How to graph magnetic field between two wires?

[zzizi]

Homework Statement

If there are two long straight wires that are 6cm apart. If I calculated the magnetic field strength at a point between the wires, which are 4cm from one wires and 2cm from the other and B= 8x10^-6 T

Sketch a graph if the variation of the magnetic field along a perpendicular line between the wires... does anyone know how I am suppose to sketch that?

Homework Equations

The Attempt at a Solution

What I do know is that B is on the Y axis and r is on the x-axis that's about it... I would really appreciate some help and explanation!

 

[eczeno]

were you able to calculate the magnetic field at the point indicated in the question?

 

[eczeno]

oh, sorry i misunderstood.

 

[eczeno]

the value of B and r that are given will be one point on the plot.

 

[eczeno]

have you plotted that point?

 

[zzizi]

Hi

I haven't plotted anything yet, that's what I'd really like advice on... how do I plot it. I have attached an image of the information I have of the graph. Please tell me, how is it supposed to be graphed?

 

[eczeno]

ok, that should work, though you may need to consider negative B values. Now, we need to partition our axes and give them some units. we can use the one data point that we know already, (2 , 8x10^-6), to help us determine the scale we should use for each axis. the x-axis is easy, just put a tick mark every centimeter. but the value of the magnetic field is pretty small, so what we should do is tuck the 10^-6 into the units and use militesla instead of tesla, so our point is now (2,8). Let's plot that point on our graph.

 

[zzizi]

Thank you eczeno, but should I plot that point (2,8) under where it says 'position wire 2'?

Like this?

 

[eczeno]

no, all of our action will take place between the wires. you need to make the position of wire 1 = 0cm, and the position of wire 2 = 6cm, and then fill in the rest. the field we are given is for the point located 2cm from wire one, so that is where we plot the value 8.

 

[zzizi]

Is there any chance you could draw for me what you mean?
I have made the amendments you suggested... but I'm not sure how to fill in.

 

[eczeno]

ok, that is good. that is all you can do until you figure out the currents in the wires. do you know how to do that?

 

[eczeno]

it seems like we need to know if the currents are in the same direction or in opposite directions. does the problem say anything like that?

 

[zzizi]

Yes the currents are flowing in the opposite direction to each other.. at 2.5A each.

 

[eczeno]

oh, ok, then we can solve the problem. do you know how to calculate the magnetic field due to a current carrying wire?

 

[ideasrule]

Homework Statement

If there are two long straight wires that are 6cm apart. If I calculated the magnetic field strength at a point between the wires, which are 4cm from one wires and 2cm from the other and B= 8x10^-6 T

Sketch a graph if the variation of the magnetic field along a perpendicular line between the wires... does anyone know how I am suppose to sketch that?

I really think you're leaving out crucial information. Can you post the question word-for-word?

 

[zzizi]

Yes, I think I might have.. sorry about that. Ok here is the information in full.

Two long straight wires are placed parallel to each other 6cm apart in a vacuum. Each wire carries a current of 2.5A. The current flows in opposite directions.

I calculated the resultant magnetic field at the midpoint of the two wires to be: B = 4.5 X10^-5 t

I calculated the magnetic field strength at a point between the wire 4cm from one wire and 2cm from the other to be: B = 8 x 10^-6 T

I was asked to graph the variation of Magnetic field along a perpendicular line between the wires. That's what I have been trying to graph.

I hope this helps.

* just for the record I'm quite new to the study of Physics ... so please be patient.. and I appreciate your help :-)

 

[eczeno]

yes, you have the idea, now you just need to calculate the field at a few more points and get the shape of the graph. you should try to take advantage of the symmetry of the situation.

notice the field in the middle is 45 microtesla, so you need to adjust your scale.

oops, i just noticed i wrote 'militesla' above, that should be 'microtesla'. sorry.

 

[ideasrule]

I was asked to graph the variation of Magnetic field along a perpendicular line between the wires. That's what I have been trying to graph.

Along which perpendicular line? There are an infinite number of lines perpendicular to the two wires. I doubt the question just says "graph the variation of Magnetic field along a perpendicular line" without any additional info. If you post the entire question, word for word, it'll be much easier to help you.

 

[zzizi]

That is honestly all of the information I have and that is the question in full.
The only other info that came with it.. was the empty graph with axis.
Now I'm confused

 

[eczeno]

ideas,

he quoted all the information needed in the above post. any perpendicular line between infinite wires will result in the same graph.

 

[zzizi]

I'm a she BTW.

 

[eczeno]

sorry, hard to tell, so i just guess. anyway, we are on the right track, have you calculated the field anywhere else?

 

[zzizi]

So at a point 1cm from one and 5cm from the other: B = 1.29x10^-5

and I already have the midpoint which is: B = 4.5x10^-5

...that's 3 points plotted... are they right? and do I just connect them with a line?

 

[eczeno]

hmm, that doesn't look right. one thing is my fault, you need to change your units from mT to microT.

but the graph itself looks wrong too. it should be symmetric and it should have a minimum at the center. make sure you are adding the fields from the two wires together.

 

[ideasrule]

Oops, sorry for misunderstanding the question. I was thinking of a perpendicular line in the 3rd dimension, that threads through the space between the two wires.

eczeno is correct, and has been providing great help. One suggestion: if your point is a distance "r" from the first wire, it's 6 cm - r from the other wire. Use this to write out an equation for the magnetic field, then plot the graph according to this equation.

 

[ideasrule]

but the graph itself looks wrong too. it should be symmetric and it should have a minimum at the center. make sure you are adding the fields from the two wires together.

That's true if she was plotting the absolute magnitude of the magnetic field with respect to "r". Otherwise, the field would change sign at the center because the field of the second wire, whose magnetic field is opposite to that of the first, would start dominating.

 

[zzizi]

Oops, sorry for misunderstanding the question. I was thinking of a perpendicular line in the 3rd dimension, that threads through the space between the two wires.

eczeno is correct, and has been providing great help. One suggestion: if your point is a distance "r" from the first wire, it's 6 cm - r from the other wire. Use this to write out an equation for the magnetic field, then plot the graph according to this equation.

Yes thanks very much for the help. But can you write for me the equation that you have suggested?