- #1

NasuSama

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## Homework Statement

Three long parallel wires are 3.5 cm from one another. (Looking along them, they are at three corners of an equilateral triangle.) The current in each wire is 8.00 A, but its direction in wire M is opposite to that in wires N and P. Determine the magnitude of the magnetic field midway between points M and N.

## Homework Equations

##B = \dfrac{\mu_0 I}{2\pi r}##

## The Attempt at a Solution

First, I compute the field due points M and N, which is

##B_{MN} = \dfrac{2\mu_0 I}{\pi d}##

Then, the field due point P is

##B_P = \dfrac{mu_0 I}{\pi d\sqrt{3}}##

Working component wise, I obtain:

##B_x = B_{MN}\cos(30) + B_P\cos(60) = \dfrac{7}{2\sqrt{3}}\dfrac{\mu_0 I}{\pi d}##

##B_y = -B_{MN}\sin(30) + B_P\sin(60) = -\dfrac{\mu_0 I}{2\pi d}##

So we have

##B = \sqrt{(B_x)^2 + (B_y)^2} \approx 9.52 \times 10^{-5}##

But the answer is wrong.

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