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PHYS 222 Worksheet 26 – Electromagnetic Waves Supplemental Instruction Iowa State University Leader: Course: Instructor: Date: Alek Jerauld PHYS 222 Dr. Paula Herrera-Siklódy 4/2/12 Useful Equations v 1 0 0 c 3108 m / s E Emax cos kx t ˆj B Bmax cos kx t kˆ k 2 Speed of light Harmonic EM wave propagating in x-direction. E and B are ALWAYS in phase , 2 f , c f E B Propagation direction E cB Magnitude relationship between E and B fields v 1 c m c n EM wave speed in non-vacuum medium. n is the refraction index Diagram: Related Problems 1) A sinusoidal electromagnetic wave having a magnetic field of amplitude 1.25 µT and a wavelength of 432 nm is traveling in the +x direction through empty space. (Book 32.5) (a) What is the frequency of this wave? c f 6.94(1014 ) Hz (b) What is the amplitude of the associated electric field? E cB 375 V / m (c) Write equations for electric and magnetic fields as a function of x and t Bmax 1.25 T Emax 375 V / m 2 f 5.91(1015 ) rad / s 432(109 ) m 2 E Emax cos x t ˆj 2 B Bmax cos x t kˆ 2) The electric field of a sinusoidal electromagnetic wave obeys the equation: . (Book 32.8) (a) What is the amplitude of the electric field of this wave? Emax 375 V / m (b) What is the amplitude of the magnetic field of this wave? Bmax 1.25 T (c) What is the frequency of the wave? f 9.50(1014 ) Hz 2 (d) What is the wavelength of the wave? 2 316 nm k (e) What is the period of the wave? 1 T 1.05(1015 ) s f (f) Is this light visible to humans? No, humans can see within the wavelength range of 390 to 750 nm. (g) What is the speed of the wave? v f 3(108 ) m / s 3) An electromagnetic wave with frequency 64.0 Hz travels in an insulating magnetic material that has dielectric constant 3.64 and relative permeability 5.18 at this frequency. The electric field has amplitude 7.20(10-3) V/m. (Book 32.14) (a) What is the speed of propagation of the wave? c v 9.91(107 ) m / s m (b) What is the wavelength of the wave? v 1.06(106 ) m f (c) What is the amplitude of the magnetic field? E E B 1.04(106 ) T c f