Electric Charge, Force, and Field

1. 20 Essential University Physics Richard Wolfson Electric Charge, Force,and Field

2. 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

3. 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  1018 elementary charges. • Thus e is approximately 1.6  10–19 C.

4. 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:

5. 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.

6. Clicker question • A charge q1 is located at , . What should you use for the unit vector r in Coulomb’s law if you are calculating the force that q1 exerts on charge q2 located at the point , ?

7. Clicker question • A charge q1 is located at , . What should you use for the unit vector r in Coulomb’s law if you are calculating the force that q1 exerts on charge q2 located at the point , ?

8. 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 fieldis • The electric field is analogous to the gravitational field, which gives the force per unit mass.

9. 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.

10. 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.

11. 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:

12. 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? • 400 N/C • 200 N/C • 100 N/C • 50 N/C

13. 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? • 400 N/C • 200 N/C • 100 N/C • 50 N/C

14. 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:

15. 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.

16. 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. • The proton • The carbon-13 nucleus • The electron • The helium-4 nucleus

17. 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. • The proton • The carbon-13 nucleus • The electron • The helium-4 nucleus

18. 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.

19. Summary • 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.

20. 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?

21. Problem 44 • In the figure take q1 = 25 μC and q2 = 20 μC. If the force on q1 points in the −x direction, • what is q3 and • what is the magnitude of the force on q1?