Electric Field

Dr. H. Nur Islami, S.Si., MT

Electric Force and Field Force

What? -- Action on a distance

How? – Electric Field Why? – Field Force Where? – in the

space surrounding charges

Fields Scalar Fields:

Temperature – T(r) Pressure – P(r) Potential energy – U(r)

Vector Fields: Velocity field – Gravitational field – Electric field – Magnetic field –

)(rv

)(rg

)(rE

)(rB

Vector Field Due to Gravity When you consider the

force of Earth’s gravity in space, it points everywhere in the direction of the center of the Earth. But remember that the strength is:

This is an example of an inverse-square force (proportional to the inverse square of the distance).

rrMmGF ˆ2

m

M

Idea of Test Mass Notice that the actual

amount of force depends on the mass, m:

It is convenient to ask what is the force per unit mass. The idea is to imagine putting a unit test mass near the Earth, and observe the effect on it:

g(r) is the “gravitational field.”

rrGMmF ˆ2

rrgrrGM

mF ˆ)(ˆ2

Electric Field Electric field is said to exist in

the region of space around a charged object: the source charge.

Concept of test charge: Small and positive Does not affect charge

distribution Electric field:

Existence of an electric field is a property of its source;

Presence of test charge is not necessary for the field to exist;

0qFE

+ + ++++ +

+

+

Electric Field1. A test charge of +3 µC is at a point P where an

external electric field is directed to the right and has a magnitude of 4×106 N/C. If the test charge is replaced with another test charge of –3 µC, what happens to the external electric field at P ?

A. It is unaffected. B. It reverses direction. C. It changes in a way that cannot be determined.

Electric Field

0qFE

Magnitude: E=F/q0 Direction: is that of the force that acts on the

positive test charge SI unit: N/C

Situation ValueInside a copper wire of household circuits 10-2 N/CNear a charged comb 103 N/CInside a TV picture tube 105 N/CNear the charged drum of a photocopier 105 N/CElectric breakdown across an air gap 3×106 N/CAt the electron’s orbit in a hydrogen atom 5×1011 N/COn the suface of a Uranium nucleus 3×1021 N/C

Electric Field due to a Point Charge Q

rrQqF ˆ

41

20

0

rrQ

qFE ˆ

41

200

Direction is radial: outward for +|Q| inward for -|Q| Magnitude: constant on any spherical

shell Flux through any shell enclosing Q is

the same: EAAA = EBAB

A

B

Q

q0

r

Electric Field due to a group of individual charge

nFFFF 002010 ...

n

n

EEE

qF

qF

qF

qFE

...

...

21

0

0

0

02

0

01

0

0

i

ii

i rrqE ˆ

41

20

Electric Field Lines The electric field vector is tangent to

the electric field line at each point. The line has a direction, indicated by an arrowhead, that is the same as that of the electric field vector. The direction of the line is that of the force on a positive test charge placed in the field.

The number of lines per unit area

through a surface perpendicular to the lines is proportional to the magnitude of the electric field in that region. Thus, the field lines are close together where the electric field is strong and far apart where the field is weak.

Electric Field Lines The lines must begin on a positive

charge and terminate on a negative charge. In the case of an excess of one type of charge, some lines will begin or end infinitely far away.

The number of lines drawn leaving a

positive charge or approaching a negative charge is proportional to the magnitude of the charge.

No two field lines can cross.

Electric Field3. Rank the magnitudes E of

the electric field at points A, B, and C shown in the figure.

A) EC>EB>EA

B) EB>EC>EA

C) EA>EC>EB

D) EB>EA>EC

E) EA>EB>EC

.C

.A

.B

Find an expression for dq: dq = λdl for a line distribution dq = σdA for a surface distribution dq = ρdV for a volume distribution

Represent field contributions at P due to point charges dq located in the distribution. Use symmetry,

Add up (integrate the contributions) over the whole distribution, varying the displacement as needed,

Electric Field of a Continuous Charge Distribution

rrqE ˆ

41

20

ii

i

i rrqE ˆ

41

20

rrdqr

rqE

ii

i

iq

ˆ41ˆlim

41

20

200

rr

dqEd ˆ4 2

0

dEE