28
Chapter
of Magnet!c
sources
Chap
27->
In
chap
!s
produced
Top!es
1)
:
28
B
effects of magnet!c f!eld
we
,
w!ll
f!elds due
mov!ng
a
F!eld
study
how
a
magnet!c f!eld
to
charge
2
a
current-carry!ng conductor of !nf!n!tes!mal length
3)
a
current-carry!ng
4)
a
5)
a
long stra!ght
c!rcular
6) Ampere's
loop
law
7) Soleno!d
8) Toro!d
(2) B!ot-savart Law)
conductor
conductor
of f!n!te length
F!eld
Magnet!c
of
Fat
Mov!ng Charge
-te
-
B &
P
A
-
Exper!ments
Bat
F!nd
magnet!c
show
d!rect!on
:
Q
Bav
/ra
B
B
a
B
a
!nverse-square
law
s!nc
no
r2
Us!ng
B
=
a
constant
kes!nt
at
proport!onal!ty
where
!n vector
form
B
=
klan Kayr =
=
D!rect!on
B
of
determ!ned
!s
by
RH
rule
.
!n
B
!⑰
I
Y
7 V
->
Cases
Spec!al
*
*
If
0
a
charge
=
0
does
at
po!nts
If
0
=
on
90-
There
Thus , B
180
or
!s
f!eld
s!nc
not
=
produce
of
!ts l!ne
s!nc
=
1
B-f!eld
l!nes
0 ->
->
B
even
are
gay
k
=
-
value
=
0
any
magnet!c
mot!on
f!eld
.
max!mum
beh!nd
a
charge
c!rcles
-
Numer!cal
!s
B
l!ne
ot
mot!on
of K'
permeab!l!ty of free spoke=
10
cm/s
TM
=
10-7 ?
Why
cons!der the
Electromognet!c
rat!s
>E
9x119
1
↳
=
*
↓I
=
kl
Ef!elds
1 9x10 B x 118)2
EoMe
=
=
=
>B
f!elds
an
!nf!n!tes!mal
we
dB
can
=
E,
=
kane
now
k'da V
de
0
for
a
CO
wr!te
s!nO
But
=
n
(Ade)
n
volume
P
charge of
each
carr!er
3
s!ngle charge
12
da
Current
e
-
B
C
u
~ -a
Us!ng
->
-
e
c2
F!eld of
Magnet!c
!s
wave
.
Element
dB
=
K nAded Us!ng
12
-des!nc
Th!s
result
!s
BS
exper!mentally
can
use
=
!t
we
sect!ons
-
E
Law
the
d!v!de
ver!f!ed (proved
length
de
.
any conductor
.
=
a
y
O
-Ee ,
~
/
FO
/
as
of
K'Idexr
de
/ (
magnet!c f!eld of
w!th f!n!te length
I
!f
=
can't be
law
because
!nf!n!tes!mal
!nto
B
st!ll
form
B!ot-Savart
called
Note that
we
!n vector
⑧
X
current-carry!ng
conductor
the
conductor
apply
BS law
D!v!de
and
For
dB
sect!ons
segment
one
k'EsnO
=
!nf!n!tes!mal
!nto
page at P
!nto
12
But de= dy
s!nc= S!n (H-0)
v2
2
x
=
all
magnet!c
B
=
B
=
E
y2
dyx
d!s=
S!nce
+
=
=
such
f!eld
de /
k
sect!ons
produce
.
So=S!te
kI
x
2
look
&
!ntegral table
a
s!m!l!ar
B
k'I
=
If po!nt
!nto page at p
az
!s on the
left
s!de
E
!s out
of page
-
-
↓
-
magnet!c
closed
surface
E
GB
F!eld
=
of
=
'Far
*
*
general
In
=
te
=
0
always
Long Stra!ght
↳rad al d!stance
conductor
3
Us!ng
i
B
-
çca
B
then
get
We
B
,
x
=
20
Magnet!c
Between
Force
parallel Long
Two
conductors
l
->
!
"
W
lower
I
> B
1
7
E
upper
-
↳
I
-
7
l
...
W
>I
d
-
F!nd :
Force
Magnet!c
Two
a
reasons
why
the
upper
upper
conductor
conductor
exper!ences
magnet!c force
1)
s!ts
2)
carr!es
F
E
E
on
!s
=
MoII'
=
2Hd
towards
of
the
lower conductor
current
Il
=
magnet!c f!eld
!n the
I
(4) Mate
=
force
the
per
lower
un!t
length
conductor
N3rd
L
lower
says
must
w!re
conductors attract
exper!ence
each
a
-
#
other
Appl!cat!on
How
current
much
!s
I measure
>I
exactly
1A
?
I
[
EF
↳anam
-I
F
=
Mo II
-
2Hd
h
l
=
1m
Start!ng
from
gradually
unt!l
-
F
(1)
(44x10
=
2H(10
exactly
-
I
(1)
=
0
!ncrease
,
(1)
2x155w
=
2)
1A
the currents
?
current
!s
observed
.
Pr28/10
A
stra!ght
F!nd
:
B due
Beam
B
=
space at
!n
g!ven po!nt
a
2m
protons
to
beam
-
Ma
B
=
(4π x 10
rate
away
long
l!ke a
behaves
a
of protons
2
.
5x119 protons/s
.
conductor
7) (2 5x169) (1
.
.
6
10
-
x
19)
2π(2)
=4x10-17+
Pr
of
very
small
28/18
I
1
=
3 5A
.
<
>
E30am
>
5cm{
-
*B
II
FL
long
stranger
I
2
~
=
3 5A
.
y s
ER
C
weaker
-
10cm
F!nd
the
->
Fnet=
net
magnet!c force
Etop+EBottom
FR= E
they
on
the
-
+
R!ght
concel
+
Fleft
each
other
passes
loop
.
FT
↑
④
mE
I
2
~
=
FT > FB
3 5A
.
/
>ER
C
weaker
↓F
-
10cm
F+
FB
[21B
=
=
Fnet
Son
Fz
=
=
Ia(0
!(3)
(0-1)(
00)
FT-FB
=
5
.
1 x 15-6 N
öner!s!
① Bunn dengel!cek
②
.
e
kütle
we
'SI yegu
s!stem
he
dur
?