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GR8677 #53
Problem
 GREPhysics.NET Official Solution Alternate Solutions

Electromagnetism$\Rightarrow$}Accelerating Charges

One doesn't really need to understand the mess Griffiths has on accelerating charges to solve this problem. In fact, common sense works. Since the particle spends the most time about the origin, the field there should be maximal. The origin corresponds to $\theta=90^\circ$, via the system used in the diagram. This is choice (C).

Alternate Solutions
 flyboy6212010-11-14 21:12:43 I don't know if this will help anybody, but... You can imagine standing at the origin, holding one end of a rope, the other end of which is at point P. Then you start waving the end of the rope back and forth along the x-axis. The waves in the rope will be oriented in the xy-plane and be maximum when P is on the y-axis, i.e. theta is 90 degrees. The analogy works because EM waves are transverse, just like waves in a string.Reply to this comment Herminso2009-09-22 13:56:33 For a electric dipole $\vec{P}(t)=qd\cos {(\omega t)}\hat{x}$ we have: $\vec{E}=-\frac{\mu_0qd\omega^2}{4\pi}(\frac{\sin {\theta}}{r})\cos {[\omega(t-r/c)]}\hat{\theta}$ and $\vec{B}=-\frac{\mu_0qd\omega^2}{4\pi c}(\frac{\sin {\theta}}{r})\cos {[\omega(t-r/c)]}\hat{\phi}$ Thus the oscilation of the electric field is in the xy-plane and the maximum is at $\theta=90$, just the y-axes. Reply to this comment ee7klt2005-11-11 04:54:58 hi, since oscillations happen only in the x-y plane, the E-field vector thus cannot have components in the z-direction. This eliminates (A) and (B). The minimum occurs when you're looking directly down the x-axis i.e. $\theta = 0$ (all you see is the infinitesimal tip of the field vector which doesn't look like it'll generate any waves coming towards you) - this eliminates (D). From here, I guess you'll need to remember that the field goes as $\sin \theta$ to narrow it further down to (C). Reply to this comment
santo35
2014-07-31 03:59:21
Isnt the electric field varying at all points "P" ? (since it is an oscillation ?

And if so are we considering the maximum value of variation here ?
santo35
2014-07-31 03:58:36
Isnt the electric field varying at all points "P" ? (since it is an oscillation ?

And if so are we considering the maximum value of variation here ?
santo35
2014-07-31 03:56:44
isnt that field varying at all points P ? rnrnOr is it that we are considering only the maximum value of the variation at all points P and comparing them ?
849444209
2013-10-16 07:48:56
natec
2013-08-18 17:46:35
Say point P were in the XZ plane and $\theta$ was the angle BELOW the x-axis. Would the electric field now be in the XZ plane with maximum magnitude at $\theta = 90$? I can't see why not because of the symmetry of the arrangement.
SillyMan
2013-06-19 20:17:23
The solution given above is wrong. Purely qualitatively, by Ampere's Law, B field will be in the +/- Z direction at point P. The energy flux vector S points outward (obviously). Thus E is in the XY plane (Orthogonal Triad). At 90 degrees, one "sees" the highest acceleration, which means that the power flowing past P is the highest at theta = 90 degrees. The answer was implied by Maxwell's equations and the Larmor result.
flyboy621
2010-11-14 21:12:43
I don't know if this will help anybody, but...

You can imagine standing at the origin, holding one end of a rope, the other end of which is at point P. Then you start waving the end of the rope back and forth along the x-axis. The waves in the rope will be oriented in the xy-plane and be maximum when P is on the y-axis, i.e. theta is 90 degrees.

