Chapter1_Notes_v0

# Magnetic eld lines enter magnets at two points north

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Unformatted text preview: “Like” poles repel each other, while “unlike” ones attract • While electric charges can be isolated, magnetic poles always exist in pairs (i.e. no magnetic monopoles) • When magnets are cut up, the pieces still have poles • Magnetic lines encircling a magnet are called magnetic ﬁeld lines and represent magnetic ﬂux density B . Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. Electromagnetics I: Introduction: Waves and Phasors N B S Figure 1-7 Figure 6: Magnetic ﬁeld lines around a bar magnet. Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. 15 Electromagnetics I: Introduction: Waves and Phasors 16 • Magnetic ﬁelds need not come from permanent magnets; electrical current also causes it. • Oersted made an important observation: a magnetic needle deﬂects when placed near wire carrying current. • Needle’s direction is always perpendicular to the the wire and the radial line connecting the wire to the needle. • ⇒ Current in a wire induces a magnetic ﬁeld that forms closed circular loops around the wire, as shown in Fig. 7. Biot and Savart developed a mathematical relationship between electric current and magnetic ﬂux density, called, not surprisingly, Biot-Savart law. For a very long wire in free space, the magnetic ﬂux density that is induced by a constant current is, ˆ µ0 I (T) B=φ 2πr Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. (10) Electromagnetics I: Introduction: Waves and Phasors 17 z I ^ φ B B y r B B B x B B B Figure 1-8 Figure 7: The magnetic ﬁeld induced by a steady current ﬂowing in the z-direction. Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. Electromagnetics I: Introduction: Waves and Phasors 18 as illustrated in Fig. 7. Units are given in Tesla. µ0 = 4π ×10−7 (H/m) is called magnetic permeability of free space . If you think that µ0 is somehow analogous to 0 , you are right; in fact the speed of light in free space c is (Chapter 2): 1 c= √ µ0 ≈ 3 × 108 (m/s.) (11) 0 • Some material can have permeability µ material (such as iron and nickel) µ0 ⇒ ferrmagnetic • The majority of materials are nonmagnetic (i.e. µ = µo ) • µ accounts for the magnetization of a material and can be deﬁned as µ = µr µ0 (H/m) (12) where µr is dimensionless quantity called relative magnetic permeability and H is henries. Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. Electromagnetics I: Introduction: Waves and Phasors 19 The second fundamental pair of electromagnetic quantities are magnetic ﬂux density B and magnetic ﬁeld intensity H, which are related by B = µH (13) • Static and dynamic ﬁelds • Electric ﬁeld (intensity) depends on charge q while magnetic ﬁeld (intensity) depends on the current, i.e. the rate of change of charge ﬂowing through some material. • So long...
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## This note was uploaded on 09/25/2013 for the course ECE 331 taught by Professor Martinsiderious during the Fall '12 term at Portland State.

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