# Electric field description

Statement from Electricity and Magnetism (Edward Purcell):

Perhaps you still want to ask, what is an electric field? Is it something real, or is it merely a name for a factor in an equation that has to be multiplied by something else to give the numerical value of the force we measure in an experiment? Two observations may be useful here. First, since it works, it doesn’t make any difference. That is not a frivolous answer, but a serious one.

Second, the fact that the electric field vector at a point in space is all we need know to predict the force that will act on any charge at that point is by no means trivial. It might have been otherwise! If no experiments had ever been done, we could imagine that, in two different situations in which unit charges experience equal force, test charges of strength 2 units might experience unequal forces, depending on the nature of the other charges in the system. If that were true, the field description wouldn’t work.

Couldn't understand the sentences in bold. Especially, how is field description related to it (see the last sentence in italics)? Why wouldn't it work?

## 1 Answer

The sentence obviously wants to say that the concept of an electric field makes sense because the electric force an a test charge is proportional to the magnitude of the test charge. It could well be that in two different set-ups, where you have an equal force on a unit charge test charge, the force would not be the same on a different magnitude test charge.

The funny thing is that this independence of the electric field on the magnitude of the test charge only holds approximately in the limit of very small test charges $$q \to 0$$ For example, in an electrostatic experiment, the test charge $q$ can change the charge distribution of the charges which are the sources of the electric field so that the electric force experienced by a (large) test charge is not proportional to its magnitude.

• I reread the text and things made sense all of a sudden! Thanks – suiz Apr 1 '18 at 16:17