什么时电荷---CHAPTER 33 ELECTRIC CHARGES AND FIELDS: ELECTROSTATICS "... Coulomb's law. Like charges repel, and unlike charges attract each other, with a force that varies inversely as the square of the distance between them... in all of atomic and molecular physics, in all solids, liquids, and gases, and in all things that involve our relationship with our environment, the only force law, besides gravity, is some manifestation of this simple law. Frictional forces, wind forces, chemical bonds, viscosity, magnetism, the forces that make the wheels of industry go round—all these are nothing but Coulomb's law..." —J. R. Zacharias In Science, March 8, 1957. [THE STUDY of electricity at rest—"electrostatics"—used to bulk large in elementary physics. It was all that was known of electricity two centuries ago, and tradition dies hard. It makes a poor beginning for modern electric circuits, so we have avoided it. Now you need some knowledge of it for atomic physics. How much you see and learn of this part of physics will depend on apparatus, weather, and instructor. On the whole, the less the better.] Electric Charges at Rest When an electric circuit is incomplete, there is no steady current. But when a battery is first connected to an incomplete circuit, momentary currents flow, as shown in Fig. 33-1. If the wires at the break in the circuit are expanded into large sheets of metal (a "capacitor") the momentary "charging Chart/Diagram Description: The image contains five circuit diagrams and one line graph, arranged in two columns and labeled as part of Fig. 33-1a. Diagram 1 (Top Left): - Type: Circuit Diagram. - Components: A battery (labeled with '+' and '-' terminals), a voltmeter (labeled 'V'), two resistors (labeled '1Ω' each), and two ammeters (labeled 'A'). - Connections: The battery is connected in series with the two resistors and the two ammeters. The voltmeter is connected in parallel across the battery terminals. - Annotations: Battery voltage labeled '6 volts'. Ammeters labeled '3 amps' below them. Text annotation to the right: "Complete circuit, steady current". Diagram 2 (Top Right): - Type: Circuit Diagram. - Components: A battery, a voltmeter (labeled 'V'), two resistors (labeled '1Ω' each), and two ammeters (labeled 'A'). - Connections: The circuit is incomplete (broken) between the second resistor and the positive terminal of the battery. The voltmeter is connected across the battery terminals. The ammeters are placed before and after the break. - Annotations: Battery voltage labeled '6 volts'. Ammeters labeled '0 amp' below them. Text annotation to the right: "Circuit with break; no steady current". A break symbol is shown between the resistor and the wire end. Diagram 3 (Middle Left): - Type: Circuit Diagram. - Components: A battery, a voltmeter (labeled 'V'), two resistors, two ammeters (labeled 'A'), and an open switch. - Connections: The circuit is incomplete due to the open switch, placed between the battery and the first resistor. Ammeters are placed before and after the resistors. - Annotations: Battery voltage labeled '6 volts'. Text annotation below: "Momentary current". Small plus and minus symbols are placed near the wire ends at the switch break and near the ammeters, suggesting charge accumulation. Graph (Middle Right): - Type: Line Graph. - Axes: Y-axis labeled "Current", X-axis labeled "TIME". - Plot: A sharp peak starting from zero current at TIME=0, rapidly decreasing back to zero current after a very short time. - Annotations: A vertical dashed line is drawn from the peak of the curve down to the X-axis, labeled "Switch closes". A horizontal line segment with a double-headed arrow is drawn above the peak, labeled "A very short time in most cases." - Text annotation to the right: "Circuit with break; a momentary "charging current" when switch closes; but a very sensitive meter is needed to show it." Diagram 4 (Bottom Left): - Type: Circuit Diagram. - Components: A battery, a switch, and two large parallel plates representing a capacitor, with two ammeters (labeled 'A') in the circuit. - Connections: The battery is connected to the switch, which is in series with the capacitor (parallel plates). Ammeters are placed on either side of the capacitor. - Annotations: Plus and minus symbols are placed on the capacitor plates and near the ammeters and wire ends, indicating charge flow direction and accumulation. Text annotation below: "Circuit with plates at break. Larger momentary currents when "charging" and "discharging"". Diagram 5 (Bottom Right): - Type: Circuit