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p2020chap09 - PHYS-2020 General Physics II Course Lecture...

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Unformatted text preview: PHYS-2020: General Physics II Course Lecture Notes Section IX Dr. Donald G. Luttermoser East Tennessee State University Edition 3.3 Abstract These class notes are designed for use of the instructor and students of the course PHYS-2020: General Physics II taught by Dr. Donald Luttermoser at East Tennessee State University. These notes make reference to the College Physics, 9th Edition (2012) textbook by Serway and Vuille. IX. Electromagnetic Radiation (Photons) A. Properties of Electromagnetic (E/M) Radiation. 1. Maxwell showed in 1865 that electric phenomena were related to magnetic phenomena = ⇒ Maxwell’s equations (or laws ): a) Electric fields originate on positive charges and terminate on negative charges. The electric field due to a point charge can be determined by applying Coulomb’s law. vector ∇ · vector E = ρ epsilon1 ◦ . i) This is similar to Gauss’s law given in Eq. (I-7). ii) ρ = q/V is the electric charge density (charge per unit volume). iii) The “del” symbol is from vector calculus and is defined by vector ∇ ≡ ∂ ∂x ˆ x + ∂ ∂y ˆ y + ∂ ∂z ˆ z , in Cartesian coordinates, where ‘ ∂ ’ is the partial derivative symbol from calculus. iv) The ‘ vector ∇· ’ operation is called the divergence in higher mathematics — it is the ‘dot product’ of the ‘del’ operator and the vector in question, here the electric-field vector. b) Magnetic-field lines always form closed loops = ⇒ they do not begin or end anywhere = ⇒ there are no magnetic monopoles . Mathematically, this is given by Maxwell’s IX–1 IX–2 PHYS-2020: General Physics II equation for the divergence of the B-field: vector ∇ · vector B = 0 , the ‘zero’ simply means that there are no magnetic monopoles. c) A varying B-field induces an emf and hence electric ( E ) field = ⇒ Faraday’s law re-expressed in Maxwell’s form: vector ∇ × vector E =- ∂ vector B ∂t . The ‘ vector ∇× ’ operation is called the curl in higher mathe- matics. Whereas the divergence produces a scalar, the curl produces a vector. d) Magnetic fields are generated by moving charges (or cur- rents) = ⇒ Ampere’s law re-expressed in Maxwell’s form: vector ∇ × vector B = μ ◦ vector J , where J ( ∝ ∂q/∂t ) is the current density. 2. Maxwell’s last 2 laws allow electromagnetic waves ( i.e. , radiation) to self-propagate at a velocity of c = 1 √ μ ◦ epsilon1 ◦ = 2 . 99792 × 10 8 m/s . (IX-1) a) “ c ” is called the speed of light , since visible light is a form of electromagnetic radiation. b) An oscillating electric charge produces an E-field that varies in time, which produces a B-field that varies in time, which produces a new E-field that varies in time, Donald G. Luttermoser, ETSU IX–3 and so on....
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