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One of the paragraphs in the textbook that I don't quite understand is the following:

If we were to charge a body, say a comb, electrically, and then place a charged piece of paper at a distance and move the comb back and forth, the paper will respond by always pointing towards the comb. If we shake it faster, it will be discovered that the paper is a little behind, there is a delay in action.

Why? Is he referring to the finite speed of information travel? At any rate, it shouldn't be significant in the present scale.

If we move the charged paper further out, the delay is greater. Then an interesting thing is observed. Although the forces between two charged objects should go inversely as the square of the distance it is found, when we shake a charge, that the influence extends very much farther out than we would guess at first sight.

Why? Is it because a magnetic force also comes into play?

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Why? Is he referring to the finite speed of information travel?

Yes.

At any rate, it shouldn't be significant in the present scale.

Feynman doesn't mention any scales in the passages you quoted. What do you mean by "the present scale"?

Additionally this paragraph is meant to illustrate a point of principle, the fact that the delay may be small for "lab scale" distances is not relevant.

Why? Is it because a magnetic force also comes into play?

Not really, it is because the electric field of radiation falls of as $1/r$, as opposed to the static $1/r^2$ due to Coulomb forces.

Magnetic fields are indirectly relevant in that an electromagnetic wave involves oscillations of both the magnetic and electric field. Without the magnetic field in Maxwell's equations, there would be no wave phenomena.

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