How do you determine the sign of a magnetic field?

[Vladi]

Homework Statement

Two long fixed parallel wires, A and B, are 10 cm apart in air and carry 40 A and 20 A, respectively, in opposite directions. Determine the resultant field (a) on a line midway between the wires and parallel to them and (b) on a line 8.0 cm from wire A and 18 cm from wire B. (c) What is the force per meter on a third long wire, midway between A and B and in their plane, when it carries a current of 5.0 A in the same direction as the current in A?

Homework Equations

Fm=(I)(L)(B)*sin(theta)
B=(Uo*I)/(2*pi*r)

The Attempt at a Solution

How do you determine the sign of a magnetic field? I can calculate a magnetic field. How do you calculate a resultant field? I guessed the signs and put them on the paper, but I have no clue why they belong there. The answers are within the uploads. I am only concerned about parts a and b.

 

[TSny]

Electric and magnetic fields are vector quantities. A vector doesn't really have a sign. It has a magnitude (always positive) and a direction. (However, the component of a vector along a coordinate axis, such as B_x, can be positive or negative.)

You need to determine the direction of the B field produced by each wire at the location of the point of interest. You probably covered a right-hand rule for doing this. The total field at the point of interest will be the vector sum of the fields due to each wire.

 

[Vladi]

Is there some sort of sign convention I should be following? Is a magnetic field into the page considered to be positive and out of the page considered to be negative? If so, I'll just use the right hand rule. Thank you for your time.

 

[TSny]

Is there some sort of sign convention I should be following? Is a magnetic field into the page considered to be positive and out of the page considered to be negative?

One could adopt a sign convention for a particular problem. But there is no fundamental reason why a certain direction would be considered to be "positive".

If so, I'll just use the right hand rule. Thank you for your time.

I think it's best to think in terms of vectors and use the right-hand rule to determine the directions of the vectors.

 

[Vladi]

One could adopt a sign convention for a particular problem. But there is no fundamental reason why a certain direction would be considered to be "positive". I think it's best to think in terms of vectors and use the right-hand rule to determine the directions of the vectors.

I used the right hand rule to determine where the magnetic field is in and out. I used a sign convention and came up with the right answers. Please look at the attachments. Do my diagrams make sense?

 

[TSny]

OK, I think your work is correct. (I haven't checked the actual numerical evaluations.) But it looks to me like you are using x's to denote out of the page and dots to indicate into the page. This is opposite to the usual convention.

 

[TSny]

Just to check, let me ask if you are using the "conventional current direction" in which current is in the direction that positive charge would flow. Or are you using the convention where current is in the direction that electrons are flowing?

 

[Vladi]

The answers I wrote down are correct (I got them from the back of the book). Because I was guessing which signs were correct at first, I wanted to make sure I could determine the signs using a diagram. If the diagram is good, I think I understand this problem. My issue was understanding the right hand rule. I also need to make sure to follow the right convention. Dots mean out of the page. X's mean into the page.

Just to check, let me ask if you are using the "conventional current direction" in which current is in the direction that positive charge would flow. Or are you using the convention where current is in the direction that electrons are flowing?

I believe we are supposed to use conventional current direction. Point your thumb in the direction of the current. Place your fingers across your palm. In this position, the magnetic field is "in the page". If you rotate your wrist about the wire, your fingers will be in the position where the magnetic field is "out of the page".

 

[TSny]

Just to make sure, what would be the direction of the magnetic field at point $a$ and at point $b$ in the picture below?

 

[Vladi]

Just to make sure, what would be the direction of the magnetic field at point $a$ and at point $b$ in the picture below?
View attachment 210304

B is into the page. A is out of the page.

 

[TSny]

B is into the page. A is out of the page.

OK, good. But then, I don't think your drawings in post #5 show the correct directions for the field (assuming dots mean out of the page).

 

[Vladi]

OK, good. But then, I don't think you drawings in post #5 show the correct directions for the field (assuming dots mean out of the page).

If I flip the x's and dots, It should be right.

 

[Vladi]

If I flip the x's and dots, It should be right. I'll re-post the diagrams

 

[TSny]

If I flip the x's and dots, It should be right.

Yes. No need to post a corrected diagram as long as you are sure you understand everything. For your final answers to parts (a) and (b) I would state the answers in terms of a magnitude and a direction, where the direction is very clear (such as "out of the page").

 

[Vladi]

Yes. No need to post a corrected diagram as long as you are sure you understand everything. For your final answers to parts (a) and (b) I would state the answers in terms of a magnitude and a direction, where the direction is very clear (such as "out of the page").

Thank you for all your help. It is much appreciated.

 

[TSny]

Thank you for all your help. It is much appreciated.

OK. No problem.