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Today5/2
Questions?
E-Fields and Potential Difference
(review)
E = kQs /r2
Many Charge Example
+qo
-2qo
+4qo
-3qo
What is the force on +4qo? (direction also)
Find the field at +4qo due to the “other”
charges. These are the “source” charges.
ro
E+q = kQs/r2 = k(qo)/(ro)2 = Eo
Direction?
Away from + so right
E-2q = kQs/r2 = k(2qo)/(2ro)2 = k2qo/2(ro)2= k(qo)/(ro)2 = Eo
E-3q = kQs/r2 = k(3qo)/(ro)2 = 3kqo/(ro)2 = 3Eo
E = kQs /r2
Many Charge Example
+qo
+4qo
What is the force on +4qo? (direction also)
E+q = Eo
E-2q = Eo
E-3q = 3Eo
ro Now add E-Field vectors
-2qo
-3qo
Ey = E-2q,y + E-3q,y
Ey = Eosin45 + 3Eo
Ex = E+q,x + E-2q,x
Ex = Eo - Eosin45
Ex = 0.29Eo
 = tan-1(0.29/3.7) = 4.5°
Ey = 3.7Eo
Fon +4q = (4qo)3.71Eo = 14.84qoEo
Etotal = 3.72 + 0.292 Eo = 3.71Eo Fon +4q = 14.84kqo2/ro2
same direction as Etotal
What direction would the
force point on a small positive
charge at 1,2,3?
Compare the size of the force
exerted on a small charge at
a. 1 and 2 1 larger
b. 2 and 3 3 larger
The test charge is doubled
when at 2
a. how does the force
change? 2x
b. how does the electric
field change? Stays
the
same
“Potential Energy Difference”
and “Potential Difference”
Potential Energy Difference PEA,B is the
change in PE the particular charge feels when it
is moved from one location to another.
Potential Difference VA,B is the change in PE a
positive 1C charge would feel if it were moved
from one location to another.
VA,B = +108 Volts,
and q = +1C
PEA,B = +100J
VA,B = -108 Volts,
and q = +1C
PEA,B = -100J
Which way does the E Field point?
PEA,B =
+100J, and q =
+1C What is
VA,B?
Remember:
From A to B!!!
VA,B = 108 Volts
Higher
Potential
E field
A
Higher
Potential
B
PEA,B =
E field
+100J, and q =
VA,B = -108 Volts
-1C What is
VA,B
? “downhill” with respect to potential difference
E Fields
point
At which location is the
potential highest?
At 2
downhill to 1 and 3
At which location is the
potential lowest?
At 3
uphill to 1 and 2
Energy stored
kQ
V
r
PE  qV
V  0
How much energy is stored in the assembly of
charges? All are +1 x 10-3C and 1g (1 x 10-3kg).
Energy stored is the same as
3m
the work required to
assemble the charges.
4m
5m
Move them all very far away,
bring them in one at a time,
and total up the work done.
Enet = 0
How big is E?

E 
2 0
(+)

E 
2 0
E net
Enet = 0
(-)


0
WAB = qED
What is the
change in
potential
energy in
going from
A to B?
PEAB = qED
PEAB = qVAB
VAB = EDAB
WAB = qED
FHq
B
FE = qE
A
Only applies when the
field is uniform over the
distance. VAB‘s sign
depends on the direction
of E. In this case it’s
positive.