Can a time-varying magnetic field emulate the electric field of a point charge?

In summary: No, I was referring to whether the induced electric field caused by a time-varying magnetic field could emulate the electric field of a static charge distribution.
  • #1
uby
176
0
A point charge generates electric field lines that are radially directed from the source in spherical symmetry. Similarly, a line of charge generates electric field lines that are radially directed from the line of charge in cylindrical symmetry.

Is there any way that a time-varying magnetic field generated by a time-varying current in a wire could emulate the electric field of an assemblage of static charges in the same geometry as the wire?

I suppose the question may be geometry dependent. For a straight wire carrying DC steady current, the magnetic field is time-invariant and generates no electric field outside the wire.

For the same wire carrying AC current with a single frequency, the magnetic field varies periodically and thus generates an electric field (though I have a hard time picturing the direction I believe that this induced electric field would be in the same direction as the original electric field ... parallel to the wire in this case).

For an AC current that has 'higher order' changes in its frequency (i.e. - variation in the variation in electric field), there would be 'higher order' induced electric fields though again always in the same direction of the originally generating electric field in the wire.

Therefore, I do not believe it is possible for a straight wire geometry to generate a radially-outward electric field by induction. Though, I cannot rule out that for other geometries of the current carrying wire that it is impossible. Does anyone have any insight on this?

Thanks!
 
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  • #2
You are asking if a magnetic field can emulate an electric field? If so, then the answer is no. The two are different effects and act differently.
 
  • #3
No, the electric field generated by time-varying magnetic field (vortex electric field) is distinct from that from charges (electrostatic field). The former has zero divergence while the latter has zero curl.
 
  • #4
Drakkith said:
You are asking if a magnetic field can emulate an electric field? If so, then the answer is no. The two are different effects and act differently.

Thanks for your reply Drakkith. No, I was referring to whether the induced electric field caused by a time-varying magnetic field could emulate the electric field of a static charge distribution.

netheril96 said:
No, the electric field generated by time-varying magnetic field (vortex electric field) is distinct from that from charges (electrostatic field). The former has zero divergence while the latter has zero curl.

Thanks netheril, that is a very elegant way of answering my question and is a very helpful method for thinking about this!
 
  • #5


I can provide some insight on this question. The short answer is no, a time-varying magnetic field cannot fully emulate the electric field of a point charge. This is because the electric field of a point charge is a fundamental property of the charge itself, while the magnetic field is a result of the motion of charges.

A time-varying magnetic field can induce an electric field, as described in the content, but it would only be a secondary effect and not a complete emulation of the electric field of a point charge. Additionally, the induced electric field would not have the same radial symmetry as the electric field of a point charge.

Furthermore, the geometry of the wire carrying the current does not play a significant role in this scenario. The key factor is the time-varying nature of the magnetic field, which is a result of the changing current. In order to fully emulate the electric field of a point charge, the magnetic field would need to be constant and not time-varying.

Overall, while a time-varying magnetic field can induce an electric field, it cannot fully emulate the electric field of a point charge. This is due to the fundamental differences between the two fields and the underlying physics behind them.
 

1. What is a time-varying magnetic field?

A time-varying magnetic field is a magnetic field that changes over time. This can be due to a variety of factors, such as the movement of charged particles or the use of electrical currents.

2. How does a time-varying magnetic field emulate the electric field of a point charge?

A time-varying magnetic field can create an electric field through electromagnetic induction. This occurs when a changing magnetic field induces an electric field in a nearby conductor or medium.

3. Can a time-varying magnetic field perfectly emulate the electric field of a point charge?

No, a time-varying magnetic field can only approximate the electric field of a point charge. This is because the two fields have different properties and behave differently in certain situations.

4. What are some practical applications of using a time-varying magnetic field to emulate the electric field of a point charge?

One practical application is in wireless charging systems, where a time-varying magnetic field is used to induce an electric current in a device to charge it. Another application is in electromagnetic compatibility testing, where a time-varying magnetic field is used to simulate the effects of an electric field on electronic devices.

5. Are there any limitations or drawbacks to using a time-varying magnetic field to emulate the electric field of a point charge?

One limitation is that the strength and direction of the induced electric field may not be exactly the same as that of a point charge. Additionally, the effectiveness of this method may depend on the distance between the source of the time-varying magnetic field and the point where the electric field is being measured.

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