How Do You Calculate Magnetic Field Strength at Different Points?

[BuBbLeS01]

Magnetic Field...PLEASE HELP! Going CrAzY!

Homework Statement

What is the magnetic field strength at point a? (a=2.25 cm, b=5.14 cm, I=15 A.)
What is the magnetic field strength at point b?
What is the magnetic field strength at point c?

Homework Equations

The Attempt at a Solution

So we understand how to get the magnetic field strength at a and c...B2 - B1...but why for the magnetic field at point b do we add them?

 

[belliott4488]

hm ... shouldn't those be "point 1", "point 2", and "point 3"?

Anyway, yes, the magnetic field is a vector field, so you can use vector addition to add up the contributions from all the sources of the field. You are already doing this when you use Ampere's Law, since you're adding the contributions from all the little infinitesimal current elements along the wire.

Show us what you've got, and we'll let you know if it's okay.

 

[BuBbLeS01]

I know that you need to add the vectors but since B1 points to the left its X component is negative shouldn't you minus that from B2? And it make it equal 0?

 

[BuBbLeS01]

Our answers are...
9.274e^-5 T
0.0002 T
9.274e^-5 T

 

[belliott4488]

Sorry, you're going to have to show more of your work. What are B1 and B2?

Also, did you really copy this problem correctly and in its entirety? I find it odd that the points are referred to as "a, b, and c", where the diagram shows those as distances. Also, b appears to be the distance between the two wires, so we don't know where point 2 is located ... is it supposed to be at the midpoint between the wires?

 

[belliott4488]

Also, your answers should be vectors, not just vector magnitudes ...

 

[BuBbLeS01]

B1 = UI/2*pi*a = 1.334e^-4
B2 = UI/2*pi*(a+b) = 4.061e^-5
B2-B1 = 9.279e^-5

Thats for point 1 and point 3

Point 2...
B1 = UI/2*pi*.5B = 1.168e^-4
B2 = same
B1+B2 = 2.335e^-4
Why add them and not subtract them because B1 points to the left and B2 points to the right so wouldn't it be -B1 + B2 = 0

 

[belliott4488]

I'm sorry, I'm really not following your reasoning. It would really help if you'd follow the rules of the forum and state the relevant equations as well as showing all your steps.

What is UI? Why are there no vectors? Why do you say that B1 points to the left and B2 to the right?

I think if you work this through step by step, then either you will catch where you've made a mistake or someone here will identify it for you. You should start with Ampere's Law and the Biot-Savart Law, paying particular attention to the direction of the B field. There are no components of B pointing to the left or to the right in this problem, and the field at point 2 is not zero.

 

[iloveflickr]

UI = u0*I, where u0 = magnetic permeability (probably of free space) and I = current.

 

[BuBbLeS01]

Thanks...I am sorry I just wanted to understand the second part of the question (point 2) but I haven't had time to sit and type everything I have so I will try to do it later.

 

[belliott4488]

Okay - if you do come back here before finishing this problem, though, the hint you need is that you're coming up with the wrong directions for your B vectors.