Diagram. - Components: A capacitor (parallel plates), a switch, and two ammeters (labeled 'A'). A symbol indicating "Battery out" is shown with a curved arrow. - Connections: The capacitor is connected to a switch. The switch connects the two sides of the capacitor, forming a complete loop through the ammeters. The battery is shown outside the loop with a curved arrow pointing away, labeled "Battery out". - Annotations: Plus and minus symbols are shown on the capacitor plates and near the ammeters and wire ends, indicating the direction of current during discharge. Figure Caption: - Text below the diagrams: "Fig. 33-1a. MOMENTARY CURRENTS" 534 PART FOUR • ELECTRICITY AND MAGNETISM [Diagram Section 1] Fig. 33-3. ELECTROSCOPE (a) (i) [Diagram: Battery connected via open switch to vertical rod with two hanging leaves (labeled "Leaf").] (ii) [Diagram: Battery connected via closed switch. Leaves are repelled and spread apart. Rod and leaves are marked with "+".] (iii) [Diagram: Battery removed. Leaves remain spread apart. Rod and leaves are marked with "+". Label "Battery removed" is present.] (b) [Diagram: Battery connected to two hanging balloons via threads. Left balloon connected to "+" terminal and marked "+". Right balloon connected to "-" terminal and marked "-". Balloons are shown attracting each other with dashed lines indicating movement.] (c) [Diagram: Two parts.] Left part: Battery connected via switch to two parallel plates inside a box. Plates are labeled "+" and "-". Positive terminal connected to "+", negative to "-". Right part: Cross-section of a gold leaf electroscope. Top: Contact plate. Below: Insulator supporting a vertical rod. Below: Rod inside a case. Bottom: Single leaf attached to the rod, shown tilted away from the rod. Labels: "Contact plate", "Insulator", "Rod", "Case", "Leaf". (d) [Diagram: Four pairs of objects (likely charged balloons or leaves) showing interactions.] First pair: Object A (labeled "+") and Object B (labeled "-") shown attracting. Second pair: Object A' (labeled "+") and Object A (labeled "+") shown repelling, with curved arrows indicating movement apart. Third pair: Object B (labeled "-") and Object B' (labeled "-") shown repelling, with curved arrows indicating movement apart. Fourth pair: Object A (labeled "+") and Object B (labeled "-") shown attracting. [Text Section 1] currents" are larger or last longer. A few "coulombs/ sec" run for a fraction of a second. Therefore some "coulombs" must go from the battery to the plates and be left there when the flow stops. Meters show positive current flowing to one plate and positive current flowing from the other (or negative current to it). Therefore we think there are then charges on the plates, + on one and — on the other; and we say the plates are "charged." [Text Section 2] If the battery is disconnected and replaced by a wire, momentary currents flow in reverse, the plates "discharging" through the wire. But until that is done the charges remain on the plates, pushed by the battery or held by some attraction spreading across the gap.^2 [Text Section 3] We can show that the plates while charged do attract each other. Make them light and flexible — strips of thin metal leaf — and feed charges to them from a battery. After being charged, they attract. The bigger the battery-voltage (EMF) the bigger the attraction. This can be turned to use in a simple voltmeter, keep one plate a hanging leaf and expand the other into a metal box. When a P.D. is applied between leaf and box, the leaf tilts out towards the nearest side of the box. The angle of tilt indicates the P.D.—on an uneven scale. This is an ancient instrument, still used, the "gold leaf electroscope." It is an ideal voltmeter: it takes no current (except at the start); however, it responds very little to potential differences below about 300 volts. [Text Section 4] Once charged, metal objects remain charged when the battery is disconnected, provided they are kept on insulating supports and not connected by metal wires or damp human fingers. Connect two flexible plates A and B (or two metal coated bal- loons on conducting threads) to the + and — terminals of a battery; they attract. Now park A and B, charged + and —, on insulators; and charge another pair A' and B', also + and —. Try A' near A: they repel. See Fig. 33-3(d) above. And B and B' repel; while A and B attract. That is why we need the labels "plus" and "minus." [Diagram Section 2] Fig. 33-1b. CIRCUIT FOR DEMONSTRATING MOMENTARY CURRENTS [Diagram: Circuit containing a battery, a 2-way