Static Magnetic Field

Engineering Electromagnetics

EE2011

LECTURE 3

Chen Xudong

Dept. of Electrical and Computer Engineering

National University of Singapore

NUS/ECE

EE2011

Static Magnetic Fields

1. Magnetic flux density

Earth Magnet

Bar Magnet

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Static Magnetic Fields

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Opposite poles attract

and like poles repel.

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Unlike electric charges, magnetic

poles (or magnetic charges) always

come in pairs - one north and one

south. That is, there are no individual

magnetic charges.

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Static Magnetic Fields

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Introduce the magnetic flux density B, which is the counterpart of

the electric flux density D in the electric fields.

Gauss’s Law:

The former is the differential form and the latter is the integral form

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Static Magnetic Fields

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2. Ampere’s Law

0  4  107 H/m

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Static Magnetic Fields

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Apply Stoke’s Theorem,

 B  ds    B  dA

Thus, from the last slides,

we have

This is the differential

form of the Ampere’s Law

Note:

(1)Valid for any closed contour

(2)Practical utility for cases of symmetry

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Static Magnetic Fields

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Example 1

The long straight wire of radius R carries current I that is uniformly

distributed. Calculate the B in all regions.

Solution:

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Static Magnetic Fields

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Example 2

The long solenoid (of n turns per meter) carries current I. Calculate the

B inside the solenoid.

Solution:

turns per meter

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Static Magnetic Fields

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3. Biot-Savart’s Law

When symmetry is absent, we will use the Biot-Savart’s

Law, which is in fact more general,

ˆ

0 I d s  r

B

4  r 2

Note:

The r is the distance between the d s and the observation point P;

ˆ

The r is the unit vector pointing from the d s to the P

ˆ

ˆ

The d s  r is always perpendicular to both d s and r

The derivation of the Biot-Savart’s Law can be...