77 82

83685566

8375 809091

757180

72

84

73

57

8892

7756

887364

77 82

83685566

8375 809091

757180

72

84

73

82

8892

7788

887364

Scalar field: Temperatures

Vector field: Winds

1

3. Electric field

3.1 Coulomb’s low and electric field

Q q r

EqF

q

FE

3.2 Definition

field electric - E

Units CNq

FE /

(Action at a distance?)

If the electric force on a test charge q located at point P is F, then the electric field at point P is F/q.

Because the force is always proportional to q, the electric field is independent of the test charge!

Charge Q creates an electric (electrostatic) field E. Charge q is a test charge used to find this electric field E.

2

PEq

r

Qkq

r

QqkF

22

Example: A negative charge, placed in the electric field between two charged plates, experiences an electric force as shown below. What is the direction of the electric field?

A. Left B. Right C. Upward D. Downward

• The negative charge is attracted by the positive plate and is repelled from the negative plate

• The electric field is directed from the positive to the negative charge!

Example: Between the red and the blue charges, which of them

experiences the greater electric field due to the green charge?

+2 +1+1 +1d d

Both charges feel the same electric field due to the green

charge because they are at the same point in space! 3

E-q

+

-

F

Example (Electron in a uniform electric field): Describe the motion of an electron that enters a region with a uniform electric field having initial velocity perpendicular to the direction of the field

Once the electric field is known, finding the force on a given charge is simple…

Constant acceleration in the –y direction. Identical to projectile motion!

F = –|qe|Eparabola

E

v0

electron

m

Eq

m

Fa e

4

2a) Field due to a single charge:2r

QkE

2b) Field due to a number of charges:

Principle of superposition has been used in 2b)

...21 EEE

3.3 Two most important questions:

1) How can one find force, F on the electric charge, q, exerted by field E?2) How can electrostatic field E be created?

Answers:

1)

2) Field E is due to other charges

EqF

5

Q1

Q3

Q4

Q7

Q2

Q6Q5

Q8

q

,...2,1

2

n

r

QkE

n

nn

• Charges Q1, Q2, … create electric field .

• This field is independent from the test charge q.

• If we will replace the charge q with another charge qnew, then the force on the new charge will be different than , but the electric field is independent from q.

new

new

q

F

q

FE

E

newF

F

test charge

Definition of electric field

3.4 Principle of superposition (explanation)

EqEqEqFFF

...... 2121 ...21 EEE

6

Example (Net electric field): Which of the three vectors best represents the direction of the net electric field at the location of charge Q?

Q

q1 < 0

q2 > 0

C

A

B

E1

E2

Enet

Example: Calculate the electric field at the center of a square 52.5 cm on a side if one corner is occupied by a charge +45μC and the other three are occupied by charges -27μC.

2Q

1 45.0 CQ

d

2Q

1E

2E

2 27.0 CQ

CN

m

CCNm

d

QQk

d

Qk

d

QkEEE

/107.4

2/105.52

102745/109

2/2/2/

6

22

6229

2

21

2

2

21

21

7

3.5 Electric field lines

+ -

++++

----

Definition: • Electric field lines indicate the direction of the force due to the given field on a

positive charge, i.e. electric force on a positive charge is tangent to these lines• Number of these lines is proportional to the magnitude of the chargeProperties:• Electric field lines start on positive charges or came from infinity, they end on

negative charges or end at infinity • Density of these lines is proportional to the magnitude of the field

+Q -Q

-

-2Q

8

Examples: Electric Field Lines Around Electric Charges

A single positive charge(an electric monopole)

A positive charge and a negative of equal magnitude (an electric dipole)

Two equal positive charges

9

Example:

1

32

A. E1 = E2 > E3

B. E1 > E2 > E3

C. E1 > E2 ; E3 = 0

The electric field lines in a certain region of space are as shown below. Compare the magnitude of the electric field at points 1, 2 and 3.

The magnitude of the electric field is proportional to the local density of lines. Being on the same line or being between the lines is totally irrelevant.

10

3.6 Electric field in conductors

• The electric field inside a conductor in equilibrium is always zero.

If 0 0 0

motion of charges (conductor, charges can move)

non equilibrium

E F a

• The electric field right outside a conductor in equilibrium is perpendicular to the surface of the conductor.

We cannot have a force parallel to the surface (would produce motion), but perpendicular to it is OK. E = 0

11