Transcript lecture02

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Scalar field: Temperatures
Vector field: Winds
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3. Electric field
3.1 Coulomb’s low and electric field

r
Q
q
F k
Qq
2
 qk
r
P
Charge Q creates an electric (electrostatic) field E.
Charge q is a test charge used to find this electric field E.
Q
r
2
 qE
3.2 Definition


F  qE


F
E
q

E - electric field
Units
If the electric force on a test charge q located at
point P is F, then the electric field at point P is F/q.
Because the force is always proportional to q, the
electric field is independent of the test charge!


F 
E     N /C
q

(Action at a distance?)
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Example: A negative charge, placed in the electric field between two
charged plates, experiences an electric force as shown below.
What is the direction of the electric field?
A. Left
B. Right
C. Upward
+
D. Downward
• The negative charge is attracted by the positive
plate and is repelled from the negative plate
• The electric field is directed from the positive to
the negative charge!
q

F
-
-

E
Example: Between the red and the blue charges, which of them
experiences the greater electric field due to the green charge?
+1
d
+2
+1
d
+1
Both charges feel the same electric field due to the green
charge because they are at the same point in space!
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Example (Electron in a uniform electric field): Describe the motion of an
electron that enters a region with a uniform electric field having initial
velocity perpendicular to the direction of the field
v0
E
electron
parabola
F = –|qe|E
Once the electric field is known, finding the force on a given charge is simple…


 F  qe E
a 
m
m
Constant acceleration in the –y direction. Identical to projectile motion!
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3.3 Two most important questions:
1) How can one find force, F on the electric charge, q, exerted by field E?
2) How can electrostatic field E be created?
Answers:
1)


F  qE
2) Field E is due to other charges
2a) Field due to a single charge:
2b) Field due to a number of charges:
Ek
Q
r2



E  E1  E 2  ...
Principle of superposition has been used in 2b)
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3.4 Principle of superposition (explanation)
  



F  F1  F2  ...  qE1  qE2  ...  qE
Q2
q
Q3
test charge
Q1
Q6
Q4
Q7
  
E  E1  E2  ...
En  k
Qn
rn2
n  1,2,...
Q5
Q8

• Charges Q1, Q2, … create electric field E .
• This field is independent from the test charge q.

• If we will replace the charge q with another
 charge qnew, then the force Fnew
on the new charge will be different than F , but the electric field is
independent from q.



Fnew
F
E

q
qnew
Definition of electric field
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Example (Net electric field):
Which of the three vectors
best represents the direction
of the net electric field at the
location of charge Q?
Example: Calculate the electric field at
the center of a square 52.5 cm on a side
if one corner is occupied by a charge
+45μC and the other three are occupied
by charges -27μC.
Q2  27.0 C
Q2
E1
q1 < 0
A
Enet
E1
q2 > 0
Q
B
E2
d
C
E2
Q2
Q1  45.0 C
Q2
Q1  Q2
Q1
E  E1  E 2  k 2
k 2
k

2
d /2
d /2
d /2
6
9
2
2 45  27   10 C
 9  10 Nm / C

2
2
52.5  10 m / 2

 4.7  10 6 N / C

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3.5 Electric field lines
Definition:
• Electric field lines indicate the direction of the force due to the given field on a
positive charge, i.e. electric force on a positive charge is tangent to these lines
• Number of these lines is proportional to the magnitude of the charge
Properties:
• Electric field lines start on positive charges or came from infinity, they end on
negative charges or end at infinity
• Density of these lines is proportional to the magnitude of the field
+
-
-
+Q
-Q
-2Q
+
+
+
+
-
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Examples: Electric Field Lines Around Electric Charges
A single positive charge
(an electric monopole)
A positive charge
and a negative of
equal magnitude
(an electric dipole)
Two equal positive charges
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Example:
The electric field lines in a certain region of space are as shown below.
Compare the magnitude of the electric field at points 1, 2 and 3.
A. E1 = E2 > E3
B. E1 > E2 > E3
1
2
3
C. E1 > E2 ; E3 = 0
The magnitude of the electric field is proportional to the local density of lines.
Being on the same line or being between the lines is totally irrelevant.
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3.6 Electric field in conductors
• The electric field inside a conductor in equilibrium is always zero.
If E  0  F  0  a  0
 motion of charges (conductor, charges can move)
 non equilibrium
• The electric field right outside a conductor in equilibrium is
perpendicular to the surface of the conductor.
We cannot have a force parallel to
the surface (would produce motion),
but perpendicular to it is OK.
E=0
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