Physics 2113 Jonathan Dowling Benjamin Franklin 1705 1790

Physics 2113 Jonathan Dowling Benjamin Franklin (1705– 1790) Physics 2102 Lecture 04: FRI 23 JAN Electric Charge I Version: 11/9/2020 Charles-Augustin de Coulomb (1736– 1806)

Let’s Get Started! Electric Charges… • Two Types of Charges: Positive/Negative • Like Charges Repel • Opposite Charges Attract Atomic Structure: Structure • Negative Electron Cloud • Nucleus of Positive Protons, Uncharged Neutrons The Unit of Electric Charge is the “Coulomb” which is “C”. Proton Charge: e = 1. 60 × 10– 19 C

Rules of Electric Attraction and Repulsion Discovered by Benjamin Franklin: Electrical Insulators Benjamin Franklin (1705– 1790)

Rules of Electric Attraction and Repulsion Discovered by Benjamin Franklin: Electric Conductors Benjamin Franklin (1705– 1790)

Rules of Electric Attraction and Repulsion: ICPP Benjamin Franklin (1705– 1790) C and D attract B and D attract

Force Between Pairs of Point Charges: Coulomb’s Law Charles-Augustin De Coulomb (1736– 1806) Coulomb’s Law — the Force Between Point Charges: • Lies Along the Line Connecting the Charges. • Is Proportional to the Product of the Magnitudes. • Is Inversely Proportional to the Distance Squared. • Note That Newton’s Third Law Says |F 12| = |F 21|!!

Force Between Pairs of Point Charges: ICPP (a) (b) (c)

Coulomb’s Law The “k” is the electric constant of proportionality. Usually, we write: Units: F = [N] = [Newton]; r = [m] = [meter]; q = [C] = [Coulomb]

Coulomb’s Law: ICCP (a) a > c > b (b) less

Coulomb’s Torsion Balance Experiment For Electric Force Identical to Cavendish’s Experiment For Gravitational Force! The experiment measures “k” the electric constant of proportionality and confirms inverse square law. http: //www. dnatube. com/video/11874/Application-Of-Coulombs-Torsion-Balance

Two Inverse Square Laws Newton’s Law of Gravitational Force Coulomb’s Law of Electrical Force Area of Sphere = 4πr 2 Number of Lines of Force is Constant. Hence #Force Lines Per-Unit. Area is Proportional to 1/r 2

Superposition • Question: How Do We Figure Out the Force on a Point Charge Due to Many Other Point Charges? • Answer: Consider One Pair at a Time, Calculate the Force (a Vector!) In Each Case Using Coulomb’s Law and Finally Add All the Vectors! (“Superposition”) • Useful To Look Out for SYMMETRY to Simplify Calculations!

Feel the Force! Example d • Three Equal Charges Form d an Equilateral Triangle of q 3 Side 1. 5 m as Shown • Compute the Force on q 1 • ICPP: What are the Forces q 1= q 2= q 3= 20 m. C d = 1. 0 cm q 1 d q 2 Fnet on the Other Charges? y 1 θ x d Solution: Set up a Coordinate System, Compute Vector Sum of F 12 and F 13 d 2 3 d

Feel the Force! Example q 1= q 2= q 3= 20 m. C d = 1. 0 cm Fnet y 1 θ x d d 2 ICPP: What are the magnitudes and directions of the forces on 2 and 3? 3 d

Another Example With Symmetry r +q Charge +q Placed at Center F What is the Force on Central Particle? All Forces Cancel Except From +2 q!