Waves Electromagnetic waves HW-126 2. A radio-frequency EM plane wave (not shown
ID: 1771119 • Letter: W
Question
Waves Electromagnetic waves HW-126 2. A radio-frequency EM plane wave (not shown) propagates in the +-direction. A student finds that her portable radio obtains the best reception of the wave when the antenna is parallel to the x-y plane making an angle of 60° with respect to the y-axis. (See the diagram below.) Consider an instant when the fields are non-zero at the location of the antenna. a. 60° On the diagram at right, draw and label arrows to indicate (1) the direction of the electric field and (2) the direction of the magnetic field. Explain your reasoning. (Note: More than one answer is possible.) +y Antenna r.x Portable radio b. How would your answers to part a be different if the wave were propagating in the -z-direction instead of the +2-direction? (Note: More than one answer is possible.) Explain.Explanation / Answer
a] The directions of electric field, magnetic fields and direction of propagation of the waves are such that all are mutually perpendicular to each other. Therefore, for an EM wave propagating in +z direction, the direction of electric field can be anywhere in the xy plane.
Let us choose, the direction of electric field here to be upwards along the antennae. The magnetic field direction will be perpendicular to the electric field and so its direction will be at an angle of 90+30 = 120ocounter-clockwise from positive x axis (due to right hand rule).
b] If the direction of propagation is now made in negative z direction, the electric field can still be anywhere in the xy plane. Let us again, choose it to be in upwards along the antennae. Now, the magnetic field thus will be in a direction which is at an angle of 60oclockwise from positive x axis.
These directions are decided since the direction of propagation is decided by the cross product of Electric field direction and magnetic field direction (through the Poynting vector relation).
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