switch, two ammeters (labeled "A" and "A"), and a capacitor (represented by two parallel plates labeled "+" and "-"). The 2-way switch is connected to route the circuit through the capacitor and ammeters. The diagram shows the switch in the position connecting the battery to the capacitor and ammeters. Label "2-way switch" is present.] The 2-way switch connects the battery in circuit, or removes battery and completes the circuit without it. The two am- meters, A and A', show similar momentary currents, into one plate, out of the other. (Experiment G in Ch. 41) [Diagram Section 3 / Footnote 2] ^2 The water-circuit analog of a break in the circuit (or a capacitor) is not just a blocked pipe, but an elastic diaphragm, like a rubber sheet, across the pipe. Then a pump can drive a momen- tary current, making the diaphragm bulge. WATER CIRCUIT [Diagram: Closed loop of pipes. One section shows a pump symbol (labeled "P"). Another section shows a barrier with a bulging flexible diaphragm (labeled "diaphragm").] Fig. 33-2. HYDRAULIC ANALOG OF CAPACITOR ```plaintext CHAPTER 33 • ELECTROSTATICS 535 Two plates connected to a battery have opposite charges, and attract; and those charges disappear ("neutralize") when the battery is removed and the plates are connected by a wire. There is no special electrical virtue in flexible leaves or floating balloons—those were chosen to balance small electrical forces with small gravity forces. Any metal objects will do (provided they are supported by insulators to prevent currents carrying charges away). Charges run freely over a conductor (metal, carbon, etc.). That is why we can charge a metal object completely with one touch of the battery wire. Insulators can gather charges too, but only where the wire touches them. FIG. 33-4. MOVING CHARGES A battery connected to two insulated metal objects pushes charges quickly on to them, until the P.D. between them is the battery's EMF. Sometimes we seem to have given charge to one object alone, and we wonder where the opposite charge has gone. We usually find it on the surroundings: the box of the electroscope, the walls of the room, the Earth itself. If we are careless, the other wire from the battery trails on a damp table or floor and drives the opposite charge to "ground." Or we may intentionally connect the other wire to the water pipe which runs to ground. With one terminal of the battery "grounded," we can charge objects with the ungrounded wire. Then we speak of the potential of a charged object, meaning the p.d. between it and ground. However, there is another way of charging things, that works magnificently with all materials. It has been known for centuries as part of the science of electrostatics, electricity at rest. We shall now make a fresh start with those simple phenomena. Forget for the moment your knowledge of currents and charges and watch the ancient knowledge being built. A Fresh Start: Charging by "Friction" Rub a stick of plastic or hard rubber or dry glass with cloth or fur (or better still, "Saran Wrap"), and it will pick up dust and small pieces of paper. Two similar rubbed rods repel each other. We say they are charged. At this stage "charged" is merely a name for the properties "will pick up bits of paper" and "will repel similar things." We imagine the rods have gathered something on their surface, something that we call electricity and we call this imagined collection of electricity a charge of electricity, or an electric charge, or just a charge. We can show by skinning the surface off a rod that the charge judged as above stays on the surface. Conductors and Insulators Wires can carry charges away from a surface and so can fingers or wet threads; but insulators such as glass or lucite do not do so. By putting samples on insulating handles, so that any charges they gain cannot run away, we find that any two dissimilar materials become charged when touched together—metals, non-metals, elements, compounds. Footnotes: *In some cases—e.g., when dealing with atomic structure—we shift the zero of potential from "ground" to infinity. ²We use the word to recognize the special state of affairs, but we are only naming the state of affairs, not giving an explanation. An earlier age might have used "bewitched." Diagram Description: FIG. 33-4. MOVING CHARGES Type: Schematic diagrams illustrating charging of objects. Main Elements: - Two panels, left and right. - Both panels show a battery (vertical lines representing terminals) connected by wires to two insulated objects suspended above the