What is the flux density at point p?

[Adventure123]

Homework Statement

1)
What is the flux density at point p in Fig "see link below". due only to the 3-A current in the portion of wire 2 shown?

1) 1.64 x 10^-5 Wb/m^2
2) 2.45 x 10^-5 Wb/m^2
3) 3.11 x 10^-5 Wb/m^2
4) 3.65 x 10^-5 Wb/m^2

2)
In which direction does the flux at point p of Question 1 point
1) Out of the page.
2) To the left of the page.
3) To the right of the page.
4) Into the page.

Fig Link
sellmontana.com/math/math.jpg
ignore the red marks.

Answers 2 and 2.. Is this correct?

Thanks

Homework Equations

B=I x 10^-7 (Integral sign) sinΘ/r^2 dl

The Attempt at a Solution

B= I x 10-7 (Integral sign) sin Θ /r^2 rdΘ/sin0

B= I x 10^-7/0.0200 (Integral sign) sinΘ dΘ

B=.5 x 10^-7 [-(-2)-(-5)] = ??

Does anyone have a real good document on how to Find flux density at a point? My current book does not fully explain it. Is there a online calculator that would help?

Thanks.

 

[alphysicist]

Hi Adventure123,

I think you have a couple of problems with your integral. It's difficult for me to tell because I don't know how you set up the geometrey, but here are some notes:

In the first line of section 3, it looks like you are writing dl in terms of d(theta). That's good, but since your expression for dx has r in it, it looks like you forgot to take into account dr (since r is also variable). If so, it would probably be better to write dl in terms of theta and the perpendicular distance from the wire to the point (2 cm in your diagram). If we call that distance x, then dx would be zero.

In your second line of section 3, you brought r out of the integral, but it depends on theta and so cannot be removed like that. (If you write dl in terms of x, that constant x value would come out of the integral.)

But like I said, I could just be misinterpreting your method.

 

[Moetasim]

I would first clarify the question by asking for more information about the wire and the point p in the figure. Without this information, it is difficult to accurately calculate the flux density at point p.

However, based on the given information, the correct answer would be 3) 3.11 x 10^-5 Wb/m^2. This can be calculated using the formula for magnetic field at a point due to a current-carrying wire, B=I x 10^-7 (Integral sign) sinΘ/r^2 dl. Since the wire is carrying a current of 3A and the distance from the wire to point p is 0.0200 m, we can substitute these values into the formula and integrate over the portion of wire 2 shown.

Regarding the direction of the flux at point p, it would depend on the direction of the current in the wire and the orientation of the wire with respect to point p. Without this information, it is not possible to accurately determine the direction of the flux at point p.

As for resources on finding flux density at a point, there are several online calculators available such as the one provided by HyperPhysics (http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magcur.html) or by using software such as Mathematica. Additionally, there are various textbooks and online resources that provide explanations and examples on how to calculate flux density at a point. It is important to have a thorough understanding of the underlying principles and equations in order to accurately calculate flux density at a point.