Chapter 21 opener. This comb has acquired a static electric charge, either from passing through hair, or being rubbed by a cloth or paper towel. The electrical charge on the comb induces a polarization (separation of charge) in scraps of paper, and thus attracts them. Our introduction to electricity in this Chapter covers conductors and insulators, and Coulomb’s law which relates the force between two point charges as a function of their distance apart. We also introduce the powerful concept of electric field.
Figure 21-1. (a) Rub a plastic ruler and (b) bring it close to some tiny pieces of paper.
Figure 21-2. Like charges repel one another; unlike charges attract. (Note color coding: positive and negative charged objects are colored rose-pink and blue-green, respectively, in this book.)
Figure 21-5. (a) A charged metal sphere and a neutral metal sphere. (b) The two spheres connected by a conductor (a metal nail), which conducts charge from one sphere to the other. (c) The two spheres connected by an insulator (wood); almost no charge is conducted.
Figure 21-6. A neutral metal rod in (a) will acquire a positive charge if placed in contact (b) with a positively charged metal object. (Electrons move as shown by the orange arrow.) This is called charging by conduction.
Figure 21-7. Charging by induction. Figure 21-8. Inducing a charge on an object connected to ground.
Figure 21-9. A charged object brought near an insulator causes a charge separation within the insulator’s molecules.
Figure 21-10. Electroscope.
Figure 21-11. Electroscope charged (a) by induction, (b) by conduction.
Figure 21-12. A previously charged electroscope can be used to determine the sign of a charged object.
Figure 21-14. Coulomb’s law, Eq. 21–1, gives the force between two point charges, Q 1 and Q 2 , a distance r apart.
Figure 21-15. The direction of the static electric force one point charge exerts on another is always along the line joining the two charges, and depends on whether the charges have the same sign as in (a) and (b), or opposite signs (c).
Solution: Writing down Coulomb’s law for the two forces shows they are identical. Newton’s third law tells us the same thing.
Solution: Coulomb’s law gives the magnitude of the forces on particle 3 from particle 1 and from particle 2. The directions of the forces can be found from the geometrical arrangement of the charges (NOT by putting signs on the charges in Coulomb’s law, which is what the students will want to do). F = -1.5 N (to the left).
Figure 21-18. Determining the forces for Example 21–3. (a) The directions of the individual forces are as shown because F 32 is repulsive (the force on Q 3 is in the direction away from Q 2 because Q 3 and Q 2 are both positive) whereas F 31 is attractive (Q 3 and Q 1 have opposite signs), so F 31 points toward Q 1 . (b) Adding F 32 to F 31 to obtain the net force. Solution: The forces, components, and signs are as shown in the figure. Result: The magnitude of the force is 290 N, at an angle of 65 ° to the x axis.
Solution: The force on Q 3 due to Q 4 must exactly cancel the net force on Q 3 from Q 1 and Q 2 . Therefore, the force must equal 290 N and be directed opposite to the net force calculated in the previous example.
Figure 21-22. Force exerted by charge Q on a small test charge, q , placed at points A, B, and C.
Figure 21-21. An electric field surrounds every charge. P is an arbitrary point.
Figure 21-23. (a) Electric field at a given point in space. (b) Force on a positive charge at that point. (c) Force on a negative charge at that point.
Figure 21-25. Example 21–6. Electric field at point P (a) due to a negative charge Q , and (b) due to a positive charge Q , each 30 cm from P. Solution: Substitution gives E = 3.0 x 10 5 N/C. The field points away from the positive charge and towards the negative one.
Solution: The geometry is shown in the figure. For each point, the process is: calculate the magnitude of the electric field due to each charge; calculate the x and y components of each field; add the components; recombine to give the total field. a. E = 4.5 x 10 6 N/C, 76 ° above the x axis. b. E = 3.6 x 106 N/C, along the x axis.
Figure 21-33. Electric field lines (a) near a single positive point charge, (b) near a single negative point charge.
