Question

Determine the magnetic field midway between two long straight wires 2.0cm apart in terms of the current I in one when the other carries 15A. Assume these currents are (a) in the same direction, and (b) in opposite directions.

Answer 1

If they're going in the same direction, then they're going to cancel each other out. If they're going in opposite directions, then it's a bit tougher.

Answer 2

For b, we have to use Biot-Savart law: \[
\vec{B} = \frac{\mu_0I}{4\pi} \int_C \frac{d\vec{s}\times \vec{r}}{r}
\]

Answer 3

I suppose you would parametrize the bottom wire as \((x,y) = (t, -1.0), t\in(-\infty, \infty) \)

Answer 4

We'd let the origin be at the point of the magnetic field.

Answer 5

This makes means \(\vec{r}\) is just the origin minus our parametrization, and \(d\vec{s}\) is \(\vec{r}'(t)\).

Answer 6

I mean \(\vec{r}'(t)dt\)