Slide 1

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Electric Field Line= s

Electric Field Line= s, cont.

Electric Field Line Patterns

Electric Field Line Patterns

Electric Field Line Patterns

Electric Field Line Patterns

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Electric Field Line= s

A convenient aid for visualizing electric field patterns is to draw lines pointing in the direction of the field vector at any point

These are called el= ectric field lines and were introduced by Michael Faraday

Electric Field Line= s, cont.

The field lines are= related to the field by

The electric field = vector, E, is tangent to the electric field lines at each point

The number of lines= per unit area through a surface perpendicular to the lines is proportional to the strength of the electric field in a given region

Electric Field Line Patterns

Point charge=

The lines radiate e= qually in all directions

For a positive sour= ce charge, the lines will radiate outward

Electric Field Line Patterns

For a negative sour= ce charge, the lines will point inward

Electric Field Line Patterns

An electric dipole = consists of two equal and opposite charges

The high density of= lines between the charges indicates the strong electric field in this region

Electric Field Line Patterns

Two equal but like = point charges

At a great distance= from the charges, the field would be approximately that of a single charge of 2q

The bulging out of = the field lines between the charges indicates the repulsion between the charges

The low field lines= between the charges indicates a weak field in this region

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PHYSICS 1112= K

COLLEGE� PHYSICS,� 8^th�<= /b>EDITION

SERWAY, R. ;= � VUILLE, C.

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=
= SECTION� 15.1 � PROPERTIES OF ELECTRIC CHARG= ES
SECTION� 15.2� -� INSULATORS AND CONDUC= TORS

=	=			<= /td>
�� Charge may be considered a fundam= ental quantity of Electricity
and= Magnetism just as Mass, Distance and Time are for Mechanics.
How= ever historically, the unit for electric current, the Ampere, was
def= ined first and the unit for charge was defined in terms of the Amp.
An = Amp is an amount of charge per unit� t= ime. Therefore, technically,
cur= rent is the fundamental quantity that must be introduced for the
field of Electr= icity and Magnetism.

q� -� source charge;�� = q₀� -� test charge

Unit of q (S= I) : Coulomb, C

=
NOT= E: q and q₀ are not different types of charge just� different
�� roles that charge fulfills

ALSO: The text = may use q as the symbol for both roles of charge

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=
e� -� the amount of charge on the proton

-e<= span style=3D'mso-spacerun:yes'>� -� the amount of charge on the electron

e is a positive= number

e� =3D� 1.6 x 10^-19 C

=		<= /td>	<= /td>	<= /td>
In = the 18^th�Century the two types of charge that= were supposed
to = exist were dubbed �Resinous� (R) and �Vitreous� (V). These
charge types co= uld be transferred by friction
to = materials that were either glass-like (V) or rubber-like (R))
�And repulsive and attractive forces = could be produced
�(Unlike charges attract, like charges repel ).

F

R� R� R� R

V� V� V� V

F

F

V� V� V� V

V� V� V� V

F

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=	=
�� Benjamin Franklin introduced� the� designations �positive� and
and �negative�� although he did = not think that there were two kinds
of charge as we= do today.

=	<= /td>
�� Franklin thought that objects tha= t had an excess of charge were
�po= sitive� and objects with a deficit of charge were �negative�. His
model does not = explain some phenomena that are observed.

Today we accept= two kinds of charge, positive and negative

+<= /font>

-<= /font>

F�� -F

See Sec. 15.2

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<= /td>	<= /td>
CHAR= GING BY
COND= UCTION
(CONTACT)=

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THR= OUGHOUT
THE= MATERIAL.

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<= /td>		=	<= /td>	<= /td>
= EXAMPLE - �Copper has one conduction electron p= er atom and an
ato= mic mass, A =3D 64 gr/mole. Find:

(a= )	the= number of conduction electrons per gram of Cu
(b= )	q, = the total charge of the electrons in (a)

(a)

then there are = 9.4 x 10²¹ conduction electrons per gram of Cu

q� =3D� -1504� C / gr

Is there any ne= t charge due to these electrons ?

