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In the Introduction to Electrodynamics book, by David J. Griffiths, 4th edition, page 60, the author makes the following statement:

"it is not the position, velocity, and acceleration of Q right now that matter: electromagnetic "news" travels at the speed of light, so what concerns Q is the position, velocity, and acceleration Q had at some earlier time, when the message left."

In Example 7.9, page 320, he also makes the same statement:

"electromagnetic "news" travels at the speed of light, and at large distances B depends not on the current now, but on the current as it was at some earlier time (indeed, a whole range of earlier times, since different points on the wire are different distances away)."

  1. In fact, I am struggling with the idea of "electromagnetic news" and its meaning.
  2. In addition, what do we mean by "at some earlier time," because Griffiths always make this statement throughout his book?
  3. How could electromagnetic waves depend on quantities, such as the current in Example 7.9, took place "at some earlier time?"

Any help is much appreciated. Thank you so much.

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In fact, I am struggling with the idea of "electromagnetic news" and its meaning.

Electromagnetic waves travel at speed of light $c$ which has a finite value. The signal (or "news") takes a finite time to propagate from a point in the charge or current distribution (the point of cause) to another point in space (where the effect is measured). This effect is commonly known as retardation.

In addition, what do we mean by "at some earlier time," because Griffiths always make this statement throughout his book?

Retardation, a concept introduced by Lorenz, refers to the fact that $\vec{E}(\vec{r}, t)$ and $\vec{B}(\vec{r}, t)$ do not reflect the behaviour of the sources at the observation time $t$. Instead, they reflect the properties of the sources at an earlier (retarded) time $ t' = t − \displaystyle \frac{R}{c}$, where $R$ is the distance between the source and the observer. Basically, the field at a point due to a charge source is due to its past position.

We evaluate both the fields via scalar and vector potentials at retarded time. For more on calculations, see this.

How could electromagnetic waves depend on quantities, such as the current in Example 7.9, took place "at some earlier time?"

The time delay reflects the finite propagation speed $c$ of the signal and accords with our intuitive notion that cause precedes effect. This correction to the retarded time $t − \displaystyle \frac{R}{c}$ can be significant when the source is large or its time variation is rapid.

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Imagine that there was an explosion.

You are $3\times 10^8\,\rm m$ (=$1$ light second) away from the explosion.

You will receive "news" of the explosion ie see the flash of light associated with the explosion, one second after the explosion actually happened.
Here the use of the word "news" has the implication of a record of an event that has happened in the past.

So what is affecting you, the light arriving from the explosion, originated from an event, the explosion, which happened one second earlier in time.

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