Past exam of the physics B course of the University of Cambridge / 2010 / Paper 2A / Section A / 2 / Solution

Take the wires along $z$, with the first at $x=0$ carrying $+I\hat{\mathbf{z}}$, and observe at $x=-a$. The Biot-Savart law gives a first-wire field in $-\hat{\mathbf{y}}$; wire $n$ is $na$ away. ThereforePairing adjacent terms, with $N=2m$,Thus $\boxed{\mathbf{B}={\mu }_{0}IN(N+1)\hat{\mathbf{y}}/(4\pi a)}$. Its direction is opposite to the field of the first wire at the observation point. Reversing every electric current reverses this answer.