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LECTURE 7
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1
Lecture 7
Electrostatic Potential
Sections: 4.1, 4.2, 4.3, 4.4
Homework: D4.1, D4.2, D4.3, D4.4, D4.5; 4.3, 4.4, 4.5, 4.6,
4.9, 4.10, 4.12
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2
Work – 1
differential work
cos
Wd
W
d
F
d
L
α
Δ=
⋅
Δ⇒
=
⋅
=
FL
F
L
work done from
A
to
B
, J
B
A
=⋅
∫
work is positive if the applied force is in the
direction of displacement
work is negative if the applied force is opposite to
the direction
of displacement
F
Δ
L
0
WF
L
Δ
=Δ
>
F
Δ
L
0
L
Δ
=− Δ <
F
Δ
L
0
W
Δ
=
F
Δ
L
A
B
d
L
F
work is zero if force is orthogonal
LECTURE 7
slide
3
Work – 2
examples with gravity (uniform motion)
L
Δ
g
F
m
F
α
0, man does work
(expends energy)
mm
WF
L
=
Δ>
cos
0, rock gains energy
gg
L
=
Δ<
cos
mg
WW
FF
= −
=−
cos
0, gravity does work
(rock loses energy)
L
=Δ
>
L
Δ
g
F
m
F
0
L
=− Δ <
man provides enough friction to prevent
acceleration, gains energy (heat)
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4
Line Integration – 1
we have already studied the line integral of the type (see L04)
B
l
A
Qd
L
ρ
=
∫
the work integral involves a dot product
x
y
z
A
B
()
u
r
d
r
B
A
Wd
=
⋅
∫
FL
x
yz
dW
d
F dx F dy
F dz
⇒=
⋅
=
+
+
x
x
ux
u
y
u
z
u
d
d
dx
dy
dz
=++
==
+
+
ra
a
a
Lr
a
a
a
x
xy
z
FF
F
Fa
a
a
B
xyz
A
W
F dx F dy
F dz
+
+
∫
LECTURE 7
slide
5
Line Integration – 2
RC
S
:
(,,)
C
C
S
:
(,,
)
)
)
S
C
S
:
(
,,)
(
(
,,)s
i
n
B
xyz
A
B
z
A
B
r
A
W
F xyzd
x F xyzd
y F xyzd
z
WF
z
d
F
z
d
F
z
d
z
W
F
rd
r
F
rr
d
F
d
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This note was uploaded on 02/29/2012 for the course PHYS 227 taught by Professor Rabe during the Fall '08 term at Rutgers.
 Fall '08
 RABE
 Physics, Work

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