Question

find the direction of the magnetic field at each of the indicated points
figure
2 of 2
wire 1
wire 2
part d
what is the direction of the magnetic field $vec{b}_d$ at point d?
view available hint(s)
$vec{b}_d$ is out of the page
$vec{b}_d$ is into the page
$vec{b}_d$ is neither out of nor into the page and $vec{b}_d
eq0$
$vec{b}_d = 0$
submit

Explanation:

Step1: Apply right - hand rule for wire 1

For a current - carrying wire, using the right - hand rule, the magnetic field due to wire 1 (with current $I$) at point D curls around the wire. Let the direction be $B_{1D}$.

Step2: Apply right - hand rule for wire 2

For wire 2 (with current $2I$) at point D, using the right - hand rule, the magnetic field due to wire 2 curls around the wire. Let the direction be $B_{2D}$.

Step3: Analyze the directions and magnitudes

The magnetic field due to a long straight current - carrying wire is given by $B=\frac{\mu_0I}{2\pi r}$. Since wire 2 has a current twice that of wire 1 and point D is equidistant from both wires, the magnetic field due to wire 2 is twice the magnitude of the magnetic field due to wire 1 at point D. The magnetic field due to wire 1 at point D and the magnetic field due to wire 2 at point D are in opposite directions. The net magnetic field $\vec{B}_D$ is non - zero and is in the direction determined by the stronger field (from wire 2). Using the right - hand rule, the net magnetic field $\vec{B}_D$ is into the page.

Answer:

$\vec{B}_D$ is into the page.