Understanding Electric Fields, Coulomb's Law, and Field Lines in Chapter 22, Lecture notes of Law

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Read Chapter 22

• Do Ch. 22 Questions 3, 5, 7, 9
• Do Ch. 22 Problems 5, 19, 24 Chapter 22: The Electric Field

The Electric Field

• Replaces action-at-a-distance
• Instead of Q 1

exerting a force directly

on Q

2

at a distance, we say:

• Q 1

creates a field and then the field

exerts a force on Q

2

• NOTE: Since force is a vector then the

electric field must be a vector field!

E 

F qE

Field E is defined

as the force that

would be felt by a

unit positive test

charge

0 E F / q    SI units for the electric field: newtons per coulomb.

Electric Field Lines

• Lines point in the same direction as the field.
• Density of lines gives the magnitude of the field.
• Lines begin on + charges; end on – charges. We visualize the field by drawing field lines. These are defined by three properties:

Example 1 What is the electric field strength at a distance of 10 cm from a charge of 2 μC? N C r kQ E

1. 8 10 / 10 18 10 ( 10 10 ) ( 9 10 )( 2 10 ) 5 1 3 2 9 6 2             So a one-coulomb charge placed there would feel a force of 180,000 newtons.

Q.22- 1

A point charge Q is far from all other charges. At a distance of 2 m from Q, the electric field is 20 N/C. What is the electric field at a distance of 4m from Q?

1. 5 N/C

2. 10 N/C

3. 20 N/C

4. 40 N/C

5. 80 N/C

Example 2

-2Q Q

x

y

d

1. Find the electric field on the x axis.  0 y E (^1 ) ( ) 2 x d kQ x kQ E E E x     
2. Where will the field be zero? x  d  2 x x  2. 4 d

The shell theorems for E In Chapter 13 we had the shell theorems for gravity In Chapter 21 (p. 567) the shell theorems for electrostatics were stated. In Chapter 23 (p. 618) they will be proven. But we can easily understand them now from our knowledge of electric field lines.

Prove true also for electric field Use our knowledge of electric field lines to draw the field due to a spherical shell of charge: There is no other way to draw lines which satisfy all 3 properties of electric field lines, and are also spherically symmetric. Notice that both shell theorems are obviously satisfied.

r  r  Q spread over shell point Q at center Fields at r are the same!  PROOF: (1) Spherical symmetry (2) Fields far away must be equal

Q.22- 2 A shell of uniform charge attracts or repels

a charged particle that is outside the shell as if all the shell’s charge were...

1. Concentrated at the center.
2. Concentrated at the point closest to the particle.
3. Concentrated at the point opposite the particle.
4. Zero.

Electric Dipole

• The combination of two charges of equal but opposite sign is called a dipole.
• If the charges +q and – q are separated by a distance d, then the dipole moment is defined as a vector pointing from – q to +q of magnitude p = qd. p 

 q p  q