No, non ionized= atoms have net charge of zero

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SECTION� 15.4� -� THE� ELECTRIC� FIELD

E� -� the electric field

=
I� -� Charges produce E

II<= span style=3D'mso-spacerun:yes'>� -� charges respond to E

source charges,= � q

test charges, q<= sub>0

F

(1)� F� =3D� q₀ E<= /b>

q₀

E<= br>

<= /td>	<= /td>		<= /td>
NOT= E: The text uses
q0 for �test� charge in eq
15.= 3 on page 506 but
use= s q for �test� charge
in eq 15.4

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q₀

E<= br>

(1)� F� =3D� q₀ E<= /b>

(ii) E i= nteracts with q₀ to produce the force, F on q₀

=
(ii= i) (1) is a vector equation: E is a vector, F is a vector
�� F_x� =3D� q₀ E_x ;�� F_y� =3D� q₀ E_y;�� F_z� =3D� q₀ E_z

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Direction of= F � Consider E in one dimension (x) and let E_x >= 0

<= /td>
3 Cases:<= br>

(i)= q₀ > 0� (+ test charge)<= br>

F

+

E<= br>

from (1) :� F_x =3D� q₀ E_x<= br>

+x

F_x &g= t; 0

F_x� is in the direction of E<= sub>x

(ii)� q₀ < 0 ( - test charg= e )

F

F_x� =3D� q₀ E_x

-

F_x &l= t; 0

E<= br>

+x

F_x i= s opposite the direction of E_x

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E<= br>

(iii) q_{0� =3D�
0}

Then F� =3D� 0

=
Cas= es I� and� ii� show the FIRST MA= JOR CONVENTION OF
��= �� ELECTRICITY:

	<= /td>	<= /td>
+ t= est charges experience a force in the direction of the
appl= ied E

-	�test charges experience a force oppo= site the direction
of = the applied E

Equation (1) ca= n be rearranged:

(2)� E� =3D� F / q_0<=
/sub>

=
(2) shows the S= I� units for E:

for= ce / charge�� N / C

<= /td>
NOT= E: Again see eq 15.3
on p 506<= br>

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<= /td>		<= /td>	<= /td>	=	<= /td>
E= XAMPLES �
(1= )	A u= niform electric field, E_y =3D 1000 N/C is directed upward near
�� near earth�s surface. Find:
(a= )	Fy, the force it produces on a proton;� (b) F_y, the force it produces on an
��= �� electron

=
(c)= HOMEWORK� q₀ the charge on a 1 gram object if the object�s weight is to
�� be offset by the electric force= it experiences

F_y

E_y

F_y� =3D� 1.6 x 10^-16N

q₀= =3D +e

F_y i= s up , in the direction of E_y

(b) F_{y� =3D�
q₀ E_y��
and here� q₀<=
span
style=3D'mso-spacerun:yes'>� =3D�
-e (electron)}

F_y

F_y� =3D� -e E_y� =3D� -1.6x10^-19 C (1000 N/C)<= /font>

E_y

F_y� =3D� -1.6x10^-16 N

q₀= =3D -e

F_y i= s down, opposite the direction of E_y

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F_y

(c)� Use:� F_y� =3D� q₀ E_y� =3D� mg

=
How= many protons would be needed
to provide this= charge ?

W

=	=	<= /td>
(2)= An electron in a CRT is accelerated in the +x direction, from the
cat= hode through the anode and passes through a deflection region
on = its way to the screen. A uniform electric field, E_y exists in the
deflection regi= on.

-

-

-

E_y

+y

v_=
0

A<= br>

Screen

<= /td>
Defl= ection
Plates

+x

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-

-

-

E_y

+y

v_=
0

A<= br>

Screen

<= /td>
Defl= ection
Plates

+x

<= /td>
If = the acceleration of the electron due to E_y is a_y =3D -1.8x10¹⁴ m/s²,
find E_y

F_y �= electric force on the electron

From Newton�s 2= ^nd Law:�� F_y�=3D= � m a_y

where� m� is the electron mass,� m= =3D 9.11x10^-31kg

Then� F_y� =3D� -(9.11x10^-31 kg) 1.8x10¹⁴ m/s²<= /font>

F_y� =3D� -1.64x10^-16N

E_y� =3D� 1.64x10^-16N / 1.6x10^-19 C

From equation (= 1) :� F_y� =3D� q₀ E_y

E_y� =3D� 1025 N / C

E_y� =3D� F_y / q₀� =3D� F_y / -e<= /font>

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=	<= /td>
Production o= f� E �
= E due to a point charge:

�� A source� point charge, q is located at the o= rigin, O.

