Magnetic field and current of solid wire

In summary, the conversation discussed a problem on Masteringphysics involving a solid conducting wire with a current density given by J=J(0) * (1 - r/R)^k. The parts of the problem are similar to those in the textbook and the student is unsure about the correct answer for part A. They attempted to use Ampere's Law and got the correct answer for part B. However, they are unsure if they need to integrate again for part C since the current surrounded will not be from the whole wire. The conversation ends with the student thanking the expert for their help.
  • #1
gills
116
0

Homework Statement


26_77.jpg


This is also a problem on my Masteringphysics:

A solid conducting wire of radius runs parallel to the axis and carries a current density given by J=J(0) * (1 - r/R)[tex]\hat{k}[/tex] , where J(0) is a constant and r is the radial distance from the wire axis.

The parts are the same as in the textbook.


Homework Equations


biot savart law

J=I/A


The Attempt at a Solution



I haven't answered part B, or C yet.

ok, when I'm entering my answer for part A on masteringphysics, it keeps telling me "variables are case senstive, make sure that you have the right case on your variables." I've switched them around, and it keeps saying the same thing.

Anyway, my simplified answer is J(0)pi*R[tex]^{2}[/tex](1-[tex]\frac{r}{R}[/tex])


Since J is the current density of the wire, the current is just J*Area, right? That's basically what I'm doing, but something is off. Any help would be great.

Thanks
 
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  • #2
Why does your answer for total current have an r in it?

You have to integrate to find the total current, since the current density is not constant.
 
  • #3
Since the density is not constant in the wire (depends on the distance from the center), I guess you will need to integrate over the area instead of just mupliplying. Btw, what is ^k?
 
  • #4
Kurret said:
Since the density is not constant in the wire (depends on the distance from the center), I guess you will need to integrate over the area instead of just mupliplying. Btw, what is ^k?

it's [tex]\hat{k}[/tex], the vector direction.
 
  • #5
Doc Al said:
Why does your answer for total current have an r in it?

You have to integrate to find the total current, since the current density is not constant.

ok, so i integrate from 0 to R in the given formula and i get

J = J(0)*[tex]\frac{R}{2}[/tex] = [tex]\frac{I}{A}[/tex] -->

I = J(0)*(piR^3/2)


??
 
  • #6
That's not correct. Show how you did the integration:
[tex]I = \int J dA[/tex]
 
  • #7
Doc Al said:
That's not correct. Show how you did the integration:
[tex]I = \int J dA[/tex]

ok, i actually integrated only J from 0 to R then multiplied by the area after the integration. So i'll integrate what you said.

so DA = (pi*r)dr ??
 
  • #8
gills said:
so DA = (pi*r)dr ??
Almost. What's the circumference of a circle?
 
  • #9
Doc Al said:
Almost. What's the circumference of a circle?

circumference is 2pi*r

Would dA be 2pi*r dr?

why the need for the circumference?
 
  • #10
gills said:
circumference is 2pi*r

Would dA be 2pi*r dr?
Yes.

why the need for the circumference?
Because you dividing the disk into circular rings so you can integrate.
 
  • #11
Doc Al said:
Yes.


Because you dividing the disk into circular rings so you can integrate.

ahhh indeed!

i've got I = J(0)*((pi*R^2)/3))
 
  • #12
Looks good!
 
  • #13
Doc Al said:
Looks good!

it's correct, thank you..

For part B, using ampere's Law i came up with ([tex]\mu[/tex](0)*J(0)*R^2)/6r which came out to be correct.

Now for part C, do i need to integrate again since the current surrounded will not be from the whole wire? or I'm just replacing R with r for the total current now because the amperian line is inside the wire?
 
Last edited:
  • #14
gills said:
Now for part C, do i need to integrate again since the current surrounded will not be from the whole wire?
Yes.
or I'm just replacing R with r for the total current now...
Not sure what you mean... but don't do it! :wink:
 
  • #15
Doc Al said:
Yes.

Not sure what you mean... but don't do it! :wink:

gotcha, haha. Thanks for the help, i'll let you know if i get it.
 
  • #16
SOLVED!

thanks (again) Doc
 

1. What is a magnetic field?

A magnetic field is a region in space where a magnetic force can be observed. It is created by moving electric charges, such as those found in a current of electrons in a wire.

2. How is a magnetic field created by a current in a solid wire?

When a current of electrons flows through a solid wire, it creates a circular magnetic field around the wire. The direction of the magnetic field can be determined using the right-hand rule, where the thumb points in the direction of the current and the fingers wrap around in the direction of the magnetic field.

3. How does the strength of the magnetic field change with the current in a solid wire?

The strength of the magnetic field is directly proportional to the amount of current flowing through the wire. This means that as the current increases, the strength of the magnetic field also increases.

4. Can the direction of the magnetic field be changed?

Yes, the direction of the magnetic field can be changed by reversing the direction of the current flow. This will cause the magnetic field to reverse its direction as well.

5. What other factors can affect the strength of the magnetic field produced by a current in a solid wire?

The strength of the magnetic field can also be affected by the distance from the wire, the material of the wire, and the number of coils in the wire. Increasing the distance from the wire or using a material with higher magnetic permeability can increase the strength of the magnetic field. Adding more coils in the wire can also increase the strength of the magnetic field.

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