Integration to find Electric Field at a point P -- dQ or dq?

[FerPhys]

Hey everyone,
So I've been learning about electric fields and all that good stuff. So now the question arises, what is the electric field at a point P away from an object (say a rod or a ring) at a distance D away? So we know E=Kq/r² or E=KQ/r² . The difference between q and Q: q the charge for a small particle while Q is the charge of a continuous object, say a rod, ring, disk, etc. Now, when we're asked the questions aforementioned sometimes our book uses dE=kdq/r² and sometimes it uses dE=kdQ/r² where d signifies "change in". My question is, why do sometimes they use dq and sometimes dQ? How would I know which to use?
My view on it is, say a disk has a charge Q (charge of the whole disk), and that disk is changing with respect to a change in r which still gives u a circle which means that circle still has a charge of Q since it's a continious object. On a rod I would say you use dq because you can take a piece of the rod to be infinitesimally small and make a point (since you consider a rod to be "linear"). Am I correct or am I viewing things a wrong way?

 

[Qwertywerty]

Hi.

A couple of things-

1. The use of dQ vs dq typically depends on the charge given to a particular body. Say, for example, you give a charge Q to a ring. The use of dQ is simply, because you are considering a very very small portion of charge out of the total Q. For a total charge q, you may use dq. This is no hard-and-fast rule, however.

2. When you're saying dQ(or dq) you are actually referring to an infinitesimally small part, rather than a 'change in'.

3. Electric fields of continuous distributions are not typically in the format of kQ/(r∧2) or q(I hope I've cleared that).
They are usually found by integrating, or by the use of symmetry arguments.

Hope this helps,
Qwertywerty.

 

[Guneykan Ozgul]

Hi,
Q and q are can be used interchangably. You need to consider what kind of system you are dealing with. There is no such thing q is used for a continuous system and Q is used for other kind of systems (discrete etc.). So if you know what is the difference between q (or Q) and dq (or dQ) the rest is as a matter of convention. I hope it is clear.