Figure 21-36. A charge inside a neutral spherical metal shell induces charge on its surfaces. The electric field exists even beyond the shell, but not within the conductor itself.
Figure 21-37. If the electric field at the surface of a conductor had a component parallel to the surface E || , the latter would accelerate electrons into motion. In the static case, E || must be zero, and the electric field must be perpendicular to the conductor’s surface: E = E ┴ .
The field inside the box is zero. This is why it can be relatively safe to be inside an automobile during an electrical storm.
Solution: The acceleration is in the vertical direction (perpendicular to the motion) and is equal to –eE/m. Then y = ½ at 2 and x = vt; eliminating t gives the equation y = -(eE/2mv 0 2 )x 2 , which is a parabola.
Chapter 23 opener. We are used to voltage in our lives—a 12-volt car battery, 110 V or 220 V at home, 1.5 volt flashlight batteries, and so on. Here we see a Van de Graaff generator, whose voltage may reach 50,000 V or more. Voltage is the same as electric potential difference between two points. Earths potential is defined as the potential energy per unit charge.
Figure 23-1. Work is done by the electric field in moving the positive charge q from position a to position b.
Figure 23-3. (a) Two rocks are at the same height. The larger rock has more potential energy. (b) Two charges have the same electric potential. The 2 Q charge has more potential energy.
Figure 23-16. Equipotential lines (the green dashed lines) between two oppositely charged parallel plates. Note that they are perpendicular to the electric field lines (solid red lines).
Solution: Equipotential surfaces are spheres surrounding the charge; radii are shown in the figure (in meters).
Figure 23-18. Equipotential lines (green, dashed) are always perpendicular to the electric field lines (solid red) shown here for two equal but oppositely charged particles.
electric charge and electric field
Chapter 21 Electric Charge and Electric Field
21.1 Static Electricity; Electric Charge and its Conservation Objects can be charged by rubbing
21.1 Static Electricity; Electric Charge and its Conservation Charge comes in two types, positive and negative; like charges repel and opposite charges attract
21.1 Static Electricity; Electric Charge and its Conservation Electric charge is conserved – the arithmetic sum of the total charge cannot change in any interaction.
21.3 Insulators and Conductors Conductor: Charge flows freely Metals Insulator: Almost no charge flows Most other materials Some materials are semiconductors.
21.4 Induced Charge; the Electroscope Metal objects can be charged by conduction:
21.4 Induced Charge; the Electroscope They can also be charged by induction, either while connected to ground or not:
21.4 Induced Charge; the Electroscope Nonconductors won’t become charged by conduction or induction, but will experience charge separation:
21.4 Induced Charge; the Electroscope The electroscope can be used for detecting charge:
21.4 Induced Charge; the Electroscope The electroscope can be charged either by conduction or by induction.
21.4 Induced Charge; the Electroscope The charged electroscope can then be used to determine the sign of an unknown charge.
21.5 Coulomb’s Law Experiment shows that the electric force between two charges is proportional to the product of the charges and inversely proportional to the distance between them.
21.5 Coulomb’s Law The force is along the line connecting the charges, and is attractive if the charges are opposite, and repulsive if they are the same.
21.5 Coulomb’s Law Unit of charge: coulomb, C The proportionality constant in Coulomb’s law is then: k = 8.099 x 10 9 N · m 2 /C 2 Charges produced by rubbing are typically around a microcoulomb: 1 μ C = 10 -6 C
21.5 Coulomb’s Law Charge on the electron: e = 1.602 x 10 -19 C Electric charge is quantized in units of the electron charge.
21.5 Coulomb’s Law Conceptual Example 21-1: Which charge exerts the greater force? Two positive point charges, Q 1 = 50 μ C and Q 2 = 1 μ C , are separated by a distance l . Which is larger in magnitude, the force that Q 1 exerts on Q 2 or the force that Q 2 exerts on Q 1 ?
21.5 Coulomb’s Law Example 21-2: Three charges in a line. Three charged particles are arranged in a line, as shown. Calculate the net electrostatic force on particle 3 (the -4.0 μ C on the right) due to the other two charges.
