LECTURE 22 DISPLACEMENT CURRENT, MAXWELL’S EQUATIONS, AND EM WAVES Lecture 22
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¨ Reading chapter 30-1 to 30-4. ¤ Maxwell’s displacement current ¤ Maxwell’s equations ¤ Electromagnetic waves ¤ Electromagnetic spectrum ¤ Production of EM waves ¤ Antennas ¤ Energy and momentum of an EM wave Ampere-Maxwell law
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¨ Maxwell’s paradox: for the same line integral over curve C, ⃗ Ampere’s law (∮ � �� = � � ) depends on which surface is used.
¤ ⃗ ∮ � �� = � � if we use the current penetrating S1.
¤ ⃗ ∮ � �� = 0 if we use the current penetrating S2. ¨ Maxwell’s solution: he added a displacement current term that depends on the changing electric flux in the gap. � = � Displacement current ⃗ ∮ � �� = � � + � Generalized Ampere’s law Quiz: 1 Example: 1
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¨ A parallel plate capacitor with a radius R = 1.0 cm and a 1.0 mm gap is being charged at the rate of 0.50 C/s. What is the magnetic field strength in the gap at a radius of r = 0.5 cm? Quiz: 2 EM waves
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¨ Faraday’s law and Ampere’s law (with no current) yield a wave equation for electromagnetic waves.
¨ The wave equation indicates the velocity of electromagnetic wave to be 1 � = = 3.0 × 10 m⁄s = � � � ¨ The direction of propagation of an electromagnetic wave is always the direction of the vector product: Moving displacement
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¨ Suppose we wish to move a parabolic function � � = � so that it is centered at greater and greater values of the independent variable �. Then we change � to � − 2 , � − 4 , etc. ¨ Similarly, if we wish to displace some arbitrary function � � by a distance � in the positive �- direction, we replace � � by � � − � . ¨ If we wish to make the displacement increase with time, i.e., move the curve with speed �, we make � = ��, so that the function becomes � � − �� . ¨ Similarly, to displace the function in the negative � direction, we use � � + �� . ¨ So, the electric field of light traveling in the positive �-direction can be expressed as � = � sin � � − �� = � sin �� − �� Quiz: 3 Quiz: 4 & 5
10 Electric dipole antenna
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¨ Suppose two conducting rods are connected to an alternating-current generator.
¨ The E field parallel to the rod exists near the rod. The B field encircles the rods due to the current in the rods.
¨ The directions of the E and the B fields alternate at the same frequency as the AC generator. Quiz: 6 Demo: 1
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¨ Cenco 3-meter Transmitter ¤ Demonstration of radio wave and its E field direction. Energy and momentum of an EM wave
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¨ An EM wave carries energy and momentum as it propagates.
¨ The energy of an EM wave is stored in both electric field and magnetic field.
¨ The momentum of an EM wave can be transferred to a charged particle upon interaction.
¨ If an EM wave is incident normally on a surface that absorbs its momentum, radiation pressure, Pr, is exerted on the surface. Milky Way in different frequencies
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