Download Lecture 4 - McMaster Physics and Astronomy

Electric Field Lines
• Drawing electric field lines
• Motion of charged particles in an electric field
• Electric flux
Electric Field Lines
Electric field lines are a way of visualizing the field.
Rules for Drawing field lines:
1) Lines start on (+) charges, end on (-) charges, or
go to infinity
2) (# of lines)  charge
3) Lines never cross
4) Strength of field is proportional to the density
of field lines
Interpreting the picture:

E is parallel to the field line at each point.
Electric Field lines for an isolated Charge +Q
E

E
E
+
Q
E – magnitude of field
Field lines
+
Area S,

E
Where is the density of field
lines greatest?
2 Point Charges
Note:
-2Q
+Q
• number of
lines on -2Q is
twice as many
as on +Q
Quiz:
Which way will the dipole
start to move in the electric
field?
A)
B)
C)
D)
E)
up
down
left
right
nowhere – there is no net force.
-q
+q
Quiz:
Does this dipole feel a
torque ?
-q
+q
A)
B)
C)
D)
Yes - clockwise
Yes – counter clockwise
No
Depends on the strength of E
Parallel Charged Plates
 
+
-
charge
; uniform charge density
unit area
+
+
-
+
-
+
-
+
+
-
-
+
-
E approx. uniform, between the plates, except
near the edges.
Electric Force



F  qE  ma
i .e :
 q 
a  E
m


If E is uniform  a is CONSTANT
Therefore we can solve for motion as easily
as projectile motion!
Example: Uniform E
An electron enters a uniform field of E = -200N/C j with an
initial velocity of vo = 3x106 m/s i. Find:
a) The acceleration of the electron
b) The time it takes to travel through the region of the field
c) The vertical displacement of the electron while in the field
0.1m
e
-

E
Solution:
Electric Flux
Electric flux is the measure of the “number of
field lines passing through a surface S ”

For uniform E :
Define: Electric Flux
ΦE  E A
S
Units: N•m2/C

E

A
A is the surface
area perpendicular
to S, so Φ=EAcos(θ)
Notes:
1) E is a scalar called electric flux
2) Units: N•m2/C
3) E represents the “number of field lines
through surface S.”
4) For a closed surface, the area vector points
in the outward direction.
5) Flux is zero for a surface parallel to the field
(normal is at 90o to E)
Example:

E  1000 N C
S2
S1
30°
(rectangle,
1m x 2m)
Find: flux
(rectangle,
1m x 2m)
E
S3
(hemisphere,
radius 1m)
through S1, S2, S3.
solution
If E is not uniform, or S is not flat, then:
For a small surface dA,
dΦE  E dA
For the whole surface,
ΦE   E  dA
S

  E cos dA
S
Summary
•Electric field lines help show the direction of E
•Electric flux is defined as the magnitude of the
field times the area (maybe negative if the angle
between the vectors is more than 90 degrees)
•Electric flux is a quantitative equivalent to “the
number of field lines through a surface”.