Unformatted text preview: Magnetics III Exam II: Thursday, March 1st, 7:30 9:30 p.m. Practice Exam on LONCAPA LON Room schedule information on LONCAPA (same as Exam I) LON AEW: tonight from 6 8 p.m. (Hill Hall 209)
a b y BField of a Finite Length Wire
d I r P dB =
x o Id r 4 r 3 j d = dy ^ B ^ r = xi  y ^ j r = x2 + y 2 Magnetic Force: Magnetic Torque: Fmag = qv B dFmag = Id B ^ ^ j j d r = dy ^ x i  y ^ =  xdy k ( ) B = B = NIA dB =  Magnetic Dipole Moment: o I ( xdy ) ^ k 4 (x 2 + y 2 )3 / 2
dy Ix ^ B = dB =  o k 3/ 2 2 4 b (x + y 2 )
a ^ Id r o Id r BiotSavart Law: dB = o = Biot4 r 2 4 r 3
Wednesday, 28 February 2007 1 Wednesday, 28 February 2007 2 y BField of a Finite Length Wire
d y BField of a Finite Length Wire
d a b I r P dy Ix ^ B = dB =  o k 3/ 2 2 4 b (x + y 2 ) x
2 2 a a b I r P B=
x o I ^ k cos d 4x 
b a B
r x B
r x y x 1 cos r= x +y = = cos r x x d y x tan = y dy = x sec 2 d = tan = cos 2 x
a a = =
= o I sin 4x a
b ^ k y o I ^ [sin a + sin b ] k 4x
o I 4x
a a +x
2 2 Ix ^ xd cos 3 I ^ B= o k =  o k cos d 2 3 4  cos x 4x 
b b + b b + x2
2 ^ k Wednesday, 28 February 2007 3 Wednesday, 28 February 2007 4 1 y BField of a Finite Length Wire
d Question
The force that Wire 1 will feel due to Wire 2 is:
^ k a b I r P x B= B o I 4x
^ k a a +x
2 2 + b b +x
2 2 A. Zero I2 For a = b: I B= o 2x a a2 + x2 For Infinite wire: a , b  a 2 ,  b  2 II B. 2 o 1 2 down 2d o I1 I 2 down C. 1 2d o I1 I 2 up 2d II E. 1 o 1 2 up 2d
D.
2
5 Wednesday, 28 February 2007 d
I1
F1 = I1 1 B2 B2 = o I 2 2d
B2 direction?
1 F1 = I1 1 B2 =
Force per unit length = B=
Wednesday, 28 February 2007 o I ^ I ^ k = o k sin + sin 4x 2 2 2x o I1 I 2 2d
=
1 F1 o I1 I 2 2d
6 Question
The force that Wire 2 will feel due to Wire 1 is: A. Zero
I2 d I1
F2 = I 2
2 Question
The force that Wire 1 will feel due to Wire 2 is:
B1 A. Zero II B. 2 o 1 2 down 2d o I1 I 2 down C. 1 2d o I1 I 2 up 2d II E. 1 o 1 2 up 2d
D.
2
Wednesday, 28 February 2007 I B1 = o 1 2d I2 d I1
F1 = I1 1 B2 B1 direction?
2 II B. 2 o 1 2 down 2d o I1 I 2 down C. 1 2d o I1 I 2 up 2d II E. 1 o 1 2 up 2d
D.
2
Wednesday, 28 February 2007 B2 = o I 2 2d B2 direction?
1 F2 = I 2 2 B1 =
Force per unit length = o I1 I 2 2d
=
2 F1 = I1 1 B2 =
Force per unit length = o I1 I 2 2d
=
1 F2 o I1 I 2 2d
7 F1 o I1 I 2 2d
8 2 Measuring Magnetic Field Measuring Magnetic Field Negative charge carriers feel a force FB = qvd B and are pushed toward the top of the metal strip E Once enough charges are piled up such that the electric force balances out the magnetic force V Va > Vb Forces are balanced: Current Density: qE z + qvd B y = 0 E z = vd B y J x = nqvd ( Same thing happens to positive charge carriers (Va < Vb ) ) Ez =  Jx By nq nq =  J x By Ez = J x By d Vz
10 Hall Effect (1879)
Wednesday, 28 February 2007 9 Wednesday, 28 February 2007 By = nq Vz J xd Hall Probe B = ?
z y 2 mm B
1.5 cm V = 0.40 V I = 75 A x V = +0.40 V n = 11.6 10 28 m 3
By = nq Vz J xd Charge carrier? Electrons!
m ) (1.5 10 (75 )(2)10 A
2 3 =  11.6 10 28 m 3  1.6 1019 C ( )( m 0.80 10 6 V 1.5 10 2 m = 0.40 T
Wednesday, 28 February 2007 )( ( ) ) 11 3 ...
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 Fall '07
 JapGuy
 Magnetic Field, ez, Hill Hall, Finite Length Wire, Fmag, dFmag

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