# Magnitude and direction of magnetic field

## Homework Statement

http://desmond.imageshack.us/Himg37/scaled.php?server=37&filename=physicsh.jpg&res=medium [Broken]

## Homework Equations

B = $\frac{μI}{2πr}$

## The Attempt at a Solution

B = $\frac{μ(12)}{2π(0.4m)}$ - $\frac{μ(12)}{2π(0.1)}$

B = -1.8 x 10-5

I'm not sure if I am doing this correctly, am I supposed to add up the magnetic fields produced by both wires like this?

Thanks for helping!

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gneill
Mentor
Yes, add up the magnetic fields produced by each wire at location A. The directions of the individual fields is determined by the right-hand-rule for currents and fields.

If you apply the right-hand-rule, what's the direction of the field produced by I1 at A? How about I2?

berkeman
Mentor

## Homework Statement

http://desmond.imageshack.us/Himg37/scaled.php?server=37&filename=physicsh.jpg&res=medium [Broken]

## Homework Equations

B = $\frac{μI}{2πr}$

## The Attempt at a Solution

B = $\frac{μ(12)}{2π(0.4m)}$ - $\frac{μ(12)}{2π(0.1)}$

B = -1.8 x 10-5

I'm not sure if I am doing this correctly, am I supposed to add up the magnetic fields produced by both wires like this?

Thanks for helping!
Looks pretty close. But you should define your coordinate system (x,y,z directions), and be sure the signs in your equation match the coordinate system. Use the right-hand rule to determine the direction of the B field at that point, based on each of the two currents (your equation should have unit vectors multiplying each of the two B-field components, so that your answer is a vector). The problem asks for a magnitude and direction of the resultant B-field.

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The direction of the magnetic field at point A by I1 is downward. And the direction of the magnetic field by I2 is upward.

My thoughts:
So,..since I chose the downward direction to be positive, and the answer I got was negative, that means the direction of the resultant magnetic field is upward?

Thanks for the help guys!

berkeman
Mentor
The direction of the magnetic field at point A by I1 is downward. And the direction of the magnetic field by I2 is upward.

My thoughts:
So,..since I chose the downward direction to be positive, and the answer I got was negative, that means the direction of the resultant magnetic field is upward?

Thanks for the help guys!
The resultant does indeed point upward, since the closer wire's B-field contribution will dominate.

Why did you choose downward as positive? That's fine if you specify that in your answer, but it would be more traditional to choose (x,y,z) on the paper as (pointing East on the paper, pointing North on the paper, pointing out of the paper up at you).

The resultant does indeed point upward, since the closer wire's B-field contribution will dominate.

Why did you choose downward as positive? That's fine if you specify that in your answer, but it would be more traditional to choose (x,y,z) on the paper as (pointing East on the paper, pointing North on the paper, pointing out of the paper up at you).
Would the answer still be correct if I said the magnitude was + 1.8 x 10-5 T and directed out of the page. Or does it have to be negative.

berkeman
Mentor
Would the answer still be correct if I said the magnitude was + 1.8 x 10-5 T and directed out of the page. Or does it have to be negative.
Yes, that would be a correct way to say it.