Physics 2112 Unit 1: Coulomb’s Law Today’s Concepts: A) Coulomb’s Law B) Superposition

Electric Charges Electric charges come in two sign: + and - Like sign charges repel, Opposite sign charges attract. Electric charge is “quantized”. qe=1.602 X 10-19C Charge of electron is exactly same as charge of proton Why? Why? Why? How?!

Electric charges is conserved At Fermilab -1 +1 anti-proton proton

Tribo-electric Series Electric Charges Tend to lose electrons when rubbed Tribo-electric Series Tend to gain electrons when rubbed

Conductors / Insulators Conductors – charges are free to move anywhere on the conductor Insulators - charges remain where they are place except in cases of “extreme” force

Opposite signs attract Electro-static Force The force on a charge due to another charge is proportional to the product of the charges and inversely proportional to the separation squared. q2 q1 r The force is always parallel to a line connecting the charges, but the direction depends on the signs of the charges: Opposite signs attract q2 q1 q2 q1 Like signs repel

Unit of Charge is Columb (C) Coulomb’s Law k = 9 X 109 N m2/C2 Unit of Charge is Columb (C) (big!) qe=1.602 X 10-19C Charles-Augustin de Coulomb – French engineer who was a pioneer in torsion and soil mechanics.

Coulomb’s Law Our notation: is the force by 1 on 2 (think “by-on ”) is the unit vector that points from 1 to 2. Examples: If the charges have the same sign, the force by charge 1 on charge 2 would be in the direction of r12 (to the right). q2 q1 If the charges have opposite sign, the force by charge 1 on charge 2 would be opposite the direction of r12 (left). q1 q2

Example 1.1 (forces between paper clips) Two 1 gram paperclips are separated by 10 meters. Then you remove 1 electron from each atom on the first paperclip and place it on the second one. What is the force between the two clips? F = 9e9 x (1.6e-19 * 3e22)^2 / 100 = 2 e 15 Newtons Equivalent to weight of 2e14 kg object near surface of the earth paperclip 1e-3 kg textbook 1 kg person 200 kg car 2000 kg Aircraft carrier 97000 tons = 1e5 x 1e3 = 1e 8 kg Mt Everest 9000 m height,. Estimate volume as 1/3 h^3 = 1/3 * (9e3)^3 = 243 e 9 m^3. (if density = 1000 kg/m^3) = 2.43e14 kg.

Example 1.2 (forces between students) What would the force be between two 80kg students sitting two meters apart if the charge of the proton were 10-10% greater than the charge of an electron? F = 9e9 x (1.6e-19 * 3e22)^2 / 100 = 2 e 15 Newtons Equivalent to weight of 2e14 kg object near surface of the earth paperclip 1e-3 kg textbook 1 kg person 200 kg car 2000 kg Aircraft carrier 97000 tons = 1e5 x 1e3 = 1e 8 kg Mt Everest 9000 m height,. Estimate volume as 1/3 h^3 = 1/3 * (9e3)^3 = 243 e 9 m^3. (if density = 1000 kg/m^3) = 2.43e14 kg.

CheckPoint: Forces on Two Charges Two charges q = + 1 μC and Q = +10 μC are placed near each other as shown in the figure below. Which of the following diagrams best depicts the forces acting on the charges:

Superposition If there are more than two charges present, the total force on any given charge is just the vector sum of the forces due to each of the other charges: q2 F2,1 F3,1 F4,1 F1 F4,1 F2,1 q1 F1 F3,1 q4 q3

The direction of all forces changes by 180o – the magnitudes stay the same: q1 q2 q3 q4 F2,1 F3,1 F4,1 F1 q1 q2 q3 q4 F4,1 F2,1 F1 F3,1 F1 F1 F2,1 F2,1 F3,1 F3,1 F4,1 F4,1

CheckPoint: Compare Forces Compare the magnitude of the net force on q in the two cases. A) |F1 | > |F2| B) |F1 | = |F2| C) |F1 |< |F2| D) Depends on sign of q q -Q +Q Case 1 Case 2 If the CheckPoint was done before the first class, you could use this opportunity to show results. If not, the next slide (hidden) present the CheckPoint as a Clicker Question

CheckPoint: Force from Four Charges Four charged particles are placed on a circular ring with radius 3 m as shown below. A particle with charge Q is placed in the center of the ring y 3q x What is the direction of horizontal force on Q? A) Fx > 0 B) Fx = 0 C) Fx < 0 Q q q q

Example 1.3 (Force on charge) q2 2m +10uC q1 q3 -30uC 2m +25uC What is the force on q2?

+ + Charge on a Conductor Charges are free to move on conductor Charges always on very edge of conductor