Physics 2102 Lecture 04: FRI 23 JAN Electric Charge I Physics 2113 Jonathan Dowling Charles-Augustin de Coulomb (1736–1806) Version: 10/7/2015 Benjamin Franklin (1705–1790)

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

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

Force Between Pairs of Point Charges: Coulomb’s Law 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 |!! Charles-Augustin De Coulomb (1736–1806)

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

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.

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 Three Equal Charges Form an Equilateral Triangle of Side 1.5 m as Shown Compute the Force on q 1 ICPP: What are the Forces on the Other Charges? d q1q1 d d q2q2 q3q3 q 1 = q 2 = q 3 = 20 mC d = 1.0 cm Solution: Set up a Coordinate System, Compute Vector Sum of F 12 and F 13 d d d y x   θ

Feel the Force! Example q 1 = q 2 = q 3 = 20 mC d = 1.0 cm d d d y x   θ ICPP: What are the magnitudes and directions of the forces on 2 and 3?

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