Electricity & Magnetism Lecture 1: Coulomb s Law Today s Concepts: A) Coulomb s Law B) Superposi<on If you haven't done Prelecture 1 yet, please do so later today Electricity & Magne<sm Lecture 1, Slide 1
Coulomb s Law: The force on a charge due to another charge is propor<onal to the product of the charges and inversely propor<onal to the separa<on suared. 2 1 r The force is always parallel to a line connec<ng the charges, but the direc<on depends on the signs of the charges: 2 1 Opposite signs amract 2 1 2 1 Like signs repel Electricity & Magne<sm Lecture 1, Slide 2
Clicker Question: Balloons Take two balloons and rub them both with a piece of cloth. A8er you rub them they will: A) A<ract each- other B) Repel each- other C) Either it depends on the material of the cloth Electricity & Magne<sm Lecture 1, Slide 3
Balloons If the same thing is done to both balloons they will acuire the same sign charge. They will repel! Te xt + + + + + + + + We can only be sure about this if the balloons are made out of the same material. Electricity & Magne<sm Lecture 1, Slide 4
Coulomb s Law Our nota<on: 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 direc<on of r 12 (to the right). 1 2 If the charges have opposite sign, the force by charge 1 on charge 2 would be opposite the direc<on of r 12 (let). 1 2 Electricity & Magne<sm Lecture 1, Slide 5
Clicker Question: Coulomb Force Two 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. k = 9 x 10 9 N m 2 / C 2 electron charge = 1.6 x 10 19 Coulombs N A = 6.02 x 10 23 What will the direc<on of the force be? A) AMrac<ve B) Repulsive Electricity & Magne<sm Lecture 1, Slide 6
Clicker Question: Coulomb Force Two 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. k = 9 x 10 9 N m 2 / C 2 electron charge = 1.6 x 10 19 Coulombs N A = 6.02 x 10 23 Which weight is closest to the approximate force between those paperclips (recall that weight = mg, g = 9.8 m/s 2 )? A) Paperclip (1 g x g) B) Text book (1 kg x g) C) Truck (10 4 kg x g) D) AircraE carrier (10 8 kg x g) E) Mt. Everest (10 14 kg x g) Electricity & Magne<sm Lecture 1, Slide 7
CheckPoint: Forces on Two Charges Electricity & Magne<sm Lecture 1, Slide 8
CheckPoint Results: Forces on Two Charges The bigger charge will push the smaller charge harder than the smaller will push the larger. According to Newton's Third Law, the charges exert eual and opposite forces on each other. The forces of two objects are always eual and opposite. both euasions involve the charge of both parocles in the same manner, therefore they are the same.. Electricity & Magne<sm Lecture 1, Slide 9
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: 2 F 1 F 2,1 F 3,1 F 4,1 1 F 2,1 F 4,1 F 1 F 3,1 4 3 Electricity & Magne<sm Lecture 1, Slide 10
Clicker Question: Superposition What happens to Force on 1 if its sign is changed? A) F 1 increases B) F 1 remains the same C) F 1 decreases 2 D) Need more informakon to determine 1 4 3 Electricity & Magne<sm Lecture 1, Slide 11
The direc<on of all forces changes by 180 o the magnitudes stay the same: 2 2 F 4,1 F 4,1 1 F 2,1 F 1 1 F 1 F 2,1 F 3,1 4 F 3,1 4 3 F 1 F 2,1 F 3,1 3 F 1 F 2,1 F 3,1 F 4,1 F 4,1 Electricity & Magne<sm Lecture 1, Slide 12
CheckPoint: Compare Forces Compare the magnitude of the net force on in the two cases. A) F 1 > F 2 +Q +Q B) F 1 = F 2 C) F 1 < F 2 D) Depends on sign of F F 2 = 0 1 Q +Q Case 1 Case 2 In case one, both of the forces are working in the same direcoon (the downward direcoon) resulong in a greater net force as opposed to case two where the repelling forces are working in opposite direcoons in turn canceling each other out Both cases have a charged placed euidistant from charges of the same magnitudes so no ma<er charge has the forces at this instant are the same. There is no way to tell if the forces on the center charge are repulsive or a<racove without knowing the sign of the center charge. Electricity & Magne<sm Lecture 1, Slide 13
Force from Four Charges Four charged par<cles are placed as shown. A par<cle with charge +Q is placed 1/2 way between the middle + on the let and the +3 on the right What is the direc<on of horizontal force on Q? A) leftward B) none C) rightward Q y 3 x Electricity & Magne<sm Lecture 1, Slide 15
CheckPoint Results: Force from Four Charges Four charged par<cles are placed on a circular ring with radius 3 m as shown below. A par<cle with charge Q is placed in the center of the ring What is the direc<on of horizontal force on Q? A) F x > 0 B) F x = 0 C) F x < 0 3 Q y x Electricity & Magne<sm Lecture 1, Slide 16
Clicker Question: Force from Four Charges Four charged par<cles are placed on a circular ring with radius 3 m as shown below. A par<cle with charge Q is placed in the center of the ring What is the ver&cal force on Q? 3 y x A) F y > 0 B) F y = 0 C) F y < 0 Q Fy would eual 0 if all 3 of the bo<om charges were on top of each other, but because they are pulling at an angle, they will not eual the force of the 3 charge that is pulling only in the +Y direcoon. The y- direcoon components also cancel each other out since there is a charge or force of 3Q poinong both upward and downward. The two charges on the side also have an x component so their Fy is not as great thus the sum of the force from the bo<om charges in smaller than the top charge. The forces are repulsive so the charge will have a negaove Fy. Electricity & Magne<sm Lecture 1, Slide 17