From Last Time…: Magnitude Of The Electric Force

From Last Time… Magnitude of the electric force

+ Direction of the electric force

+ 1

Induced dipoles (charge redistribution)

charged rubber rod

Bring negative charge close. Electrons on sphere move away from rod. 2

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

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Study ideas:    

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

3

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.

4

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. 5

Electric field of a point charge Force on this charge…

Q2

+

+

ρ Q1Q2 F = k 2 rö r

+ Q1 …due to this charge

ρ r r E = F ( r ) /Q2 = Force/charge Units? N/C 6

+

+

Calculating the electric field ρ kQ (9 ´ 10 9 N ×m 2 /C 2 )(10- 6 C ) E = 21 = 2 r (0.1m ) = 9 ´ 10 5 N /C

+

r = 10 cm Q1=1µC

7

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.

8

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 q , E 2 2 E = E + E 1 2 

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Remember, the fields add as vectors 9

Question Which vector best represents the electric field at the red dot? A B E

C

-

D

10

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 11

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 Qp=1.6x10-19 C

+

Electric field 1Å away from proton E=

r = 1x10

-10

9 2 - 19 9 ´ 10 N ×M /C 1.6 ´ 10 C) ( )( - 10

(10

m)

2

m

= 2.9 ´ 1011 N /C (to the right)

E

12

Quick Quiz Which is the direction of the electric field at dot? A. Left B. Right C. Up

Away from positive charge (right)

D. Down E. Zero

y +

-

x

Net E field is to right.

13

Quick Quiz In this electric dipole, what is the direction of the electric field at point A? A) Up

A

B) Down C) Left D) Right

x=-a +Q

x=+a -Q

E) Zero

14

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.

15

The electric dipole • Can all be approximated •

by electric dipole. Two opposite charges magnitude q separated by distance s Dipole moment

ρ Vector p

Points from - charge to + charge Has magnitude qs

16

Calculating dipole electric field On the y-axis E = E y yö

y

E y = E + + E= kq

1 ( y - s /2)

2

+ (- kq)

1 ( y + s /2)

2

2ys = kq 2 2 y s /2 y + s /2 ( ) ( ) ≈ k (2qs)

1 y3

For y >> s

ρ Since p points from - charge to + charge r ρ 2p E =k 3 r

q s /2

s -q

x −s /2

on y-axis of dipole only 17

Question: electric dipole A and B are the same (large) distance from dipole. How do the magnitude of the electric fields at A and B compare? A) B) C) D)

ρ EA ρ EA ρ EA ρ EB

r = EB r < EB r > EB

A

B

=0

18

Pictorial representation of E: Electric Field Lines

19

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

20

Electric field of a dipole

+ -

21

Electric field of two + charges

22

Question How are the charges A and B related? A) A+, B-, A < B B) A-, B+, A < B C) A+, B-, A > B D) A-, B+, A < B E) A+, B-, A = B

A B

23