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I read in my book that "electricity and magnetism are two inseparable fields of physical science". Can someone explain it to me because I don't get it.

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Another reason they can be connected is because one can cause the other, in a power station we spin magnets around to create electricity.

Also, depending on your speed, say in a very fast spaceship, what you think is an electric field can be seen by someone else as a magnetic field.

One big difference is that electric charges can be physically separated into positive and negative chargers bodies, but you can't cut up a magnet and just keep the north pole, it will instead become a smaller magnet, with a north and south pole.

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    $\begingroup$ This is the real answer. A charge generates an electric field; a moving charge generates a magnetic field. That second part of the statement should make you think, "wait, if some particle X has some magnetic effect on some particle Y in some reference frame, does that just mean that I can choose my reference frame so that X has no magnetic effect on Y? So is magnetism some strange subjective unphysical thing?" and the answer is, "it turns out that if you do this, the electric force happens to pipe up to make all of the predictions identical." That is why they are inseparable. $\endgroup$ – CR Drost Jan 25 '17 at 23:37
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Yes, we have never seen observations defying this. Whenever there is changing magnetic field, an electric field arises. And conversely whenever there is a changing electric field a magnetic field will be there.

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It is because the equations which describe electromagnetism, Maxwell equations, couple these fields together. For example, changing in time magnetic field gives rise to non-zero electric field via $\mathrm{curl} \vec{E}=-\frac{\partial \vec{B}}{\partial t}$, and vice versa. See, for example, the article on Wikipedia on Maxwell equations.

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All the other answers describing the association through Faraday's and Ampère's laws (i.e. That a time varying magnetic field gives rise to an electric field and contrariwise) are good answers to this question.

But another important reason for your books comment is the way the fields transform when different relatively moving observers measure them. An observer at rest relative to a line of point charges sees only an electrostatic field, whereas someone moving relative to the line - say along the line- sees both charge and current and thus measures both an electrostatic and a magnetic field. Who is correct?

Of course both are. I'm guessing you haven't studied special relativity yet, but, to abridge a very long story, ultimately we conclude from this study that only relative uniform motion between observers is detectable and therefore physically significant. This being so, we are forced to conclude that the electric and magnetic fields of the two observers are the same thing from different viewpoints. Electric and magnetic fields "mix" and partially transform into one another when seen by different, relatively moving observers.

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They are different but are unseparable magnetic field always produces an electric field if the charge is moving and the electric field also produce magnetic field, This has been proven by the two experiences of Lenz and Faraday faraday's law

from this laws it was concluded that both are a manifestation of unique phenomenon , later in 1867 Maxwell came and proposed the theory of electromagnetism wich unfies them both by introducing his 4 famous equations

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