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4. (15 points) A plane electromagnetic wave is given by: E = 2 sin( 2 y + 4 x 10 V/m B=B sin( fy+41 x 10'S: Tesla The index of refraction of the media is 1.5. a. (5 points) In what direction does the wave propagate? b. (5 points) What is B. (magnitude and direction)? c. (5 points) What is the wavelength of the wave (in meters)? 5. (20 points) A donut-shaped permanent magnet (treat as dipoles) is placed on a frictionless vertical rod and held in place. Another identical magnet is placed in the opposite orientation on the rod and floats" above the first one. a. If the magnets both have mass m, and the equilibrium distance between them is h, what is the magnitude of the magnetic moment of the magnets? . If you now add a third magnet whose orientation is parallel to the first one, what is the ratio of the distance between the bottom to and the top two magnets? (Determine the actual number to three significant digits.) 6. (10 points) The dust tail of a comet points away from the sun because of radiation pressure by sunlight. a Estimate the order of magnitude of the force on a dust grain with linear dimension l um at the radius of the Earth's orbit, where the intensity of sunlight is 1300 W/m. It is easier to think of this as a cube, not a sphere. h Compare the radiation foree to the force of solar gravity on the grain, assuming the grain has density Sg om. (G = 6.67 x 10-11 Nm /kg) c. Can the radiation affect significantly the orbit of the dust grain? Explain.