FSK 126 Semester 2, 1999

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Chapter 30 - homework
2E - 7.7?10-3 T, 7E 30E - F1 (4.69?10-5 N)j,
F2(1.88?10-5 N)j, F30, F4-F2, F5-F1
43E 56E - (a) 5.33?10-4 T, (b) 4.00?10-4 T, 61P
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30-1 Calculating the Magnetic Field due to a
Current
Biot and Savart law
?0 Permittivity constant (electrostatic constant
k 1/4??0) 8.85 x 10-12 C2/N.m2 ?0
Permeability constant (magnetic induction) 1.26
x 10-6 T.m.A-1
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B-Field due to a current in a long straight wire
Direction of B-field
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Direction of induced B-Field
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Solved example Redo the previous derivation to
derive the Biot-savart law for an infinite
conductor, making use of trigonometric
relationships.
Total field at P due to all current elements from
?1 and ?2
Infinitely long, straight wire, ?1  0 and ?2  ?
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Solved problem A bare copper wire (2.6 mm in
diameter) can carry a maximum current of 50 A
without overheating. For this maximum current,
what is the magnitude of the magnetic field at
the surface of the wire?
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Solved problem The electron gun in a TV tube
fires electrons of kinetic energy 25 keV in a
beam 0.22 mm in diameter at the screen 5.46 x
1014 electrons arrive each second. Calculate the
change in magnetic field strength produced by the
beam at the beam axis to a distance 5 mm from the
beam axis.
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B-Field due to a current in a circular arc of wire
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Solved problem (3, pg. 743) In the figure two
long straight wires just pass each other
perpendicularly without touching. In which
quadrants are there points at which the net
magnetic field is zero ?
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EP 12, pg. 745 Use the Biot-savart law to
calculate the magnetic field B at C, the common
center of the semiarcs AD and HJ. The two arcs
of radii R2 and R1, respectively, form part of
the circuit ADJHA carrying current, i.
Sections AH and JD do not contribute to the
B-field at point C. (ds ? r 0)
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30-2 Two Parallel Currents
F is strongly dependent upon d B is constant
along the conductors ia and ib are in the same
direction
Force on a current-carrying wire due to a second
current-carrying wire - first find the field due
to second wire at site of first wire, then force
on wire due to that field.
Parallel currents attract Anti-parallel currents
repel
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EP 29 pg. 747 What must be the current
(magnitude and direction) in wire 2 for the
resultant magnetic field at point P to be zero.
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30-3 Amperes law symmetrical current distribution
Find any magnetic field due to any distribution
with the inverse-square law for the differential
field dB For symmetric distributions - apply
Amperes Law
Integrating around a closed loop - Amperian loop
Procedure Divide the Amperian loop in ds
elements Select B arbitrarily (? to ds) Integrate
enclosed currents - assign signs to currents.
Curl fingers of right hand around Amperian loop -
pointing in direction of integration.
Current in direction of thumb - positive Current
in opposite direction of thumb - negative
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B-field outside a long straight wire
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Current elements dB for each current element
(ids) Integrate dB to get B
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Solved problem A long straight wire of radius R
carrier a steady current i0 that is uniformly
distributed across the cross-section of the wire.
Calculate the magnetic field a distance r from
the center of the wire in the regions r ? R and
r lt R.
Region 1 (r ? R) B is constant and always ??to ds
Region 2 (r lt R) B is constant and always ??to ds
i is less than iT
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EP 40E, pg. 748 Each of the eight conductors in
the figure carries 2.0 A of current into or out
of the page. Two paths are indicated for the
line integral. What is the value of the integral
for the path (a) and (b).
(a) The net current enclosed by the path is 2.0
A out of the page. The path is in a clockwise
direction (current into the page is positive and
out of the page is considered negative.
(b) The net current enclosed by the path is zero.
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EP 44P, pg. 748 Two square conducting loops
carry currents of 5.0 A and 3.0 A. Determine the
value of the line integral (Amperes law) for
each of the two closed paths.
d a and c tie b
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30-4 Solenoids Toroids
Magnetic Field of a solenoid
Solenoids magnetic field is vector sum of fields
produced by individual turns Points close to wire
- B almost concentric circles, cancel between
adjacent turns Points inside solenoid, and far
from wire - B approximately to solenoid
axis Points outside solenoid, contributions from
top cancel with contributions from bottom - B
approximately zero Direction - curled right hand
rule
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B form concentric circles inside the toroid
N ?total number of turns
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EP 53E, pg. 749 A 200 turn solenoid having a
height of 25 cm and a diameter of 10 cm carries a
current of 0.30 A. Calculate the magnitude of
the magnetic field inside the solenoid.
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EP 55E, pg. 749 A solenoid 1.30 m long and
2.60 cm in diameter carries a current of 18.0 A.
The magnetic field inside the solenoid is
23.0 mT. Find the length of the wire forming the
solenoid.
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Solved example An infinite sheet lying in the
yz plane carries a surface current of density JS.
The current is in the y-direction, and JS
represents the current per unit length measured
along the z-axis. Find the magnetic field near
the sheet.
Rectangular path l ? w, l ??surface Net
current (l ? w) JS l Apply Amperes law,
(sides (w) no contribution to line integral
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