Final answer:
The field radiates out at the speed of light in vacuum, which is approximately 3.00×108 meters per second. The speed can change when the electromagnetic waves pass through other mediums due to differing optical properties.
Step-by-step explanation:
The speed at which a field radiates out depends on the medium through which it is traveling. If we refer to the electromagnetic field, for instance, the speed of light is the ultimate speed at which the field radiates out in vacuum, which is approximately 3.00×108 meters per second. This speed is a fundamental constant of the universe and does not depend on the velocity of the source or the observer. However, this speed can change when the electromagnetic waves pass through different mediums, such as air or glass, due to the material's optical properties.
In vacuum, all electromagnetic radiation travels at the speed of light, but when the question doesn't specify a medium, it is safe to assume that the radiation is in vacuum unless otherwise stated. Therefore, the answer to the question "How fast does the field radiate out?" is that it radiates out at the speed of light if in vacuum, but this can vary with the medium it traverses.