ground. - Objects: Irregular shapes (resembling leaves or balloons), annotated with + and - signs representing charges. - Battery: Marked with + and - terminals. - Wires: Connecting battery terminals to the objects. - Ground: Represented by dashed lines and semicircles or arcs below the objects, indicating insulation. - Annotations: - Left panel: "Momentary current" arrows pointing from battery terminals towards objects. "Charges spread over metal very fast". - Right panel: Arrow between objects labeled "P.D. ~ EMF of battery until P.D. = EMF of battery". Arrows for current are absent. Objects show accumulated charge (+ and -). FIG. 33-5. Type: Schematic diagram illustrating charging relative to ground. Main Elements: - Battery: Shown on the left, with + and - terminals. - Ground Connection: The negative terminal of the battery is connected via a wire to a "Water pipe" which is connected to "Ground". Ground is represented by multiple parallel horizontal lines of decreasing length. - Charged Object: The positive terminal of the battery is connected via a wire to a spherical object suspended above the ground. - Annotations: - Battery: Not explicitly labeled "battery". - Connection: Wire from negative terminal to "Water pipe" to "Ground". Wire from positive terminal to the sphere. - Sphere: Labeled "Potential", "V volts", "P.D. V volts (= Battery EMF)". Annotated with + signs representing charge. - Ground: Labeled "Ground", "Zero of potential at ground". A dashed line with an arrow points from the sphere down to the "Zero of potential at ground" label, indicating the potential difference measurement. - Relative Position: Sphere is above ground. Water pipe is on the ground connection. ``` Page: 536 Part: PART FOUR • ELECTRICITY AND MAGNETISM [Text Body - Left Column] Fig. 33-6. ELECTRIC CHARGES Forces: + and – Charges We soon find there are two kinds of charge; hence the need for labels + and –. Pieces of charged lucite or hard rubber repel each other; pieces of charged glass or hard rubber repel each other; pieces of charged glass (rubbed on silk) also repel each other. But a charged lucite attracts charged glass. If we rub lucite and fur together, they both become charged and attract each other. We label negative the charges on hard rubber, lucite, sulfur, and positive the charge on glass and on fur that has rubbed lucite.⁵ Charged things exert forces thus: + and + repel, – and – repel, + attracts –, and – attracts +. We sum this up in the ancient rubric: LIKE CHARGES REPEL: UNLIKE CHARGES ATTRACT ⁵ Benjamin Franklin made the choice of labels, long before batteries produced knowledge of electric currents. [Text Body - Right Column] Multiplying Charges: The Electrophorus To obtain large charges easily we use an electrophorus—a cake of lucite (or hard rubber) charged by flicking it with fur. It then sits on the table with its top surface charged. Take a metal plate with insulating handle and obtain a charge on it by the following procedure. Fig. 33-7. (1) Bring the metal plate very close to the charged cake. (It may touch the cake without harm since the cake is an insulator.) (2) With one finger, touch the metal plate, connecting it momentarily (through arm & body & shoes) to the Earth. Then take finger away. (3) Remove the plate from cake. The plate is now charged and can easily give some of its charge to other things by contact. At this stage there seems to be little rhyme or reason to the process—it is witchcraft, and we might well label the stages "mumbo," "jumbo," "mumbo." We shall use it to make charges, and explain it later—though you could puzzle out the explanation from what you already know. The charge on the cake emerges unchanged; so the process can be repeated, giving an endless stream of charges on the plate. Where does the energy come from? Experiments with Charged Plate, Electroscope, and Test Ball Brought near a finger or nose, the charged electrophorus plate makes a small spark and loses its charge. The victim feels a tiny shock, but does not remain charged unless he stands on an insulating [Diagram Description - Fig. 33-6] Type: Series of simple line drawings illustrating electrostatic interactions. Elements: - Top row (Left): Drawing of a fuzzy object labeled "Fur or cloth" rubbing another object. Text "Fur becomes charged as well as plastic". - Top row (Right): Drawing of a bar labeled "Brass" with "Insulating handles" rubbing a fuzzy object labeled "Fur". Text "Fur and brass rubbed together become charged" and "Unless samples are insulated the charges may run away". - Middle row (Left): Two suspended horizontal rods labeled "Glass" pushing each other away. Text "Repulsion between similarly charged rods". - Middle row (Right): A suspended horizontal rod labeled "Glass" attracting a suspended horizontal rod labeled "Plastic". Text "Attraction between charged glass and charged plastic". - Bottom row (Left): Two suspended horizontal rods pushing each other away. Text "LIKE CHARGES REPEL". - Bottom row (Right): Two suspended horizontal rods attracting each other. Text "and 'UNLIKE ATTRACT'". [Diagram Description - Fig. 33-7] Type: Series of four simple line drawings illustrating the steps of operating an electrophorus. Elements: - Common elements: A base object labeled "cake" (with dots on top), a plate with an insulating handle. - Diagram 1 (Labeled 1): Plate held above the cake, arrow points down from plate to cake. Labels "MUMBO". - Diagram 2 (Labeled 2): Plate held above the cake, a stick figure is shown touching the top of the plate with a finger. Labels "JUMBO". - Diagram 3 (Labeled 3): Plate held above the cake, the stick figure's finger is lifted away from the plate. Labels "MUMBO". - Diagram 4: Plate held above the cake, a spark symbol is shown between the edge of the plate and the knuckle of a stick figure (partially shown). Here is the extracted content from the image: **Page Header:** CHAPTER 33 · ELECTROSTATICS 537 **Text Content:** damp threads or metal wires. Offered a chance to share its charge with the Earth, it seems to lose all charge—if sharing is in proportion to size, there will indeed be little left on the original object. Metal-coated balloons on silk threads can be given large charges and repel visibly. Or we can make a “gold leaf” electroscope⁷ with one or two strips of metal leaf hung from an insulator. This is a sensitive instrument for testing charges.⁸ It measures the force on its leaf due to the charge there by balancing it against gravity. The usual form has one leaf hung from a metal rod that passes through an insulator in the top of a metal case. A knob or plate on the top of the rod, outside the case, enables charges to be given to the leaf easily. Even bringing a charge near makes the leaf swing out—while it remains near. We use a small test ball to bring *sample* charges from a big charged object to the leaf. Each dose of charge makes the leaf rise more. If after giving the leaf some positive charge, we bring it a small negative charge, the leaf falls slightly, suggesting that the new charge has neutralized some of the old one. So the labels + and – seem suitable. This provides an easy test for + and – charges. ⁷ “Scope” means “look at.” This name means “instrument for looking at effects of electric charge.” ⁸ The electrical force is due to repulsion by charges on the leaf’s support and attraction by opposite charges on the walls of the electroscope’s case. If the leaf is connected to some large charged object, it takes only a small fraction of the total charge; and the charge it takes is a measure of the voltage of the combined object & leaf. So the leaf’s tilt indicates the P.D. between [object & leaf] and the surrounding walls or Earth. table. The plate can be recharged, and an insulated metal object can be fed with charge after charge till it gains little more from further applications.⁶ Then the charged object can make a big spark and give a shock. Or it can share its charge with other insulated objects by contact, or by conduction along ⁶ In terms of voltage: the plate is charged to a certain voltage (p.d. from ground). The victim’s potential rises nearer and nearer to that of the plate, and the victim can remove a smaller and smaller share of the plate’s charge. **Section Header:** ELECTROSCOPE **Figure 33-8:** Caption: FIG. 33-8. ELECTRIC CHARGES Description: Three diagrams illustrating electric charges. (a) Title: (a) Shocks. Two figures standing on the ground, near a horizontal line representing the ground. One figure points at the other figure. A spark symbol (jagged line) connects their heads. To the right, a box with text "Note the symbol for ground" and a diagram of the ground symbol (three horizontal lines decreasing in length). (b) Title: (a, b) Shocks. Diagram shows two figures on the ground. One figure is holding a device with a rotating disc (an electrophorus). The other figure is touching the disc, and a spark symbol connects his hand to the disc. A thought bubble above the figure touching the disc says "Mumbo Jumbo Mumbo". (c) Title: (c) Balloons charged by repeated use of electrophorus repel visibly. Diagram