Monday, August 21, 2006

Questions on Electromagnetic Waves

When an electromagnetic wave is propagating through any medium including empty space, the direction of propagation of the wave is related to the directions of the electric and magnetic field vectors (E and B) in a definite manner. Many students are found to commit mistake in marking the directions of these vectors. If you remember that the vector product E×B always points along the direction of propagation of the electromagnetic wave, you wont commit mistake in specifying the directions of these vectors. Now consider the following M.C.Q.:
In a plane electromagnetic wave, the magnetic field vector is along the negative X-direction and the direction of propagation is along the positive Y-direction. Then the direction of the electric field vector must be along
(a) positive Z-direction (b) negative X-direction (c) negative Z-direction
(d) positive Y-direction (e) negative Y-direction

Since the direction of the E has to be perpendicular to both the direction of B and the direction of propagation, it has to be in the positive or negative Z-direction. Since there are two options [(a) and (c)] you have a 50-50 chance to hit the bull’s eye. But don’t take such chances. The magnetic field vector B is along the negative X-direction and so you can get the vector product E×B along the positive Y-direction only if E is along the negative Z-direction [option(c)].
You might have noted that our eyes are most sensitive to light of wave length about 550 nm because the sun radiates maximum energy in the form of light at this wavelength. This wavelength is related to the surface temperature T of the sun in accordance with Wein’s law which states that λm T = constant where λm is the wave length at which maximum energy is radiated. If you express λm in cm and T in Kelvin the constant is 0.29 cmK. Now consider the following question:
If the temperature of the sun were twice the present value, the radiation of the sun would be mostly in
(a) microwave region (b) infra red region (c) visible region (d) X-ray region (e) ultraviolet region.
The correct option is (e) because the wave length of maximum energy radiation has to be reduced to half the present value when the temperature is doubled (in accordance with Wien’s law). The present value of λm is about 550 nm and so when the temperature is doubled, the value of λm should become 275 nm, which is in the ultra violet region.

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