What is the definition of the electric field according to Purcell's textbook?

[y.moghadamnia]

hi there
I have been studying Purcell textbook and I think I have some trouble understanding the E dfinition it gives.
ok first of all when it starts to define it, it says :"suppose we have some arrangment of charges fixed in space". so they don't move at all.
then it says "we are not interested in the forces these carges exert on one another but only in their effect on some other charge q0, {as a test charge}".
so the definition for E will be to add up all the coloumb forces the fixed charges have on the q0.
so then E is "another way of describing the systemof charges, by giving the force per unit charge in magnitude and directionm that an exploring charge q0 would experience at any point". fine, understandable. but then it critisizes the definition some books give, that the limit of F/q0 while q0\rightarrow0, will be the definition for E. it says this definition is wrong because "we have never observed a chargesmaller than e" and q0 can never be zero. so if we "take the first one our definition of E, without refrence to a test charge, no problem arises and the charges need not be fixed."
now here is my question. we said we need to fix them because if we have the test charge around it might move them and the forces might be wrongly added. is that the ONLY reason we need to get them fixed? arent they going to create magnetic field if they accelerate? isn't that going to effect it too? and finally, what happens to transposition here?
the whole thing is mixed up in my head, so fix it if u can!

 

[cragar]

We need to fix them down so they don't repel each other. And so we can look at the E field produced by them being stationary. And yes if they started to move we would have a current and that would produce a B field .

 

[Rap]

I think they say as q->0 because that way the test charge does not push around the charges creating the field. If you could hold those charges still, then I think you do not need the q-> 0 constraint. Also, the test charge has to be (practically) a point charge to define the E field as a function of position.