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EM waves and the direction of E-fields & B-Fields

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What I'm wondering is whether or not the E-fields and B-fields making up an EM wave always point outwards. Would it be possible to have an EM wave where either the E-fields or B-fields, or both, point inwards towards the path of propagation? The only diagrams I see in books and the internet alike either have them both point outward, or not have any indication of direction at all.

I understand that an EM wave consists of E-fields and B-fields changing in such a way that they are self-sustaining, and that this change doesn't necessarily have to be sinusoidal. However, I don't know exactly how this is done, such as what equations describes how changing E-fields create B-fields (and vice versa) in a straightforward manner. I know there are Maxwell Equations, but they don't directly tell you, for instance, the type of E-field created, when you have a given changing B-field, although that could be because I haven't studied those equations in enough depth to know how to apply them in such a way. Please forgive me as the only knowledge I have about EM waves is from a lower division General Physics course.

The reason why I wonder this is because of a question asked on Yahoo! Answers.
If it is true that the E-fields only point outwards from the path of an EM wave, wouldn't that break some sort of symmetry? I mean, I know symmetry isn't something to expect in everything, but wouldn't the fact that the E-fields only point outwards give the photon similar properties as a positively charged particle? So for instance, if you had positively charged particles arranged so that they are located within of the E-fields of an EM wave, wouldn't the EM wave cause those positively charged particles to be deflected away?

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