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Waves

1) The chapter covers magnetostatics, including Biot-Savart's law relating magnetic field to current, Ampere's circuital law relating magnetic field circulation to enclosed current, and definitions of magnetic flux density and permeability. 2) Biot-Savart's law gives the magnetic field from a current element as a function of its location and orientation, while Ampere's law relates the circulation of magnetic field to enclosed current. 3) Key equations also define magnetic flux density B and material permeability, and present the Lorentz force law relating force on a charge to electric and magnetic fields.

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Ali Ibrahim
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59 views10 pages

Waves

1) The chapter covers magnetostatics, including Biot-Savart's law relating magnetic field to current, Ampere's circuital law relating magnetic field circulation to enclosed current, and definitions of magnetic flux density and permeability. 2) Biot-Savart's law gives the magnetic field from a current element as a function of its location and orientation, while Ampere's law relates the circulation of magnetic field to enclosed current. 3) Key equations also define magnetic flux density B and material permeability, and present the Lorentz force law relating force on a charge to electric and magnetic fields.

Uploaded by

Ali Ibrahim
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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CHAPTER 3

MAGNETOSTATICS
MAGNETOSTATICS

3.1 BIOT-SAVART’S LAW

3.2 AMPERE’S CIRCUITAL LAW

3.3 MAGNETIC FLUX DENSITY

3.4 MAGNETIC FORCES

2
Chapter 3: Lecture 4: Problems
SUMMARY (1)

•For a differential current element I1dL1 at point 1,


the magnetic field intensity H at point 2 is given by
the law of Biot-Savart,
I1dL1  a12
dH 
4 R12
2

Where R12  R12a12 is a vector from the source


element at point 1 to the location where the field is
desired at point 2. By summing all the current
elements, it can rewritten as: IdL  a
H R
4R 2
4
SUMMARY (2)

•The Biot-Savart law can be written in terms of


surface and volume current densities:

KdS  a R
H Surface current
4R 2
Jdv  a R
H Volume current
4R 2
•The magnetic field intensity resulting from an
infinite length line of current is:
I
H a
2
5
SUMMARY (3)

and from a current sheet of extent it is:

1 Where aN is a unit vector normal from


H  K  a N the current sheet to the test point.
2
•An easy way to solve the magnetic field intensity
in problems with sufficient current distribution
symmetry is to use Ampere’s Circuital Law,
which says that the circulation of H is equal to the
net current enclosed by the circulation path

 H  dL  Ienc
6
SUMMARY (4)

• The point or differential form of Ampere’s circuital


Law is:
H  J
• A closed line integral is related to surface integral by
Stoke’s Theorem:

 H  dL     H  dS
• Magnetic flux density, B in Wb/m2 or T, is related
to the magnetic field intensity by

B  H

7
SUMMARY (5)

Material permeability µ can be written as:   0 r


and the free space permeability is:

0  4 107 H m
• The amount of magnetic flux Φ in webers through
a surface is:
   B  dS
Since magnetic flux forms closed loops, we have
Gauss’s Law for static magnetic fields:

 B  dS  0
8
SUMMARY (6)

• The total force vector F acting on a charge q moving


through magnetic and electric fields with velocity u is
given by Lorentz Force equation:

F  qE  u  B
The force F12 from a magnetic field B1 on a current
carrying line I2 is:

F12   I 2dL2  B1

9
VERY IMPORTANT!

From electrostatics and magnetostatics, we can


now present all four of Maxwell’s equation for
static fields:

 D  dS  Qenc   D  v
 B  dS  0 B  0
 E  dL  0 E  0
 H  dL  I enc H  J
Integral Form Differential Form

10

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