The Electrical Force makes current flow in electronics, moves ions through nerve cells and powers electric cars, etc.

Coulomb’s Law tells us the magnitude of the electric force (F) between two charged particles a distance r apart.

NOTE: “q1” is the charge of the first particle in Coulombs… even if the first particle is labeled with the variable “q3” or “q” or “Q”.

“r” is the distance between of the particles in meters.

Force is a vector, so it has magnitude and direction.

Coulomb’s Law gives the magnitude of electric force.

The direction is along the line connecting the charges.

attractive

repulsive

repulsive

opposite

like

like

S.2

Notation for Forces

F12 = -F21

are Equal and Opposite Forces

F12 = Force Particle 1 feels due to Particle 2

F21 = Force Particle 2 feels due to Particle 1

Force VectorsElectric Charges Create Forces

Since Force is a vector, it has a magnitude and a direction.

It can also be expressed in terms of its components: F = Fx x + Fy y

F = [Fx,Fy]

^ ^ F

Fx

Fy

The Net Force F

We can find the magnitude a Force vector (F), and its direction (Θ) using its x and y components (Fx & Fy)

Fx

Fy

Θ tan (Θ) = Fy / Fx

(F )2 = (Fx)2 +(Fy)2

Typically ‘a charge’ (q1) experiences Forces from several other charges (q2, q3 & q4)We label the forces: F12, F13 & F14

Question: “Which direction will Charge q1 move?”To answer, compute the Net Force: FNET = m a

FNET = the vector sum of all forces

Your “Net Worth” is the sum of all your assets (positive) minus your debts (negative).

“Net Charge” means add all positive and negative charges.

Example: The net charge of a Sodium ion (Na+) is +1e[Because Na+ has 11 protons (+e) and 10 electrons (-e)]

Net Force (F) means take the vector sum of all forces acting at one point.

“Net”

Superposition Principle: To find the Net Force, add each vector add head to tail.

F1: Net Force (total force on q1)

Force Addition Puzzle:Is the Net Force on a charge: -q stronger at point A or B?

To review Vectors: See Walker, Ch. 3

What is the Direction of the net force on charge q1? (Answer by pointing, then give an answer in degrees)

What is the Direction of the net force on charge q2?What is the Direction of the net force on charge q3?

Conceptual Question19-25

Force VectorsElectric Charges Create Forces

Since Force is a vector, it has a magnitude and a direction.

It can also be expressed in terms of its components: F = Fx x + Fy y

F = [Fx,Fy]

^ ^ F

Fx

Fy

The Net Force F

We can find the magnitude a Force vector (F), and its direction (Θ) using its x and y components (Fx & Fy)

Fx

Fy

Θ tan (Θ) = Fy / Fx

(F )2 = (Fx)2 +(Fy)2

Adding Vectors

To add vectors graphically, place them head to tail.

To add vectors numerically, add their x and y components separately.

Note: variables appearing in bold (eg. F) are vectors!

q3q2

q1

Example If q3 = q2, what is the Net Force on q1 ?(direction & magnitude)

q3q2

q1

F12 F13

q3q2

q1

F12

F13

What is the Net Force on q1 ?

q3q2

q1

F12

F13

F1

q3q2

q1

Example If q3 = q2, what is the Net Force on q1 ?(direction & magnitude)

just gives magnitudes...

Coulomb’s Law

q3q2

q1 just gives magnitudes...

Coulomb’s Law

Given for this problem: q3 = q2

F12 =k |q1q2 |

d2 F13 =

k |q1q3 |d2

The Net Force (F1) on q1 is the vector sum of the forces dueto charges 2 & 3:

F1 =F12 + F13

WARNING: This is a vector equation.

So it is really three equations!!!

F1,x = F12,x + F13,x

F1,y = F12,y + F13,y

F1,z = F12,z + F13,z

Adding Vector Components

boardOur Goal: Find each of these components & add them.

Find Dr. McCarthy’s videos for solving this problem:

http://www.physics.sfsu.edu/~chris/physics121/videos/videos.html

And videos on solving this type of problem:

Force Components

F12 F13

F1,x = F12,x + F13,x

= F12,x - F12,x = 0

The force components (F12,x F12,y F13,y F13,x) are projections of the vectors F12 & F13 onto the x and y axes. The magnitudes F12 & F13 are given by Coulomb’s Law. (Here they are equal since the charges are equal: q3 = q2)

F13,xThe x-components are of opposite sign, and so cancel when we add them:

F12,x

F1,y = F12,y + F13,y = 2 F12,y

The y-components are of the same sign and magnitude: (F12,y = F13,y) .So their sum is just double:

F12F12,y

To determine the value of F1, note that F12 is the hypotenuse of a 30o triangle.So: F12,y = F12 cos(30o). Thus:

The entire force is in the y direction and has a value of twice the value of F12,y.

F1 = 2 F12,y y (y =y unit vector)

30o

F1 = 2 x F12 cos(30o) y = 1.7 F12 y

^^

^ ^

Solution:

The force on particle 1 (F1):

Has a magnitude: 1.73 k q1 q2 /d2

And a direction of: 90 degrees from the x-axis (0 degrees from the positive y-axis)

What’s Inside a Proton?

Every proton and neutron is made of three charged particles called “quarks” ...which can come in two types.

Two “Up” quarks have positive charge (q = +2/3 e)One “Down” quarks have negative charge (q = -1/3 e)

They repel (and attract) each other with tremendous force!

q3q2

q1

d = 1.0 x10-15 mq1 = -5.3 x10-20 Cq2 = 1.1 x10-19 Cq3 = q2

Quark Model of a Proton

Should Protons Explode?The electric force inside a proton is huge: 50 Newtons!

The (+) quarks would accelerate out of the nucleus in an instant! So, are protons exploding?

No. There is another, stronger, binding them together.

This Strong Nuclear Force also keeps protons inside the nucleus.

......stay tuned......