Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley PowerPoint ® Lecture prepared by Richard Wolfson Slide Electric Charge, Force, and Field Essential University Physics Richard Wolfson

Slide 20-2 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley In Chapter 20 you learnt How matter and many of its interactions are fundamentally electrical About electric charge as a fundamental property of matter To describe the electric force between charges The concept of electric field How to calculate the fields of discrete and continuous charge distributions How charges respond to electric fields

Slide 20-3 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Electric charge Electric charge is a fundamental property of matter. Many particles, including the electron and proton, carry electric charge. Charge comes in two varieties, positive and negative. Most charged particles carry exactly one elementary charge, e, either positive or negative. The proton carries exactly +e, the electron exactly –e. The quarks, which make up protons, neutrons, and other particles, carry ±1/3 e or ±2/3 e. But they’re never observed in isolation. The charge in a closed system is conserved, in that the algebraic sum of charges remains unchanged. This is true even if new particles are created or destroyed. The SI unit of charge is the coulomb (C), equal to approximately 6.25  elementary charges. Thus e is approximately 1.6  10 –19 C.

Slide 20-4 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Coulomb’s law and the electric force Like charges repel, and opposite charges attract, with a force that depends on The product of the two charges The inverse square of the distance between them Mathematically, the electric force is described by Coulomb’s law:

Slide 20-5 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley The superposition principle The electric force obeys the superposition principle. That means the force two charges exert on a third force is just the vector sum of the forces from the two charges, each treated without regard to the other charge. The superposition principle makes it mathematically straightforward to calculate the electric forces exerted by distributions of electric charge. The net electric force is the sum of the individual forces.

Slide 20-6 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Clicker question A charge q 1 is located at,. What should you use for the unit vector r in Coulomb’s law if you are calculating the force that q 1 exerts on charge q 2 located at the point, ? A. B. C. D.

Slide 20-7 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Clicker question A charge q 1 is located at,. What should you use for the unit vector r in Coulomb’s law if you are calculating the force that q 1 exerts on charge q 2 located at the point, ? A. B. C. D.

Slide 20-8 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley The electric field The electric field at a point in space is the force per unit charge that a charge q placed at that point would experience: The force on a charge q in an electric field is The electric field is analogous to the gravitational field, which gives the force per unit mass.

Slide 20-9 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Fields of point charges and charge distributions The field of a point charge is radial, outward for a positive charge and inward for a negative charge. The superposition principle shows that the field due to a charge distribution is the vector sum of the fields of the individual charges.

Slide Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley The dipole: an important charge distribution An electric dipole consists of two point charges of equal magnitude but opposite signs, held a short distance apart. The dipole is electrically neutral, but the separation of its charges results in an electric field. Many charge distributions, especially molecules, behave like electric dipoles. The product of the charge and separation is the dipole moment: p = qd. Far from the dipole, its electric field falls off as the inverse cube of the distance.

Slide Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Continuous charge distributions Charge ultimately resides on individual particles, but it’s often convenient to consider it distributed continuously on a line, over an area, or throughout space. The electric field of a charge distribution follows by summing—that is, integrating—the fields of individual charge elements dq, each treated as a point charge:

Slide Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Clicker question Far from a dipole, you measure an electric field strength of 800 N/C. If you double your distance from the dipole, what will the electric field strength be at your new location? A.400 N/C B.200 N/C C.100 N/C D.50 N/C

Slide Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Clicker question Far from a dipole, you measure an electric field strength of 800 N/C. If you double your distance from the dipole, what will the electric field strength be at your new location? A.400 N/C B.200 N/C C.100 N/C D.50 N/C

Slide Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Two examples The electric field on the axis of a charged ring: The electric field of an infinite line of charge: The line carries charge density C/m:

Slide Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Matter in electric fields For a point charge q in an electric field, Newton’s law and the electric force combine to give acceleration: A dipole in an electric field experiences a torque that tends to align the dipole moment with the field: If the field is not uniform, the dipole also experiences a net force.

Slide Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Clicker question A proton, an electron, a carbon-13 nucleus (6 protons, 7 neutrons), and a helium-4 nucleus (2 protons, 2 neutrons) all find themselves in a uniform electric field. Which of these particles exhibits the second-highest acceleration? Assume that the mass of a proton equals the mass of a neutron. A.The proton B.The carbon-13 nucleus C.The electron D.The helium-4 nucleus

Slide Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Clicker question A proton, an electron, a carbon-13 nucleus, and a helium-4 nucleus all find themselves in a uniform electric field. Which of these particles exhibits the second-highest acceleration? Assume that the mass of a proton equals the mass of a neutron. A.The proton B.The carbon-13 nucleus C.The electron D.The helium-4 nucleus

Slide Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Conductors, insulators, and dielectrics Materials in which charge is free to move are conductors. Materials in which charge isn’t free to move are insulators. Insulators generally contain molecular dipoles, which experience torques and forces in electric fields. Such materials are called dielectrics. Even if molecules aren’t intrinsically dipoles, they acquire induced dipole moments as a result of electric forces stretching the molecule. Alignment of molecular dipoles reduces an externally applied field.

Slide Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Electric charge is a fundamental property of matter. Charge comes in two varieties, positive and negative. Charge is conserved. The force between two charges is given by Coulomb’s law: The electric force obeys the superposition principle, meaning the forces due to individual charges sum vectorially. The electric field describes the force per unit charge at a given point: The field of a dipole follows from Coulomb’s law: The fields of discrete charge distributions are calculated by summation. The fields of continuous charge distributions are calculated by integration. A point charge experiences a force in an electric field. A dipole experiences a torque in an electric field, and a force if the field is not uniform. Summary

Slide Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Read Problem-Solving Strategy for using Coulomb’s Law on p 330 Interpret: identify the source charge Develop: draw coordinates and position of charges determine unit vectors (are any along the axes?) Evaluate: using Coulomb’s law remembering force is a vector Assess: is the force in the direction you expect for the sign of the charges?

Slide Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Problem 44 In the figure take q 1 = 25 μC and q 2 = 20 μC. If the force on q 1 points in the −x direction, (a) what is q 3 and (b) what is the magnitude of the force on q 1 ?