shows two figures on the ground, one holding an electrophorus device. Arrows indicate charge transfer from the electrophorus to the figures' hands. Three balloons are suspended by strings from a horizontal support. Two balloons are labeled with '+' signs and repel each other, shown by arrows pointing outwards from the balloons. The third balloon is labeled with a '+' sign. A thought bubble above the figure holding the electrophorus says "M-J-M". Arrows indicate charge transfer from the electrophorus to the figures' hands. **Figure 33-9:** Caption: FIG. 33-9. THE ELECTROSCOPE Description: Five diagrams illustrating the electroscope. (a) Title: (a) Principle. Diagram shows a vertical support with a horizontal bar at the top. Two flexible strips (leaves) hang from the horizontal bar. An arrow labeled "charge added" points towards the leaves. The leaves are initially hanging parallel and then repel each other, spreading apart. (b) Title: (b) Practice. Diagram shows a rectangular case with a vertical rod passing through the top via an insulator. A single leaf hangs from the bottom of the rod inside the case. The leaf is repelled from the rod. The rod and leaf are labeled with '+' signs. The case walls are labeled with '-' signs. An arrow points from the rod to the case, labeled "Grounded Case". (c) Title: (c) Symbol. Diagram shows a simplified representation of an electroscope: a vertical line with a horizontal line segment at the top, from which a slanted line segment (representing the leaf) extends downwards. (d) Title: (d) Electroscope given several + charges. Five diagrams showing an electroscope symbol (vertical line, top horizontal segment, slanted leaf) with different levels of positive charge. The leaf's angle increases with more positive charges added to the knob at the top (represented by a circle labeled B1). The diagrams show increasing angles as more '+' symbols are added around the circle and the vertical rod/leaf. The last diagram shows the leaf nearly horizontal. (e) Title: (e) - charge brought near an electroscope which already has + charge. Two diagrams. The first shows an electroscope with positive charge (indicated by '+' symbols and the leaf deflected) and a negative charge (indicated by '-' symbols) being brought near the knob (labeled B2). An arrow indicates the movement of the negative charge towards the knob. The second diagram shows the leaf deflecting less, suggesting the negative charge has partially neutralized the positive charge on the electroscope. Both the electroscope and the approaching charge are near a vertical support structure. PART FOUR • ELECTRICITY AND MAGNETISM [Introductory Text] a long metal object. Use a small test ball and electroscope to look for charges on the “sausage.” Suppose the large ball is charged +. Then — charges are found on the near end of the sausage; little or no charge on the middle, and + charge at the far end. We guess that these + and — charges were there originally in the uncharged sausage, and have been pulled apart by the charge on the big ball. Charges must travel easily on the sausage, so the big ball’s + charge can pull negative charges towards it and push + charges away. Now join the sausage to the Earth by touching it with a finger. Remove the finger and re-test. The sausage still has the — charges near the ball; the + charges at the far end have disappeared. We say they have run away still farther, to ground through our finger. (Route: arm—body—legs—damp shoes—damp floor, etc.) As you know, this motion of charges can be shown with a microammeter. Now remove the original ball, with its + charge still on it. The sausage is left with a — charge distributed over it, extra thickly at the pointed ends. We have “manufactured” a — charge on the sausage (without losing the big ball’s original + charge). Remove that — charge and put it to some use. The process can then be repeated any number of times, supplying a series of negative charges which could then be fed along a wire in a tiny stream of current. Notice the sequence, starting with the original charged ball: (1) bring sausage near; (2) touch sausage momentarily with finger; (3) remove sausage, and find that it has a charge available for use. This process is called **charging by induction**. Where have you met it before? Where does the energy gained with this charge come from? [Diagrams] **Fig. 33-10. CHARGE DISTRIBUTION** **Diagram (a):** * Type: Schematic diagram illustrating charge distribution on a charged conductor shape. * Elements: * A conductor shape, elongated and