# Direction of Magnetic Field of a Parallel Conducting Wire

1. Apr 20, 2015

### sugz

1. The problem statement, all variables and given/known data
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.
2. Relevant equations
B = uI1/(2pia)

3. 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?

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2. Apr 20, 2015

### rude man

They said I2 is into or out of the page, not any B field.

3. Apr 20, 2015

### 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?

4. Apr 20, 2015

### rude man

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

5. Apr 20, 2015

### 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?

6. Apr 20, 2015

### rude man

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!

7. Apr 20, 2015

### sugz

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

8. Apr 21, 2015

### rude man

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.

9. Apr 21, 2015

### sugz

my question is why is I2 out of the paper?

10. Apr 21, 2015