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## Homework Statement

Two parallel wires carry a current I and 2I in different directions. What is the magnetic field halfway between the two wires?

## Homework Equations

Ampere's law

Int (B dot dA) = permissivity x enclosed current

## The Attempt at a Solution

Draw a circle around wire 1

B x 2 pi r = mu x I

B = mu x I / 2 pi r

if d = distance between two wires, r = d/2

Where I'm confused is at the part where I add the two B vectors to find the total B. According to the rule of vector addition, I can add vectors to find the net vector. BUT I thought Ampere's law was supposed to describe all of the B at a point as proportional to ONLY the current inside and that currents outside the Amperian loop were not supposed to make any net contribution to B. So how can I add together two vectors when Ampere's law is supposed to describe a magnetic field with all the B vectors already added up? This is a more conceptual question. Thanks.