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 squared. q2
q1
r
The force is always parallel to a line connec/ng the charges, but the direc/on depends on the signs of the charges:
q2
q1
q2
q1
q2
q1
Opposite signs aEract
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. AGer you rub them they will:
A) AHract 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 acquire the same sign charge. They will repel!
Text
+
+
+
+
+
+
+
+
We can only be sure about this if the balloons are made out of the same material.
Electricity & Magne/sm Lecture 1, Slide 4
Comment
What does the r with a hat mean? Is it like the unit vectors i-­‐hat, j-­‐hat and k-­‐hat, or does it mean something else? The video didn't really explain it that well.
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 r12 (to the right).
q1
q2
If the charges have opposite sign, the force by charge 1 on charge 2 would be opposite the direc/on of r12 (leN).
q1
q2
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 109 N m2 / C2
electron charge = 1.6 x 10−19 Coulombs
NA = 6.02 x 1023
What will the direc/on of the force be? A) AErac/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 109 N m2 / C2
electron charge = 1.6 x 10−19 Coulombs
NA = 6.02 x 1023
Which weight is closest to the approximate force between those paperclips (recall that weight = mg, g = 9.8 m/s2)?
A) Paperclip (1 g x g)
B) Text book (1 kg x g)
C) Truck (104 kg x g)
D) AircraG carrier (108 kg x g)
E) Mt. Everest (1014 kg x g)
Electricity & Magne/sm Lecture 1, Slide 7
CheckPoint: Forces on Two Charges
Two charges q = + 1 µC and Q = +10 µC are placed near
each other as shown in the figure.Which of the following
diagrams best depicts the forces acting on the charges:
Electricity & Magne/sm Lecture 1, Slide 8
CheckPoint Results: Forces on Two Charges
Two charges q = + 1 µC and Q = +10 µC are placed near
each other as shown in the figure.Which of the following
diagrams best depicts the forces acting on the charges:
“The bigger charge will push the smaller charge harder than the smaller will push the larger. “
“They both repel each other, and according to the F = kQq/r^2 and newton's third law, the forces have to be the same.”
“The forces of two objects are always equal and opposite. both equasions involve the charge of both par<cles 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:
q2
F2,1
F4,1
F1
q1
F3,1
F1
F3,1
F2,1
F4,1
q4
q3
Electricity & Magne/sm Lecture 1, Slide 10
Clicker Question: Superposition
What happens to Force on q1 if its sign is changed?
A) |F1| increases
B) |F1| remains the same
C) |F1| decreases
q2
D) Need more informa<on to determine
q1
q4
q3
Electricity & Magne/sm Lecture 1, Slide 11
The direc/on of all forces changes by 180o – the magnitudes stay the same:
q2
q2
F4,1
F4,1
F1
q1
F2,1
F1
F3,1
q3
F2,1
F2,1
F3,1
q4
q3
F1
q1
q4
F2,1
F3,1
F3,1
F4,1
F1
F4,1
Electricity & Magne/sm Lecture 1, Slide 12
CheckPoint: Compare Forces
Compare the magnitude of the net force on q in the two cases.
A) |F1 | > |F2|
+Q
+Q
q
q
B) |F1 | = |F2|
C) |F1 |< |F2| F2 = 0
F1
−Q
+Q
D) Depends on sign of q
In case one, both of the forces are working in the same direc<on (the downward direc<on) resul<ng in a greater net force as opposed to case Case 1
Case 2
two where the repelling forces are working in opposite direc<ons in turn canceling each other out Both cases have a charged placed equidistant from charges of the same magnitudes so no maHer charge q has the forces at this instant are the same. The magnitude of charge of an electron is the same as the magnitude of a proton. So, while the distance is the same, the magnitude of Force between both cases will be the same.
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 +q on the leN and the +3q on the right
What is the direc/on of horizontal force on Q? y
x
q
q
Q
3q
A) leftward B) none C) rightward
q
Electricity & Magne/sm Lecture 1, Slide 15