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Electric Fields

Definition: Electric Field E
q
?
q
Force
Field Picture:
The “source” charge q produces an electric
field in space. The field pushes on the “test”
charge q0 .
Definition:
Electric Field =
F
E
q
Force on tiny “test charge” q0
charge q0
Units: N/C
• A vector
• Exists before test charge is introduced
• Is produced by other charges (not q0)
• q0 is small so as to not disturb the charges
producing the field
• it is a mathematical construct
Example:
q

E  1000 N


C
Calculate the force on an alpha particle (q = +2e) if
it is placed in the field.
Repeat for an electron.
E Fields are Produced by positive charges,
and terminate on negative charges
Which way will a + or – charge move in this field?
E Fields between two charged plates
-
+
+
+
+
+
+
+
+
Which way will a + or – charge move in this field?
E Fields are Produced by positive Charges
+q

r
q
Coulomb:

qq
F  ke 2 rˆ
r

q
 E  ke r 2 rˆ
E
But also:


F  qE
Field of a positive
point charge q
The field decreases in strength (magnitude) with distance
Several Charges:

E is the (vector) sum of the fields produced by the
individual charges:
qi
E   E i  ke 2 rˆi
i 1
i
ri
n
q1

E2

r1
q2

r2

E

E1
What are the signs of
the 2 charges?
Find the electric field of the three charges at the
origin:
y-axis
q2  20C
q  40C
4
300mm
400mm
x-axis
q1  10C
Quiz

What is the direction of E at point B ?
B : (0,y)
y
a
-q
A) +i (right)
B) –i (left)
C) +j (up)
D) –j (down)
a
A : (x,0)
+q
x
Example: Electric Dipole

Derive an expression for E at point B.
y
B : (0,y)
a
-q
a
A : (x,0)
+q
x
Dipole solution:
For fun: find E at point A, and show that it is
approximately proportional to x 3, at large distances x.
Summary
Define:
F
E
q


F is force exerted on q by E .

E is produced by other charges.
Point charge “q” produces:
 k q
E  e 2 rˆ
r