can't send more.
c. When the light beam is on and you're not in its way, charges can move through the photoconductor. What has happened inside the photoconductor that allows it to conduct electricity so that those charges can move together?
Answer: The light is shifting electrons from the valence levels to the conduction levels and allowing those electrons to respond to electric fields.
Why: Once electrons can shift easily between levels, they can respond to electric fields and can begin to flow across the material. Light makes this flow possible, so the illuminated photoconductor is an electric conductor.
d. Because the photoconductor is exposed to light, the battery can continue to send charges to it. How has light made it possible for the battery to keeps sending charges?
Answer: The photoconductor conducts current, so the positive charges on one wire can flow through it to the negative charges on the other wire. Since charge no longer accumulates anywhere, the battery can keep sending more.
Why: Once the photoconductor is exposed to light, the circuit is complete. Positive charge can flow to the photoconductor through one wire and return from the photoconductor through the other wire.
e. You bend down to play with the electric eye. You block the market's light beam with your back and shine your own flashlight onto the photoconductor. The bell turns off, as though you were out of the way. But when you shine red light from your bicycle taillight onto the photoconductor, it doesn't respond. Why doesn't red light (which has relatively low energy photons) affect the photoconductor?
Answer: Red light photons don't have enough energy to shift electrons in the photoconductor from the filled valence levels to the empty conduction levels.
Why: The electrons in the photoconductor need enough energy to shift them from the valence levels to the conduction levels before they will be able to carry electric current through the material. Red light photons don't carry enough energy to make that shift in some photoconductors.
Question 3: A magnetic resonance imaging (MRI) machine uses an enormous and extremely strong magnet to study a patient's body. The magnet, which has its north pole at the patient's head and its south pole at their feet, is actually a coil of superconducting wire through while electric charges flow.
a. This fancy electric system seems unnecessary; why can't the technicians simply put a large number of north magnetic poles near the patient's head and an equal number of south magnetic poles near their feet?
Answer: There aren't any isolated north poles or any isolated south poles (north and south poles always come in equal pairs).
b. The needle of your magnetic compass has its north magnetic pole painted red and its south pole painted white. Why does the white end turn toward the patient's head?
Answer: The white end (a south pole) is attracted toward the north pole at the patient's head.
c. The compass is a magnetic dipole, with no net magnetic pole. So why do you feel it pulled toward the patient's head more and more strongly as you get closer to the magnet?
Answer: The compass's south pole is attracted to the north pole of the MRI magnet while the compass's north pole is repelled by the MRI magnet's north pole. However the south pole of the compass is closer to the north pole of the MRI magnet and experiences a larger force. There is thus a net attraction between the compass and the MRI magnet's north pole.
d. Aluminum isn't normally magnetic and a refrigerator magnet won't stick to it. But as you carry a large aluminum tray up to the magnet, you find that the magnet repels the aluminum. Explain.
Answer: As you approach the MRI magnet with the tray, the magnetic field in the tray changes. This changing magnetic field produces an electric field. The electric pushes charges through the aluminum as a current and this current is magnetic. As recognized by Lenz's law, the magnetic forces between the MRI magnet and the tray are repulsive.
e. Eventually you manage to get the aluminum tray up to the magnet. As long as the tray doesn't move, it experiences no magnetic forces. But when you drop it, it falls past the magnet remarkably slowly. What slows down its fall?
Answer: The magnetic drag force that occurs when metal moves past a magnet or a magnet moves past metal.
Why: As it falls, the tray experiences a changing magnetic field. It experiences an electric field, a current flows through it, and it becomes magnetic. The tray and MRI magnet repel one another. However the strongest magnetic poles in the tray are those at its top, where they have just been created. The poles near the bottom of the tray are older, having been created earlier. The currents associated with those older poles have slowed down and lost energy and are less strong than those at the top of the tray. So the top of the tray is pushed upward harder than the bottom of the tray is pushed downward and the tray experiences an upward magnetic force. It can't fall at its normal rate. It falls slowly.
Question 4: Electric shavers come in two different types: reciprocating and rotary.
a. When you turn on a corded reciprocating shaver, AC current from the power company travels through a coil of wire inside the shaver. A permanent magnet attached to the cutting blades vibrates back and forth near this coil, taking the blades with it. Why does the permanent magnet vibrate back and forth?
Answer: As the AC current flows through the coil, the coil becomes magnetic. But its poles reverse 120 times a second as the current reverses. This magnetic coil alternately pulls and pushes on the permanent magnet and the blades shift back and forth.
b. How many complete cycles (back and forth) do the blades complete each second?
Answer: 60 per second.
Why: Since the current through the coil undergoes 60 complete reversals (over and back) each second, the coil completes 60 full cycles of attraction and repulsion each second.
c. A cordless reciprocating shaver doesn't just send current from its battery through a coil of wire. Why wouldn't that arrangement work?
Answer: If the current through the coil doesn't change, it will simple attract (or repel) the permanent magnet steadily and the magnet will not shift back and forth.
d. A corded rotary shaver uses a small universal motor to turn its circular blade. Why doesn't the shaver run backward if you plug it in backward?
Answer: The universal motor has no permanent magnets in it. When you reverse the current passing through it, all the north poles become south poles and all the south poles become north poles. The forces between the poles don't change as a result and the motor continues to turn as it did before.
e. A cordless rotary shaver uses a small DC motor. This shaver runs backward if you reverse its batteries. Why?
Answer: The DC motor contains permanent magnets. When you reverse the current passing through it, all the electromagnets inside reverse their poles. This reverses all the forces between the poles of the permanent magnets and the poles of the electromagnets. The forces inside the motor reverse and it turns backward.
Question 5: A home burglar alarm uses various sensors to detect an intruder. These sensors are connected to the main unit by wires.
a. Each sensor is attached to the main unit via two wires, rather than just one. Why?
Answer: With only one wire, you can't have a circuit. It's very hard to tell what happens at the end of a single wire because you can't send a current through it.
b. One of the simplest sensors is just a thin strip of metal foil that runs along the edge of a window. If a burglar breaks the window, the foil strip will be severed. How can the main unit determine that the strip has broken, using its two wires?
Answer: If the two wires are connected by the foil strip, they can be part of a circuit. When the foil strip is severed, the circuit will be opened and no current will flow through it.
c. A more sophisticated sensor can tell when a door is opened. It uses a magnet attached to the door and a small device called a reed switch attached to the door frame. This switch contains two iron strips that are arrange head to tail in a line, but normally don't quite touch-they're bent slightly apart and must bend back to make contact. When the magnet's north pole is near the end of one of the iron strips, that strip becomes magnetic. Why?
Answer: When a north pole approaches a piece of iron, the magnetic domains in the iron rearrange so that their south poles point toward the north pole. The iron then develops a large south pole near the approaching north pole and a large north pole at its other end.
d. The first iron strip, now magnetic, attracts the other the other strip and they pull together and touch. Why does it attract the other strip?
Answer: When the first iron strip becomes magnetic, its north pole is near the second iron strip. It magnetizes the second iron strip. Since the second iron strip develops a south pole near the north pole of the first strip, the two attract and touch.
e. When the door is closed, the magnet is near the reed switch. How can the main unit tell when the door opens?
Answer: The main unit sends current through one wire, through the reed switch, and through the second wire. When the door opens, the iron strips in the reed switch pull apart and the current stops flowing through the circuit.