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

In summary: Hi.Electric fields of continuous distributions are typically found by integrating or by the use of symmetry arguments.
  • #1
FerPhys
16
0
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?
 
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  • #2
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.
 
  • #3
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.
 

What is integration used for in finding the electric field at a point P?

Integration is used to find the electric field at a point P by summing up the contributions of all the small electric charges (dQ or dq) distributed in space. This allows us to calculate the total electric field at a point P due to the entire charge distribution.

What is the formula for calculating the electric field at a point P using integration?

The formula for calculating the electric field at a point P using integration is given by:
E = k∫(dQ or dq)/(r^2) * cosθ
where k is the Coulomb's constant, r is the distance between the point P and the small charge, and θ is the angle between the direction of the electric field and the line connecting the point P and the small charge.

How do we choose the limits of integration when calculating the electric field at a point P?

The limits of integration are chosen based on the geometry of the charge distribution. They represent the boundaries of the region where the small charges (dQ or dq) are located. For example, if the charge distribution is a point charge, the limits of integration will be from 0 to the distance between the point P and the point charge.

Can we use integration to find the electric field at a point P for any charge distribution?

Yes, integration can be used to find the electric field at a point P for any charge distribution, as long as the charge distribution is continuous and the charge density is known at every point in space. This includes point charges, line charges, and surface charges.

What are the advantages of using integration to find the electric field at a point P?

Using integration allows us to take into account the contributions of all the small charges in a charge distribution, which may not be possible with other methods. It also allows us to calculate the electric field at a point P for complex charge distributions, which may not have a simple mathematical formula. Additionally, integration provides a more accurate and precise calculation of the electric field at a point P compared to approximations or simplifications.

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