1

From Last Time…

Magnitude of the electric force

Direction of the electric force +

+

2

Induced dipoles (charge redistribution)

Bring negative charge close. Electrons on sphere move away from rod.

charged rubber rod

3

Exam 1 Tue. Sep. 29, 5:30-7 pm, 145 Birge

Covers Chap. 21.5-7, 22, 23.1-4, 23.7, 24.1-5, 26 + lecture, lab, discussion, HW

Study ideas: Exam 1 Practice problems at Mastering Physics Sample exams on website (blank & solutions) Group/Quiz (blank & solutions). Review lab question sheets.

8 1/2 x 11 handwritten note sheet (both sides) allowed

4

Unusual dipoles:Electrogenic fish

• Dipole + nearby conducting object

Some fish generate charge separation - electric dipole.

Dipole is induced in nearby (conducting) fish

Small changes detected by fish.

5

The idea of electric fields• EM wave made up of

oscillating electric and magnetic fields.

• But what is an electric field?

• Electric field is a way to describe the force on a charged particle due to other charges around it.

• Force = charge electric field

• The direction of the force is the direction of the electric field.

6

Electric field of a point charge

+

+

Force on this charge…

…due to this charge

+++

€

rF = k

Q1Q2

r2ˆ r

Q1

Q2

€

rE =

r F

r r ( ) /Q2

= Force/charge

Units? N/C

7

Calculating the electric field

+Q1=1µC

r = 10 cm

€

rE =

kQ1

r2=

9 ×109 N ⋅m2 /C2( ) 10−6C( )

0.1m( )2

= 9 ×105 N /C

8

Electric field• Electric field vector defined at every point in

space.

• Gives magnitude and direction of force on test particle

e.g. wind velocity (speed and direction) in different parts of the country.

9

Superposition with Electric Fields

• At any point P, the total electric field due to a group of source charges equals the vector sum of electric fields of all the charges

Find the electric field due to q1, E1

Find the electric field due to q2, E2

E = E1 + E2Remember, the fields add as vectors

10

QuestionWhich vector best represents the electric

field at the red dot?

-

A

B

C

-D

E

11

Electric Field Direction

• a) q is positive, F is directed away from q

• b) The direction of E is also away from the positive source charge

• c) q is negative, F is directed toward q

• d) E is also toward the negative source charge

12

Relationship Between F and E

• Fe = qE Valid for a test charge

that does not disturb the source charge distribution

• If q is positive, F and E are in the same direction

+

r = 1x10-10 m

Qp=1.6x10-19 C

E

(to the right)

€

E =9 ×109 N ⋅M /C2

( ) 1.6 ×10−19C( )

10−10 m( )2 = 2.9 ×1011N /C

Electric field 1Å away from proton

13

Quick QuizWhich is the direction of the electric field at dot?

A. Left

B. Right

C. Up

D. Down

E. Zero

+ - x

y

Away from positive charge (right)

Net E field is to right.

14

Quick QuizIn this electric dipole, what is the direction of the

electric field at point A?

A) Up

B) Down

C) Left

D) Right

E) Zero

+Q -Q

x=+ax=-a

A

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Electric field: summary

• Electric field -> will be a force on a charged particle.

• This force ( and electric field) can arise from electric charges (via Coulomb’s law)

• But once electric field is known, don’t need to know the charges that produce it.

16

The electric dipole

Dipole moment

Vector

Points from - charge to + charge

Has magnitude qs

€

rp

• Can all be approximated by electric dipole.

• Two opposite charges magnitude q separated by distance s

17

Calculating dipole electric field

On the y-axis

€

s /2

€

−s /2

x

y

€

E = E yˆ y

E y = E+ + E−

€

≈k 2qs( )1

y 3 For

€

y >> s

Since points from - charge to + charge

€

rp

€

rE = k

2r p

r3 on y-axis of dipole only

s

q

-q

€

=kq1

y − s /2( )2 + −kq( )

1

y + s /2( )2

€

=kq2ys

y − s /2( )2

y + s /2( )2

18

Question: electric dipoleA and B are the same (large) distance from dipole.

How do the magnitude of the electric fields at A and B compare?

A

B

A)

B)

C)

D)

€

rE A =

r E B

€

rE A <

r E B

€

rE A >

r E B

€

rE B = 0

19

Pictorial representation of E: Electric Field Lines

20

Electric field lines

• Local electric field tangent to field line

• Density of lines proportional to electric field strength

• Fields lines can only start on + charge

• Can only end on - charge.

• Electric field lines can never cross

21

Electric field of a dipole

+

-

22

Electric field of two + charges

23

Question

How are the charges A and B related?

A) A+, B-,

B) A-, B+,

C) A+, B-,

D) A-, B+,

E) A+, B-,

€

A < B

€

A < B

€

A > B

€

A < B

€

A = B

A

B