Physics 2102 Lecture 04: WED 03 SEP Jonathan Dowling Benjamin Franklin (1705–1790) Physics 2102 Lecture 04: WED 03 SEP Electric Charge I Charles-Augustin de Coulomb (1736–1806) Version: 5/6/2018

Let’s Get Started! Electric Charges… Two Types of Charges: Positive/Negative Like Charges Repel Opposite Charges Attract Atomic 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

Electrical Insulators 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 |F12| = |F21|!!

Force Between Pairs of Point Charges: ICPP

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 > c > 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 = 4πr2 Number of Lines of Force is Constant. Hence #Force Lines Per-Unit-Area is Proportional to 1/r2

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 Fnet d q1 q2 q3 q1= q2= q3= 20 mC d = 1.0 cm Three Equal Charges Form an Equilateral Triangle of Side 1.5 m as Shown Compute the Force on q1 ICPP: What are the Forces on the Other Charges? d 1 2 3 y x Fnet θ Solution: Set up a Coordinate System, Compute Vector Sum of F12 and F13

Fnet Feel the Force! Example q1= q2= q3= 20 mC d = 1.0 cm θ y x Fnet θ ICPP: What are the magnitudes and directions of the forces on 2 and 3?

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