Today 2/21 E-Field and Coulomb’s Law 18.4-5 Examples HW: “2/21 2-D E Field ” Due Wednesday 2/26

Many Charge Example (Like HW)E = kQs /r2

Q1

Q2

Q3

Each Square is ro on a side, Q1 = -4qo, Q2 = +2qo, Q3 = -6qo

(See how this simplifies the math)

Find the E field at Q1’s location.

EQ2,x = k Qs

r2

k 2qo

(4ro)2

kqo

ro2

1

8

Up, (away from Q2)

EQ3,x = k Qs

r2

k 6qo

(6ro)2

kqo

ro2

1

6Down, (toward Q3)

Add vectors to get

Enet,x kqo

ro2

1

6

1

8

kqo

ro2

1

24 Down at the x

FOthers,q1 = q1Enet,x

q1

kqo2

ro2

4

24

Many Charge Example (Like HW)E = kQs /r2

Q1

Q2

Q3

Each Square is ro on a side, Q1 = -4qo, Q2 = +2qo, Q3 = -6qo

(See how this simplifies the math)

Find the E field at Q2’s location.

EQ1,x = k Qs

r2

k 4qo

(4ro)2

kqo

ro2

1

4

Up, (toward Q1)

EQ3,x = k Qs

r2

k 6qo

(2ro)2

kqo

ro2

3

2 Down, (toward Q3)

Add vectors to get

Enet,x kqo

ro2

3

2

1

4

kqo

ro2

5

4 Down at the x

FOthers,q2 = q2Enet,xkqo

2

ro2

5

2

q2

Many Charge ExampleE = kQs /r2

+qo

-3qo

+4qo

-2qo

ro

What is the force on +4qo? (direction also)

Find the field at +4qo due to the “other” charges. These are the “source” charges.

E+q = kQs/r2 = k(qo)/(ro)2 = Eo

Direction? Away from + so right

E-2q = kQs/r2 = k(2qo)/(2ro)2 = Eo= k2qo/2(ro)2= k(qo)/(ro)2

E-3q = kQs/r2 = k(3qo)/(ro)2 = 3Eo= 3kqo/(ro)2

Many Charge ExampleE = kQs /r2

+qo

-3qo

+4qo

-2qo

ro

What is the force on +4qo? (direction also)

E+q = Eo E-2q = Eo E-3q = 3Eo

Now add E-Field vectors

Ex = E+q,x + E-2q,x

Ex = Eo - Eosin45

Ex = 0.29Eo Ey = E-2q,y + E-3q,y

Ey = Eosin45 + 3Eo

Ey = 3.7Eo

= tan-1(0.29/3.7) = 4.5°

Etotal = 3.72 + 0.292 Eo = 3.71Eo

Fon +4q = (4qo)3.71Eo = 14.84qoEo

Fon +4q = 14.84kqo2/ro

2

same direction as Etotal