irregularly shaped, labeled "charged". * The conductor is shown with positive (+) signs distributed over its surface. The density of the signs is higher at the pointed ends and lower on the flatter sides. * A stand with a pole and horizontal bar. * A small ball suspended by a thread from the horizontal bar, shown approaching the conductor. **Diagram (b):** * Type: Schematic diagram illustrating charge distribution on a conductor induced by an external charge. * Elements: * An irregularly shaped conductor (labeled "sausage" in text description, but not labeled in diagram). * An external charged object (labeled "charged ball" in text description, depicted as a sphere with + signs) is shown near the left end of the conductor. * Negative (-) signs are shown concentrated on the end of the conductor near the charged ball. * Positive (+) signs are shown concentrated on the end of the conductor far from the charged ball. * Four test probes/balls, each on a stand with a vertical pole, are shown positioned below the conductor. Each probe has a thread suspending a small ball that is deflected away from the conductor by some force (presumably electrostatic repulsion from the charge on the conductor's surface). The deflection is larger at the ends and smaller in the middle, suggesting higher charge density at the ends. * A curved arrow indicates a connection to the Earth (grounding), shown connecting to the middle of the conductor via a line labeled "touch". **Diagram (c):** * Type: Schematic diagram illustrating charge distribution on a hollow charged conductor. * Elements: * A hollow, roughly cylindrical metal can on a stand. * Positive (+) signs are shown distributed over the *outer* surface of the can. * The *inner* volume of the can is shown with no charge signs. * Three test probes/balls (similar to those in (b)) are shown positioned below the can. The suspended balls below the *outer* surface are deflected, indicating charge. The suspended ball positioned below the *inner* cavity of the can is not deflected, indicating no charge inside. [Caption and Description for Fig. 33-10] Fig. 33-10. CHARGE DISTRIBUTION (a) Investigating charge distribution on conductor. (b) Area with + signs indicates surface density of charge. (c) Charge distribution on and in hollow, charged metal can. We use a sampling ball and electroscope to explore the "charge density" all over some charged body. We find that charge is not spread evenly, but is thickest near sharp points, and thinnest at hollow places. Pursuing the latter observation, we charge a hollow metal can and explore. Result: outside, plenty of charge; inside, no charge. **PROBLEM 1** Suppose an uncharged metal can is placed on an insulating support, and a charged metal ball is lowered on silk thread into the can, allowed to touch the can inside, and withdrawn. (a) How much charge would you expect left on the ball? (b) How much if the ball touches the can outside instead of inside? **Charging by Induction** Merely bringing a charge near the electroscope has some effect. Investigate that effect ("inducing" charges, as it is called). Investigate that effect ("inducing" charges, as it is called). Charge a large metal ball; place it near **PROBLEM 2** (a) Given a glass rod with a small + charge from rubbing, you can charge an electroscope by scraping some charge off the rod on to the electroscope. Would the electroscope be charged + or —? (b) Or you can produce charges on the electroscope by holding the + charged rod near it. How would you then proceed to leave some charge permanently on the electroscope, without bringing the rod any nearer? Would that charge be + or —? You can now charge an electroscope + or —, from a positively charged glass rod. You should try adding + and — charges to an electroscope which is already charged. **Hollow Conductors (See Fig. 33-12)** Place a small metal can, C, on the top of an electroscope, so that the leaf takes a sample of the can's charge. Charge a metal ball, B, on an insulating thread or rod, and place it near the outside of the can C. The nearer B is to C, the higher the leaf rises—the bigger the positive charge driven away to the electroscope by the ball's positive charge. If you touch the can or electroscope, the leaf falls to zero. But if you touch and remove your finger and then remove the ball, the can and electroscope are left with a negative charge—charging by induction. Earlier, when the electroscope read zero there was a negative charge on the can but it was attracted by the ball’s + charge and none ran down to