Chp. 30 Magnetic Fields

1

• Chapter 30
• Magnetic Fields due to Currents
• Summary - Chapter 29
• Magnetic field
• Magnetic force on a charge
• Crossed E and B fields
• Orbit of charge in a magnetic field
• Magnetic force on a current carrying conductor

AIMS Magnetic Field strength Biot-Savart
law Amperes law Long straight
conductor Circular arc of wire Two parallel
currents Solenoid Toroid

2
30-1 Calculating the Magnetic Field due to a
Current
Biot-savart Law
Moving charge (electric current) ? B-field
3
Derivation
?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
4
Direction of induced B-Field
5
B-Field due to a current in a long straight wire
6
(No Transcript)
7
(No Transcript)
8
B-Field due to a current in a circular arc of wire

• B - single current element
• ids dB
• Net field - integrate
• B-field at center of curvature
• ? (r and ds) 900
• r R

Checkpoint 1Relative magnitudes
9
Sections AH and JD do not contribute to the
B-field at point C. (ds ? r 0)
10
30-2 Two Parallel Currents
11

• Current elements
• dB for each current element (ids)
• Integrate dB to get B

12
Checkpoint 2 Draw field lines, determine
magnitude of field, B.
30-3 Amperes law symmetrical current
distribution

• Procedure
• Divide the Amperian loop in ds elements.
• Select B arbitrarily (? to ds)
• Integration of enc. Currents

13
B-field outside a long straight wire
B-field inside a long straight wire
14
Checkpoint 3 Determine iencl.
15
(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.
16
(No Transcript)
17
http//www3.hmc.edu/jengel/rail2.html
http//www.utexas.edu/research/cem/rd/rd02/02.html
http//www.cstp.umkc.edu/mrappard/physics/railgun
.html
18
30-4 Solenoids Toroids Magnetic Field of a
solenoid Assumptions length of solenoid
gtgt diameter (ideal solenoid) tightly
packed turns of wire external B-field is
zero
Magnetic Field of a Toroid
19
(No Transcript)
20
(No Transcript)
21
(No Transcript)
22
(No Transcript)
23
Chapter 30 solutions
2E A 10 gauge bare copper wire (2.6 mm in
diameter) can carry a current of 50 A without
overheating. For this current what is the
magnetic field at the surface of the wire
7E At a position in the Philippines, Earths
magnetic field of 39?T is horizontal and
directed due north. Suppose the net field is
zero exactly 8.0 cm above a long straight
horizontal wire that carries a constant current.
What are (a) the magnitude and (b) the direction
of the current?

• The field due to the wire, at a point 8.0 cm from
  the wire, must be 39 ?T and must be directed due
  south.
• (b) The current must be from west to east to
  produce a field to the south at points above it.

24
30E The figure below shows five long parallel
wires in the xy plane. Each wire carries current
i 3.00 A in the positive x direction. The
separation between adjacent wires is d 8.00
cm. In unit-vector notation, what is the
magnetic force per meter exerted on each of
these five wires by the other wires?
Label these wires 1 through 5, left to right.
Then  
 
25
43E The figure below shows a cross section of a
long cylindrical conductor of radius a, carrying
a uniformly distributed current I. Assume that
a 2.0 cm and I 100 A, and plot B(r) over the
range 0 lt r lt 6.0cm.
Use Eq. 30-22 for the B-field inside the wire
and 30-19 for that outside the wire. The plot is
shown below      
 
56E. A toroid having a square cross section,
5.00 cm on a side, and an inner radius of 15.00
cm has 500 turns and carries a current of 0.800
A. (It is made of a square solenoid instead of
round as in Fig 30-17 bent into a doughnut
shape.) What is the magnetic field inside the
toroid at (a) the inner radius and (b) the outer
radius of the toroid?   ( a)   Use Eq.
30-26. The inner radius is r 15.0 cm so the
field there is     ( b) The
outer radius is r 20.0cm. The field there is  
26
61P. A long solenoid has 100 turns/cm and carries
a current i. An electron moves within the
solenoid in a circle of radius 2.30 cm
perpendicular to the solenoid axis. The speed of
the electron is 0.0460c (c speed of light).
Find the current i in the solenoid.
27
(No Transcript)
28
(No Transcript)
29
(No Transcript)
30
(No Transcript)
31
ANSWERS (SELF-EVALUATION)
1. d 2. a 3. e 4. d 5. d 6. e 7. b
8. d 9. e 10. a 11. a 12. c 13. d 14.
c 15. c 16. a 17. c 18. d