Chapter 24 Electric Fields 第二十四章 電場. Action at a distance q1q1 q1q1 q2q2 q2q2.
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Transcript of Chapter 24 Electric Fields 第二十四章 電場. Action at a distance q1q1 q1q1 q2q2 q2q2.
Chapter 24 Electric Fields
第二十四章 電場
Action at a distance
1 212 212
21
ˆkq q
F rr
q1
q1
q2
q2
21r̂
9 2 29.0 10 /k Nm C
Another point of view -- Fields
1 212 212
21
ˆkq q
F rr
)( 212112 rEqF
rr
qr
r
kqrE ˆ
4
1ˆ)(
22
022
2
where E2 is the electric field generated by charge q2 and r is a position vector from the position of q2 to any point in space.
22120 /10854.8 NmC
Electric field lines
Electric field linesThe concept of electric field lines was originally due to Faraday who envisioned that the space around a charge is filled with “lines of force”.
The field lines are originated from positive charges and terminated at negative charges, and they are unbroken in vacuum.
The relationship between the electrical field and field lines
Electric field lines with arrows indicate the local field directions, and their density in a plane perpendicular to the local field represents the magnitude of the local field.
Suppose that there are N field lines originated from a positive charge q, then we have the density of field lines given by N / 4πr2 at a distance r from the charge.
Note that if N = q / ε0 then we recover E = q / 4πε0 r2.
Field lines repel each other
Field lines are smooth
The electric field due to a point charge
)(4
13
0i
i
ii rr
rr
qE
)(...)()()( 21 rErErErE n
Sample problem
What is the electric field at point P?
Sample problem
What is the electric field at point P?
The electric field due to an electric dipole
x
y
-a a
P
3 30
( )4
r r r rqE
r r r r
r
r
r
ˆr ax
ˆr ax
Electric dipole moment:
ˆ( ) 2p q r r qax
2p qa
The electric field due to an electric dipole
Along x-axis: ˆr xx
For 2 2 2
0
21
4 ( )
x pE
x a
For 2 2
2 2 20
1 ( )
4 ( )
a x pE
a a x
30
1 2
4
pE
x
:ax
:ax
:ax
The electric field due to an electric dipole
In y-z plane: ˆ ˆr yy zz
2 2 2 3/ 20
1
4 ( )
pE
y z a
30
1
4
pE
r
Note that 2
1E
r for net charge 0
3
1E
r for net charge 0
but net dipole moment 0
:ar
Electric field due to a line of charge
Electric field due to a line of charge
Electric field due to a line of charge
Electric field due to a line of charge
Electric field due to a charge disk
A point charge in an electric field
F qE
Millikan oil-drop experiment (1910-1913)
Cathode-ray tube
Deflecting charge particles
A dipole in an electric field
2
306.2 10H Op Cm
A dipole in an electric fieldThere is no net force on a dipole.
But there is a torque.
sin ( )( sin )
sin
qEa qE a
pE
p E
Potential energy of a dipole in a uniform electric field
cosU pE
ˆ ˆ( ) sinU
pE
Home work
Question ( 問題 ): 6, 8, 19
Exercise ( 練習題 ): 5, 10, 16
Problem ( 習題 ): 8, 18, 31, 32