Induced Electric and Magnetic Fields Creating Each Other

• I
• bgq
In summary: There is only one electromagnetic field, which you can interpret as an electric and a magnetic field. If you care to look at it that way, the electric field is induced by the magnetic field and vice versa. There are no extra fields created anywhere.
bgq
Hi,

We know that a varying magnetic field creates and induced electric field, and a varying electric field creates an induced magnetic field.

If there is a varying electric field (let's say sinusoidal), then this electric field creates an induced magnetic field. And if this produced magnetic field varies, then it produces an induced electric field. This produced electric field again (if varies) produced another magnetic field and so on. So eventually, we will have an infinite number of electric and magnetic fields. How can we calculate the resultant electric field and the resultant magnetic field? Do Maxwell's equations give the resultant fields, or should we add them by some way?

Thank you.

bgq said:
If there is a varying electric field (let's say sinusoidal), then this electric field creates an induced magnetic field.
Yes. We usually call this light, or electromagnetic radiation generally.

Your "infinite number of electric and magnetic fields" isn't right, though. There's only one EM field, which you can interpret as an electric and a magnetic field. If you care to look at it that way, the electric field is induced by the magnetic field and vice versa. There are no extra fields created anywhere.

bgq
Ibix said:
Yes. We usually call this light, or electromagnetic radiation generally.

Your "infinite number of electric and magnetic fields" isn't right, though. There's only one EM field, which you can interpret as an electric and a magnetic field. If you care to look at it that way, the electric field is induced by the magnetic field and vice versa. There are no extra fields created anywhere.
Thank you

This is a very common misconception. As can be seen from formulating Maxwell's equations in its natural way as a relativistic field theory one sees that there is one electromagnetic field which can be described by electric and magnetic field components, but this is dependent on the (inertial) frame of reference you perform this split. Only all components together build a physically interpretible observable, the electromagnetic field.

Maxwell's equations also show that you cannot easily interpret the relation between electric and magnetic components in a fixed inertial reference frame as "causing each other". The correct interpretation of, e.g., Faraday's Law
$$\vec{\nabla} \times \vec{E}=-\frac{1}{c} \partial_t \vec{B}$$
is that an electromagnetic field with time-dependent magnetic components implies that there must be electric components forming a vortex, but it does NOT say that the time dependence of the magnetic field causes an electric vortex field or vice versa.

It's of course possible to try to solve for (the solenoidal part of) ##\vec{E}## in terms of ##\partial_t \vec{B}##, but finally this leads to complicated non-local relations, which are not of much use for a physical interpretation.

What is causing an electromagnetic field are rather the charge and current distributions. That's clear from looking at "Jefimenko's equations", which express the electromagnetic field as retarded (causal!) integrals over the charge and current distributions (and their derivatives).

1. How do induced electric and magnetic fields create each other?

Induced electric and magnetic fields are created through the process of electromagnetic induction. This occurs when a changing magnetic field, such as one produced by a moving magnet or a changing current, induces an electric field in a nearby conductor. Similarly, a changing electric field can induce a magnetic field in a nearby conductor.

2. What is the relationship between induced electric and magnetic fields?

Induced electric and magnetic fields are closely related and are both components of the electromagnetic force. They are perpendicular to each other and work together to create electromagnetic waves, which are responsible for many natural phenomena such as light and radio waves.

3. Can induced electric and magnetic fields be manipulated?

Yes, induced electric and magnetic fields can be manipulated through various methods such as changing the strength or direction of the current or magnet, or by using materials with different electrical and magnetic properties. This allows for the creation of devices such as generators and transformers.

4. How are induced electric and magnetic fields used in technology?

Induced electric and magnetic fields are used in many technological applications, including generators, transformers, electric motors, and wireless charging. They are also used in communication systems, such as antennas and satellite transmissions.

5. Are there any potential health risks associated with induced electric and magnetic fields?

There is ongoing research on the potential health risks of exposure to induced electric and magnetic fields, particularly from power lines and electronic devices. While there is no conclusive evidence of harm, some studies suggest a possible link to increased risk of certain health conditions. As a precaution, it is recommended to limit exposure to these fields when possible.

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