Can you clarify this step (charge density and integrals).

In summary, the conversation is about the integration step in Example 23.8 on page 675 of the book "Physics for Scientists and Engineers 8E" by Serway Jewett. The question is about the transformation from "2r dr" in the numerator to d(r^2) and the request for information or a link to the property of integrals that explains this. The response explains that d(r^2)/dr = 2r is the fundamental formula of derivatives and multiplying dr on both sides results in d(r^2) = 2r dr.
  • #1
DannyPhysika
30
0
Hi, if you have the book: Physics for Scientists and Engineers 8E, Serway Jewett

On page 675 (Chapter 23), Example 23.8 there is a step taken during the integration I don't understand:

How do you go from "2r dr" in the numerator to d(r^2)? If there is info or link to the property of integrals which explains this, I would appreciate seeing it. Thank you.
 
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  • #2
hhhmmm...well, what do you get when you take the derivative or r2 ? In other words, what's d(r2)? is it 2rdr?
 
  • #3
Hi.

d（r^2）/dr = 2r is fundamental formula of derivative.

multiplying dr on both sides,

d（r^2） = 2r dr

Regards
 

Related to Can you clarify this step (charge density and integrals).

1. What is charge density?

Charge density is a measure of the electric charge per unit volume in a given space. It is typically denoted by the symbol ρ and is measured in coulombs per cubic meter (C/m³).

2. How is charge density calculated?

Charge density can be calculated by dividing the total electric charge in a given volume by the volume of that space. It can also be calculated by integrating the charge distribution function over a given volume.

3. What is the importance of charge density?

Charge density plays a crucial role in determining the electric field and potential in a given space. It also affects the properties of materials, such as their conductivity and dielectric constant.

4. What are integrals in relation to charge density?

Integrals are mathematical tools used to calculate the total electric charge in a given volume. They involve summing up the charge density over infinitesimal volumes to get the total charge.

5. How is charge density related to the concept of electric flux?

Charge density is directly related to electric flux, which is a measure of the electric field passing through a given surface. The electric flux is equal to the charge density multiplied by the surface area it passes through.

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