The analogy works because EM waves are transverse, just like waves in a string.
 deafmutemouse2011-09-20 14:10:54 This analogy is awesome! Thanks!
 OptimusPrime2017-04-08 04:47:54 This is really helpful! The point of fastest velocity of the rope shaking happens when crossing the y-axis, which is maximum E amplitude in this case.
faith
2010-11-11 23:14:24
here's another way to look at it.

cross product! v=ExB since particle is moving along the x direction, E field max should only be along y.
 faith2010-11-11 23:18:35 yikes.. sorry, this solution is wrong. i had it by luck.
wittensdog
2009-09-28 21:43:42
The one thing I'm seeing over and over again is that every physics GRE problem has a quick and simple way to do it. Sometimes it's a calculation trick, sometimes it's just knowing something by heart.

In this case, I strongly recommend remembering two basic facts which have a good chance of coming up on any test:

1.) an oscillating charge never radiates in the direction of its oscillation axis

2.) the polarization of an oscillation charge is parallel to the oscillation axis

Don't bother wondering why (at least not for the sake of the GRE), just memorize that. If you use those two pieces of information, you immediately see that the E-field should be in the xy plane from the restriction on the polarization, and also that the maximum field strength should be at 90 degrees, since along the x axis it has no magnitude, and increases as you move away from the x axis.

So far, in all of my studying, I've never come along a GRE problem that required a formula with more than 3 or 4 terms in it. Maybe that's a slight exaggeration, but you get the point.
 apr20102010-04-09 09:22:19 Does not the dipol radiate also in the z-direction? This looks like a trap again, as the Point P lies only in the x-y-plane, meaning A and B are not even available.
Herminso
2009-09-22 13:56:33
For a electric dipole $\vec{P}(t)=qd\cos {(\omega t)}\hat{x}$ we have:

$\vec{E}=-\frac{\mu_0qd\omega^2}{4\pi}(\frac{\sin {\theta}}{r})\cos {[\omega(t-r/c)]}\hat{\theta}$ and $\vec{B}=-\frac{\mu_0qd\omega^2}{4\pi c}(\frac{\sin {\theta}}{r})\cos {[\omega(t-r/c)]}\hat{\phi}$

Thus the oscilation of the electric field is in the xy-plane and the maximum is at $\theta=90$, just the y-axes.
 Herminso2009-09-22 14:22:02 Where $\theta$ is measured from the positive x-axes on the xy-plane.
a19grey2
2008-11-03 22:14:06
I recommend just learning what the picture of an oscillating dipole looks like. rnhttp://en.wikipedia.org/wiki/DipolernrnIt'll help you later in your physics life anyway...
 physicsisgod2008-11-05 20:32:44 Here's a cool video of it: http://www.vis.uni-stuttgart.de/ufac/dipole/
jw111
2008-09-14 11:09:42
You see the maximum OSCILATION of charge when you stand on y axis, and minimum oscilation when you stand on x axis.

=> max field take place on y axis

the ocilation is on x-y plane, the field line wave mainly on x-y plane.

=>oscilating field on x-y plane
ee7klt
2005-11-11 04:54:58
hi,

since oscillations happen only in the x-y plane, the E-field vector thus cannot have components in the z-direction. This eliminates (A) and (B).

The minimum occurs when you're looking directly down the x-axis i.e. $\theta = 0$ (all you see is the infinitesimal tip of the field vector which doesn't look like it'll generate any waves coming towards you) - this eliminates (D). From here, I guess you'll need to remember that the field goes as $\sin \theta$ to narrow it further down to (C).
 Simplicio2009-03-31 17:13:47 It's oscillating along the x-axis so you can't just say "it is in the x-y plane". It might as well been the x-z plane ...
physicsDen
2005-11-09 22:04:58
is it me, or is this a poor attempt at a solution?
 alpha2005-11-09 22:15:19 it's a quick and dirty way to arrive at the right answer.
 mpdude82012-04-19 14:19:49 Definitely a poor attempt at a solution, but a great solution for the sake of the GRE. You do not have the time to use any formulas on a problem like this. It really has to be 100% intuition in order for you to finish. You don't have 3-4 minutes to think of a relevant formula, you just have to see the problem and know what to look for instinctively. Thus, many of the solutions to these problems on this site are not rigorous whatsoever, but the GRE couldn't care less about rigor.

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