Electromagnetic waves lecture in an undergrad course
- 2. Advanced Topic: Electromagnetic Waves A changing magnetic field creates an induced electric field, and a changing electric field creates an induced magnetic field. If the process can get started, it can propagate self- sustainably → Electromagnetic Wave Electricity & Magnetism
- 3. Generating Electromagnetic Waves Producing Electromagnetic Waves Classically, an EM Wave is created by accelerating charges. • Stationary charges produce only electric fields, • whereas charges in uniform motion (i.e., constant velocity) produce electric and magnetic fields, but no electromagnetic waves. • In contrast, accelerated charges produce electromagnetic waves as well as electric and magnetic fields. An accelerating charge also radiates energy.
- 4. Antennas: Producing Electromagnetic Waves An antenna powered by an AC source creates an oscillating electric dipole! An Oscillating Electric Field is Aligned parallel to the Dipole
- 5. Properties of Electromagnetic Waves - 1 • The electric and magnetic fields are always perpendicular to the direction in which the wave is traveling. – The wave is a transverse wave
- 6. Properties of Electromagnetic Waves - 2 • The electric field is always perpendicular to the magnetic field.
- 7. Properties of Electromagnetic Waves - 3 • The cross product always gives the direction in which the wave travels. • Right hand rule – Fingers: electric field – Curl fingers: magnetic field – Thumb: velocity of electromagnetic waves
- 8. Properties of Electromagnetic Waves - 4 • The fields always vary sinusoidally. – E and B fields vary with the same frequency and in phase with each other https://sites.google.com/site/elizabethsomma/electromagnetics/plane-
- 9. Speed of Electromagnetic Waves • Speed of light in vacuum: • The speed of an EM wave doesn’t depend on wavelength λ or frequency f, but rather it restricts what values λ and f can take.
- 10. Electromagnetic Waves Note: These sinusoidal curves just represent the fact that the fields have different strengths at different locations. The fields still exist outside of these curves. The electric field is always perpendicular to the magnetic field and both are perpendicular to the direction of propagation. E0 = maximum value of electric field B0 = maximum value of magnetic field Hold x constant (i.e., stay at the same location): The fields change with time. Hold t constant (i.e., look at one instant in time): The fields change with location. o o
- 12. Visible Light Visible light is the segment of the electromagnetic spectrum that we can see. Visible light extends from the violet end (400 nm) to the red end (700 nm), as shown in the table below.
- 13. Question: EM Waves Which of the following types of light travels the fastest? A) radio waves B) visible C) ultraviolet D) gamma rays E) They all have the same speed.
- 14. Question: EM Waves Which of the following types of light travels the fastest? A) radio waves B) visible C) ultraviolet D) gamma rays E) They all have the same speed.
- 15. Energy Carried by….? • https://www.youtube.com/watch?v =bHIhgxav9LY
- 16. Energy Carried by Electromagnetic Waves • Poynting Vector: represents the flow of electromagnetic energy through space. • Its direction is the direction of propagation of the wave (and flow of the energy). • SI units: W/m2
- 17. A planar EM wave is propagating through space. Its electric field is given by Which of the following gives the correct magnetic field vector? A) B) C) D) Question: Electromagnetic Waves
- 18. A planar EM wave is propagating through space. Its electric field is given by Which of the following gives the correct magnetic field vector? A) B) C) D) Question: Electromagnetic Waves Wave propagates along +z E field oscillates along x
- 20. Electromagnetic Waves: Example Problem An electromagnetic wave is described by: where is the unit vector in the +y direction. A B C D Which of the following graphs represents the z - dependence of Bx at t = 0? X E and B are “in phase” (or 180o out of phase) X x y z E B x y z Wave moves in +z direction ĵ B E Points in direction of propagation t kz B i B cos ˆ 0 t kz E j E cos ˆ 0 t kz E j E cos ˆ 0
- 21. The Poynting vector is a function of time, oscillating from zero to Smax = E0 2 /cμ0 and back to zero twice during each period of the wave’s oscillation. Of more interest is the average energy transfer, averaged over one cycle of oscillation, which is the wave’s intensity I. The intensity of an electromagnetic wave is: The intensity of electromagnetic waves at a distance r away from an isotropic source with power Psource is Energy Carried by Electromagnetic Waves
- 22. Example: Fields of a Cell Phone A digital cell phone broadcasts a 0.60 W signal at a frequency of 1.9 GHz. What are the amplitudes of the electric and magnetic fields at a distance of 10 cm, which is about the distance to the center of the user’s brain? You may treat the cell phone as a point source (i.e., an isotropic source) of electromagnetic waves. The magnetic field amplitude is very small, especially when compared to the electric field amplitude. This implies that the interaction of electromagnetic waves with the human body is mostly due to the electric field.
- 23. Polarizer Demo Same Orientation Orientation Crossed (Perpendicular) https://www.youtube.com/watch?v=E9qpbt0v5Hw
- 24. Polarization • The polarization of an electromagnetic wave refers to the direction of its electric field. • Polarized light has its electric fields all in the same direction. • Unpolarized light has its electric fields in random directions (i.e., all directions).
- 25. Polarizers • A beam of unpolarized light can be polarized by passing it through a polarizer, which allows only a particular component of the electric field to pass through. • The polarization of the light after passing through the filter is in the same direction as the orientation of the polarizer.
- 26. Question: Polarization If unpolarized light is incident from the left, in which case will no light get through? A. Only case 1 B. Only case 2 C. Only case 3 D. Cases 1 and 3 E. All three cases
- 27. Question: Polarization Answer If unpolarized light is incident from the left, in which case will no light get through? A. Only case 1 B. Only case 2 C. Only case 3 D. Cases 1 and 3 E. All three cases In cases 1 and 3, light is the polarizer are not perpendicular so not all light is blocked out.
- 28. Example: Polarizing Sunglasses • Light is partially polarized due to reflections (polarized horizontally) • Polarizing filters in the lenses block the horizontal polarization and only allow the vertical polarization to go through.
- 29. Example: Liquid Crystals Displays (LCDs) LCDs use liquid crystals, whose direction of polarization can be rotated depending on the voltage across them.
Editor's Notes
- #17: \vec{E}=E_{0} \cos \left(kz - \omega t\right) \, \hat{i} Ans: B \vec{B}=B_{0} \cos \left(kz - \omega t\right) \, \hat{j} \vec{B}=B_{0} \cos \left(kz - \omega t\right) \, \hat{z}
- #18: \vec{E}=E_{0} \cos \left(kz - \omega t\right) \, \hat{i} Ans: B \vec{B}=B_{0} \cos \left(kz - \omega t\right) \, \hat{j} \vec{B}=B_{0} \cos \left(kz - \omega t\right) \, \hat{z}
- #20: Answer: C
- #36: Answer: A
- #37: Answer: A