Lecture19 - Units
of
magne-c
field:
Tesla


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Unformatted text preview: Units
of
magne-c
field:
Tesla
 1
T
=
10000
Gauss
 Surface
of
earth:
0.5×10‐4
T
 Bar
magnet:


1.5
T
 Strong
superconduc-ng
magnet:
30
T
 Biot‐Savart
Law
 Current
 dS r dB µ0 I dS × r ˆ dB = 4π r 2 µ0 = 4π × 10 −7 T i m / A Infinite
straight
wire
example
 Z
 a
 The
segment
of
wire
(total
length
=
6R)
is
formed
into
the
shape
 shown
and
carries
a
current
I.
What
is
the
magnitude
of
the
 resul-ng
magne-c
field
at
the
point
P?
 a
.
 b
.
 c
.
 d
.
 e
.
 The
segment
of
wire
(total
length
=
6R)
is
formed
into
the
shape
 shown
and
carries
a
current
I.
What
is
the
magnitude
of
the
 resul-ng
magne-c
field
at
the
point
P?
 a.

 b.
 c.

 d.
 e.
 Ques-on
1:
Equal
currents
of
magnitude
I
travel
into
the
page
in
 wires
M
and
N.
Eight
direc-ons
are
indicated
by
leYers
A
 through
H.

 The
direc-on
of
the
magne-c

 field
at
point
P
is
 a. 
B.
 b. 
C.
 c.  D.
 d.  E.
 e. 
F.
 Solenoid
 Z
 a
 µ0 I B= 2 Approximate
solenoid
as
bunch
of
separate
loops
 a2 ( a2 + z ) 3 22 Magne-c
field
at
the
center
of
the
solenoid
 L/2
 L
:
length
of
solenoid
 n:
coil
density
(#/m)
 a:
radius
of
the
coil
 Looks
like
integra-on
is
required
again,
but
how?
 a
 dz
 Current
through
each
coil:
I
 Number
of
coils
in
dz:
ndz
 Z
 µ0 I dB = n 2 a 2 dz ( µ0 nI B=∫ − L /2 2 a2 + z ) 3 22 a 2 dz L /2 ( a2 + z ) 3 22 ⎡ ⎤ ⎢ ⎥ ⎥ µ0 nIa 2 ⎢ L/2 −L / 2 B= ⎢ 1− 1⎥ 2⎢ L2⎞ 2 L2⎞ 2 ⎥ 2⎛ 2 2⎛ 2 ⎢a ⎜a + ⎟ a ⎜a + ⎟ ⎥ 4⎠ 4⎠⎥ ⎝ ⎢⎝ ⎣ ⎦ Current
through
each
coil:
I
 Number
of
coils
in
dz:
ndz
 dz
 Z
 ⎡ ⎤ ⎢ ⎥ ⎥ µ0 nIa 2 ⎢ L/2 −L / 2 B= ⎢ 1− 1⎥ 2⎢ ⎛ 2 L2⎞ 2 ⎛ 2 L2⎞ 2 ⎥ ⎢ a2 ⎜ a + ⎟ a2 ⎜ a + ⎟ ⎥ 4⎠ 4⎠⎥ ⎝ ⎢⎝ ⎣ ⎦ µ0 nIa 2 B= 2 L ⎛ 2 L2⎞ a ⎜a + ⎟ 4⎠ ⎝ 2 If
L>>a
 µ0 nIa 2 B~ 2 L ⎛L ⎞ a⎜ ⎟ ⎝4 ⎠ 2 2 1 2 = 1 2 µ0 nI L = µ0 nI 2 L/2 What
about
the
field
at
the
very
end?
 dz
 B= ∫ L 0 µ0 nI 2 Z
 a 2 dz ( a2 + z ⎡ µ0 nIa ⎢ L B= 2 ⎢2 2 ⎢ a a + L2 ⎣ 2 ( If
L>>a
 ) 1 2 ) 3 22 ⎤ 0 ⎥ − 1⎥ 2 22 aa ⎥ ⎦ () µ0 nIa 2 L B= 2 a 2 (a 2 + L2 )1/ 2 µ0 nIa 2 B~ 2 L 2 () 1 22 aL = µ0 nI L µ0 nI = 2L 2 µ0 nI B
 Ampere’s
Law
 Amperian
Loop
 Current
 B ⋅ dS = µ0 I ∫ Integral
evaluated
around
any
closed
path
where
I
is
the
total
current
passing
through

 any
surface
defined
by
the
path
 Example
1:
Inside
and
outside
of
a
wire
 Example
2:
Solenoid
 d
 Magne-c
Flux
 Φ B = ∫ B ⋅ dA From
last
Thursday:
Torque
on
current
loop
in
magne-c
field
 µ = IA µ
:
magne-c
moment
 Magne-c
field
applies
torque
on
magne-c
moment
 Example:
Torque
on
magne-c
moment
 B µ Clicker
ques-on
#3:
Which
way
will
the
magne-c
field
try
to
orient
the
moment?
 a.  b.  c.  d.  Clockwise
 Counter
clockwise
 Out
of
the
board
 Into
the
board
 ...
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