Direction of Magnetic Field of a Parallel Conducting Wire

[sugz]

Homework Statement

Two long, straight, parallel wires carry currents that are directed perpendicular to the page as shown in Figure P30.9. Wire 1 carries a current I1 into the page (in the negative z direction) and passesthrough the x-axis at x a. Wire 2 passes through the x-axis at x 5 22a and carries an unknown current I 2. The total magnetic field at the origin due to the current-carrying wires has the magnitude 2uI1/(2pia). The current I 2 can have either of two possible values. (a) Find the value of I 2 with the smaller magnitude, stating it in terms of I 1 and giving its direction. (b) Find the other possible value of I 2.

Diagram is attached as well as the solution.

Homework Equations

B = uI1/(2pia)

The Attempt at a Solution

I understand how to do the question but determining the direction of the magnetic field due to I2. I1 is directed into the page (+j). They get the answer to (a) as +j as well but they said the direction of the magnetic field is out of the page, why?

 

[rude man]

Homework Statement

Two long, straight, parallel wires carry currents that are directed perpendicular to the page as shown in Figure P30.9. Wire 1 carries a current I1 into the page (in the negative z direction) and passesthrough the x-axis at x a. Wire 2 passes through the x-axis at x 5 22a and carries an unknown current I 2. The total magnetic field at the origin due to the current-carrying wires has the magnitude 2uI1/(2pia). The current I 2 can have either of two possible values. (a) Find the value of I 2 with the smaller magnitude, stating it in terms of I 1 and giving its direction. (b) Find the other possible value of I 2.

Diagram is attached as well as the solution.

Homework Equations

B = uI1/(2pia)

The Attempt at a Solution

I understand how to do the question but determining the direction of the magnetic field due to I2. I1 is directed into the page (+j). They get the answer to (a) as +j as well but they said the direction of the magnetic field is out of the page, why?

You misread the answer to the problem.
They said I2 is into or out of the page, not any B field.

 

[sugz]

Yeah I understand that it can be into or out of the page, but for the answer to (a) they said I2=2i1 (out of the page), why is that?

 

[rude man]

Yeah I understand that it can be into or out of the page, but for the answer to (a) they said I2=2i1 (out of the page), why is that?

You said they said the B field is out of the page.
They did'nt.

 

[sugz]

I meant the current not the magnetic field, sorry it was a mistake! Why is I2 in (a) out of the page if it's in the +j direction?

 

[rude man]

I meant the current not the magnetic field, sorry it was a mistake! Why is I2 in (a) out of the page if it's in the +j direction?

Show me where it says I2 is in the j direction.
I do find it unfortunate that in a couple of places in the solution set an equation is written with a vector on one side and a scalar on the other. Poor form!

 

[sugz]

If you look at the 2nd picture, where it says (a), the second line after that!

 

[rude man]

If you look at the 2nd picture, where it says (a), the second line after that!

2nd line after (a) says B₂ is in the j direction, which is right.
Last line says I₂ is out of the paper, which is also right.
Your turn.

 

[sugz]

my question is why is I2 out of the paper?

 

[rude man]

my question is why is I2 out of the paper?

What, specifically, is your problem with the given answer?