ELECTRIC FIELD LINES (19.6)
There is an electric field vector for every point in
space around a charge
 Electric field fills space around charge.

Can REPRESENT E in a region of space by Electric Field Lines (EFL)
“RULES” for drawing/interpreting Electric Field Lines:

 E vector at a point in space is tangent to the EFL through that point
 “Density” of EFLs (i.e. number of lines through unit area perpendicular to
lines) is proportional to E (magnitude) in that region
o Larger E → lines closer together
 EFLs start on positive charges and end on negative charges
o BUT lines may end on charges FAR AWAY from region of interest
 Number of EFLs starting/ending on charge is proportional to its magnitude
o Must be consistent within a given diagram
o Be careful counting lines: lines point in 3 dimensions from real charge
 Electric field lines do not cross

 The real E field is continuous → fills space around a charge
o (IMPORTANT: read pitfall prevention 19.2 on p. 634)

Examples of Electric Field Line representations of E near charges:
Near positive and negative charges of the
same magnitude
Dipole: opposite point charges, equal magnitudes
 Higher field between charges
 EFLs nearly radial at charges
 Same number of EFLs start/stop on
positive/negative charge
Two positive point charges:
 Electric field lines don’t cross
 Magnitude of E in the centre is zero!
Unequal charges:
 Higher field (higher density of lines) near +2q than near –q
 Field lines really radiate in 3 dimensions so number of field lines starting
and ending on each charge is not quite proportional to what is shown in 2
dimensions. (IMPORTANT: read pitfall prevention 19.2 on p. 634

Motion of a charged particle in a uniform E field
 Important point: motion is not necessarily parallel to electric field lines!

For a charge q in E ,


 the force on the charge is F  qE


F

m
a
Because of Newton’s 2 law,
,
nd
 acceleration of an electron in an electric field is

 qE
a
m

How can we make a uniform E field?
 Between large, parallel, oppositely charged plates;

o E has same direction and same magnitude
EVERYWHERE between plates

For charge q and E in the x direction;
ax 
Eq
m ,
ay  0
Application: electron gun in TV or cathode ray tube.
 Can accelerate electron between plates and eject through small hole in
positive plate
Example: An electron (q=-e) starts with vi  0 at x  d and accelerates toward
x  0 . What is v when x  0 ? What is the kinetic energy of the electron at x  0 ?

For charge q and E in the y direction;
Eq
ax  0 , a y 
m ,

A charge moving across E field lines is deflected:
 For an electron projected into a uniform field


E  Eˆj with vi  v xi iˆ , acceleration is:
eE
a


ax  0 , y
m

 This is like projectile motion EXCEPT that E field only exists for range of x.

Example: An electron is projected into a uniform field E  Eˆj

v
with i  v xi iˆ . The field exists between x  0 and x  l .
(a) What is the electron velocity when it leaves the region of electric field?
(b) Relative to its starting level, what is the vertical displacement of the electron
when it leaves the region of electric field?
Application: Cathode ray tube:
 can accelerate AND steer electrons to a point on the screen.