21.5 Coulomb’s Law Example 21-3: Electric force using vector components. Calculate the net electrostatic force on charge Q 3 shown in the figure due to the charges Q 1 and Q 2 .
21.5 Coulomb’s Law Conceptual Example 21-4: Make the force on Q 3 zero. In the figure, where could you place a fourth charge, Q 4 = -50 μ C , so that the net force on Q 3 would be zero?
21.6 The Electric Field The electric field is defined as the force on a small charge, divided by the magnitude of the charge:
21.6 The Electric Field An electric field surrounds every charge.
21.6 The Electric Field Force on a point charge in an electric field:
21.6 The Electric Field Example 21-6: Electric field of a single point charge. Calculate the magnitude and direction of the electric field at a point P which is 30 cm to the right of a point charge Q = -3.0 x 10 -6 C.
21.6 The Electric Field Example 21-8: E above two point charges. Calculate the total electric field (a) at point A and (b) at point B in the figure due to both charges, Q 1 and Q 2 .
21.6 The Electric Field <ul><li>Problem solving in electrostatics: electric forces and electric fields </li></ul><ul><li>Draw a diagram; show all charges, with signs, and electric fields and forces with directions </li></ul><ul><li>Calculate forces using Coulomb’s law </li></ul><ul><li>Add forces vectorially to get result </li></ul><ul><li>Check your answer! </li></ul>
21.8 Field Lines The electric field can be represented by field lines. These lines start on a positive charge and end on a negative charge.
21.8 Field Lines The number of field lines starting (ending) on a positive (negative) charge is proportional to the magnitude of the charge. The electric field is stronger where the field lines are closer together.
21.8 Field Lines Electric dipole: two equal charges, opposite in sign:
21.8 Field Lines The electric field between two closely spaced, oppositely charged parallel plates is constant.
21.8 Field Lines <ul><li>Summary of field lines: </li></ul><ul><li>Field lines indicate the direction of the field; the field is tangent to the line. </li></ul><ul><li>The magnitude of the field is proportional to the density of the lines. </li></ul><ul><li>Field lines start on positive charges and end on negative charges; the number is proportional to the magnitude of the charge. </li></ul>
21.9 Electric Fields and Conductors The static electric field inside a conductor is zero – if it were not, the charges would move. The net charge on a conductor resides on its outer surface.
21.9 Electric Fields and Conductors The electric field is perpendicular to the surface of a conductor – again, if it were not, charges would move.
21.9 Electric Fields and Conductors Conceptual Example 21-14: Shielding, and safety in a storm. A neutral hollow metal box is placed between two parallel charged plates as shown. What is the field like inside the box?
21.10 Motion of a Charged Particle in an Electric Field The force on an object of charge q in an electric field E is given by: F = q E Therefore, if we know the mass and charge of a particle, we can describe its subsequent motion in an electric field.
21.10 Motion of a Charged Particle in an Electric Field Example 21-16: Electron moving perpendicular to E. Suppose an electron traveling with speed v 0 = 1.0 x 10 7 m/s enters a uniform electric field E, which is at right angles to v 0 as shown. Describe its motion by giving the equation of its path while in the electric field. Ignore gravity.
23.1 Electrostatic Potential Energy and Potential Difference The electrostatic force is conservative – potential energy can be defined Change in electric potential energy is negative of work done by electric force:
23.1 Electrostatic Potential Energy and Potential Difference Electric potential is defined as potential energy per unit charge: Unit of electric potential: the volt ( V ). 1 V = 1 J / C .
23.1 Electrostatic Potential Energy and Potential Difference Analogy between gravitational and electrical potential energy:
23.1 Electrostatic Potential Energy and Potential Difference Electrical sources such as batteries and generators supply a constant potential difference. Here are some typical potential differences, both natural and manufactured:
23.5 Equipotential Surfaces An equipotential is a line or surface over which the potential is constant. Electric field lines are perpendicular to equipotentials. The surface of a conductor is an equipotential.
