Question

<module 4a
direction of the magnetic field due to a wire conceptual question
find the direction of the magnetic field at each of the indicated points
figure
2 of 2
wire 1
wire 2
part c
what is the direction of the magnetic field \\(\vec{b}_c\\) at point c?
view available hint(s)
\\(\vec{b}_c\\) is out of the page
\\(\vec{b}_c\\) is into the page.
\\(\vec{b}_c\\) is neither out of nor into the page and \\(\vec{b}_c\
eq0\\)
\\(\vec{b}_c = 0\\)
submit
part d
what is the direction of the magnetic field

Explanation:

Step1: Apply right - hand rule

For a long straight wire, the magnetic field direction is given by the right - hand rule. Curl the fingers of your right hand in the direction of the current, and your thumb points in the direction of the magnetic field around the wire.

Step2: Analyze fields from both wires

Wire 1 has current $I$ and Wire 2 has current $2I$. The magnetic field due to a long - straight wire at a distance $r$ is $B=\frac{\mu_0I}{2\pi r}$. At point C, the magnetic field due to Wire 1 and Wire 2 will be in opposite directions. Since the current in Wire 2 is larger and point C is closer to Wire 1 but the effect of the larger current in Wire 2 dominates, using the right - hand rule for each wire, the net magnetic field at point C is into the page.

Answer:

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