E_r

P

r

q

O

The electric fi= eld, E_r�produced by q� at point P, a distance r from q is:=

(3)

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<= /td>
or:<= /font>
(4)�� E_r� =3D� k q / r²

= 49;� -� electric permittivity; ε₀ � value of ε� in� a� �free space� environm= ent

<= /td>
A vacuum is a free space environment and air is treated as �approximately=
free= space�.

=
In a dielectric medium, ε > ε₀.� If a charge distribution produces an electric
Fie= ld of magnitude, E₀ in air, the field in a dielectric would be <= ; E₀.

Diel= ectric, ε > ε₀

<= /td>
air gap
^= 9; =3D ε₀

-

-

-

-

-

+

+

+

+

+

+

+

+

+

+

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-�� +

E= ₀

E=

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E_r� =3D� k q / r²

then:

=
Use= (4) to find� E_r�due to
�single point charges

=
NOTE: (i) q in = (4) is the source of the
�� electric field, Er, hence the term �source charge�

=
(ii= ) (4) is only valid for discreet point charges
�� not for continuous charge distributions

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Er

<= /td>
Direction of E_r �
(i) = q > 0

P

r

<= /td>
Er =3D (k q) / r² > 0

E points away from q

+q

(ii)= � q < 0

Er

P

r

Er =3D (k q) / r²�< 0

-q

= E points toward q

=	=
(i) and (ii) show : the second major convention of electricity
�� E �POINTS AWAY FROM + SOURCE CHARGE = AND
�� TOWARD � SOURCE CHARGE<= /font>

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=
It�s often said that �Electric Field Lines start on + charge and end on nega= tive
cha= rge or at infinity.

= 49;₀� =3D� 8.85x10^-12 C² / N m²�� and

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file:///C:/C6F2A655/PHYSICS1112K-WEB-CH15_files/v3_slide0024.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="windows-1252" Slide 1

= Electric Field Lines

See� SECTION� 15.5

<= /td>		=	<= /td>
�<= /font>	A c= onvenient aid for visualizing electric

	fie= ld patterns is to draw lines pointing in

	the= direction of the field vector at any point

�<= /font>	The= se are called electric field lines and

	wer= e introduced by Michael Faraday

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= Electric Field Lines, cont.

<= /td>			<= /td>		=	=	<= /td>	<= /td>
�<= /font>	The= field lines are related to the field by

	�<= /font>	The= electric field vector, E, is tangent to the

	ele= ctric field lines at each point

	�<= /font>	The= number of lines per unit area through a
	sur= face perpendicular to the lines is

	pro= portional to the strength of the electric field
	in = a given region

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= Electric Field Line Patterns

<= /td>		<= /td>	<= /td>		<= /td>	<= /td>	<= /td>
�<= /font>	Poi= nt charge

�<= /font>	The= lines radiate
	equ= ally in all

	dire= ctions

�<= /font>	For= a positive source
	cha= rge, the lines will

	rad= iate outward

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= Electric Field Line Patterns

<= /td>		=	<= /td>
�<= /font>	For= a negative source
	cha= rge, the lines will
	poi= nt inward

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= Electric Field Line Patterns

<= /td>		<= /td>	<= /td>		<= /td>	<= /td>
�<= /font>	An = electric dipole
	con= sists of two equal
	and= opposite charges

�<= /font>	The= high density of
	lin= es between the
	cha= rges indicates the
	str= ong electric field in
	this= region

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file:///C:/C6F2A655/PHYSICS1112K-WEB-CH15_files/v3_slide0029.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="windows-1252" Slide 1

= Electric Field Line Patterns