Phys 0175 - Lecture 32

Phys 0175 - Lecture 32 - Lecture 32(Apr 6 2009 Maxwell’s...

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Unformatted text preview: Lecture 32 (Apr. 6, 2009): Maxwell’s Equations; Magnetism (Ch. 32): ► Gauss’ Law for magnetic fields ► Induced magnetic fields ► Displacement current ► Maxwell’s equations and em radiation ► Magnetism and electrons ► Magnetic materials Chapter 32: Maxwell’s Equations Gauss’ Law for Magnetic Fields All experimental evidence to date points to the fact that there are no magnetic monopoles ; the simplest magnetic structure that produces a magnetic field is a single current loop (a magnetic dipole). This fact can be described in terms of Gauss’ Law applied to magnetic fields: Recall Gauss’ Law for electric fields: enc q E dA ε = ∫ r r g Ñ B dA = ∫ r r g Ñ Induced Magnetic Fields: Faraday’s law of induction was expressed as Symmetry suggests the question: If a changing magnetic flux induces an electric field, will a changing electric flux induce a magnetic field? The answer is yes: Maxwell’s law of induction 0 0 E d B ds dt μ ε Φ = ∫ r r g Ñ B d E ds dt Φ = - ∫ r r g Ñ Consider a parallel-plate capacitor with circular plates. Assume that the charge on the capacitor plates increases at a constant rate by a constant current i in the connecting wires. It follows that the electric field in the space between the plates will also increase at a constant rate. Fig. (b) is a view of the right-hand plate in Fig. (a) from between the plates. The electric field points into the page. Consider the electric flux passing through a circular hoop of radius r that is smaller than the radius of the plates. According to Maxwell’s law of induction there must be an induced magnetic field around the loop. This has been observed experimentally. If one considers a loop of radius r that is greater than the radius of the plates, one finds that a magnetic field is induced around that loop as well. Once the capacitor plates are fully charged, the electric field remains constant and the induced magnetic field becomes zero. Displacement current: Combining Maxwell’s law of induction with Ampere’s Law yields the Ampere-Maxwell law : Define displacement current:...
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Phys 0175 - Lecture 32 - Lecture 32(Apr 6 2009 Maxwell’s...

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