- #1

Dextrine

- 102

- 7

## Homework Statement

Two parallel wires are a distance 2 b apart from the origin and carry current I out of the plane of the paper.

Find the magnitude and direction of the magnetic field B(y) along the y axis.

## Homework Equations

∫B⋅dl=μI[/B]

## The Attempt at a Solution

If we take ∫dl = 2πr

B=μI/(2πr)

r=√(b^2+y^2)

Clearly the y components cancel so we are left with only the horizontal components, that is

B_total=2Bcos(θ)

cos(θ)=b/√(b^2+y^2)

However, in the answer key provided, it says that cos(θ)=y/(b^2+y^2)

I don't understand why this would give this horizontal component. It seems like this would give the vertical component.