another problem of electromagnetism

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another problem of electromagnetism

Postby kolndom » Wed Oct 26, 2005 6:07 am

85. A charged particle oscillates harmonically along the x-axis as shown above. The radiation from the particle is detected at a distant point P, which lies in the xy-plane. The electric field at P is in the
(A) z direction and has a maximum amplitude at =90
(B) z direction and has a minimum amplitude at =90
(C) xy-plane and has a maximum amplitude at =90
(D) xy-plane and has a minimum amplitude at =90
(E) xy-plane and has a maximum amplitude at =45

thank u in ad:)

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Postby danty » Wed Oct 26, 2005 10:01 am

In spherical coordinates, the electric field E has the direction of the unit vector e_theta, so it lies on the xy plane. The Poynting vector( describing the
propagation of radiation) has the following dependence on theta: S~sin(theta)^2 , so it has a maximum amplitude at theta=90. The same applies to E. So the correct answer is C.

You may want to have a look at the electric dipole radiation pattern. Just focus on the S vector and you will be able to answer a lot of similar problems.

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Postby twistor » Wed May 23, 2007 9:26 pm

I think there is another, simpler way of thinking about this problem. Recall that the magnitude of the field is proportional to the perpendicular component of the acceleration (as seen from the observation point) when you're speaking of electric dipole radiation.

Now, in this means when your observation point P is on the x-axis you will not see any field because there is no perpendicular component to the acceleration as viewed from this point. Similarly, when you view the accelerating particle at 90 degrees offset from the x-axis the total acceleration is the same as the perpendicular component. Therefore the radiation has a maximum at 90 degrees from the x-axis and the correct answer is C, as danty indicated.

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