23.5 Equipotential Surfaces Example 23-10: Point charge equipotential surfaces. For a single point charge with Q = 4.0 × 10 -9 C, sketch the equipotential surfaces (or lines in a plane containing the charge) corresponding to V 1 = 10V, V 2 = 20V, and V 3 = 30V.
23.5 Equipotential Surfaces Equipotential surfaces are always perpendicular to field lines; they are always closed surfaces (unlike field lines, which begin and end on charges).
<ul><li>INTRODUCTION </li></ul><ul><ul><li>In the past chapters we have been discussing interactions of electric charges “ at rest ” (electrostatic). </li></ul></ul><ul><ul><li>Now we are ready to study charges “ in motion ”. </li></ul></ul>ELECTRIC CURRENTS <ul><ul><li>An electric current consists of motion of charges charges from one region to another. </li></ul></ul><ul><ul><li>When this motion of charges takes place within a conductor that forms a closed path, the path is called an electric circuit . </li></ul></ul>Chapter 18
THE ELECTRIC CURRENT Chapter 18-2 <ul><li>We can also define current through the area as the net charge flowing through the area per unit time . </li></ul><ul><li>CURRENT (Electric Current) </li></ul><ul><ul><li>It is the rate of flow of electric charge through a cross-sectional area. </li></ul></ul>
OHM’S LAW: RESISTANCE AND RESISTORS <ul><li>RESISTANCE </li></ul><ul><ul><li>The proportionality of J to E for a metallic conductor at constant temperature was discovered by G.S. Ohm . </li></ul></ul>Chapter 18-3 <ul><li>For Ohmic materials (those that obey Ohm’s law), the potential V is proportional to the current I . </li></ul><ul><li>The behavior will always trace a linear relationship. </li></ul>
OHM’S LAW: RESISTANCE AND RESISTORS <ul><li>RESISTOR </li></ul>Chapter 18-3 Current I enters a resistor R as shown. (a) Is the potential higher at point A or at point B? (b) Is the current greater at point A or at point B?
ELECTRIC POWER <ul><li>The POWER is the work done per unit time or the time rate of energy transfer </li></ul>Chapter 18-5 Power dissipated in a conductor Power dissipated in a resistor <ul><li>A CIRCUIT is a closed conducting path current flow all the way around. </li></ul>
EMF AND TERMINAL VOLTAGE Chapter 19-1 Ideal Emf Source Real Battery <ul><li>Electromotive Force (emf) Source </li></ul><ul><ul><li>It is a device that supplies electrical energy to maintain a steady current in a circuit. </li></ul></ul><ul><ul><li>It is the voltage generated by a battery. </li></ul></ul>
RESISTORS IN SERIES AND PARALLEL Chapter 19-2 <ul><li>RESISTORS IN SERIES </li></ul><ul><ul><li>The magnitude of the charge is constant. Therefore, the flow of charge, current I is also constant. </li></ul></ul><ul><ul><li>The potential of the individual resistors are in general different. </li></ul></ul>The equivalent resistance of resistors in series equals the sum of their individual resistances.
RESISTORS IN SERIES AND PARALLEL <ul><li>RESISTORS IN PARALLEL </li></ul><ul><ul><li>The upper plates of the capacitors are connected together to form an equipotential surface – they have the same potential. The lower plate also have equal potential. </li></ul></ul><ul><ul><li>The charges on the plates may not necessarily be equal. </li></ul></ul>Chapter 19-2
Problem set <ul><li>Three charged particles are placed at the corners of an equilateral triangle of side 1.20m (shown in the figure). (a) Calculate the magnitude and direction of the net force and electric field on each due to the other two. (b) calculate for the electric potential at the midpoint of the triangle. </li></ul><ul><li>(a)What is the equivalent resistance of the circuit shown.(b) What is the current in the 18-ohm resistor, 12-ohm resistor (c) power dissipation in the 4.5 –ohm reistor. </li></ul>