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This is the problem I'm working on:

A loop of wire has the shape of two concentric semicircles connected by two radial segments (See figure). The loop carries a current $I = 280.00 A$. Find the magnetic field at point $P$. ($R = 21.00 cm$)

enter image description here

So I the magnetic field due to an arc to be $B = (\mu_0I/2\pi)(\alpha/r)$, which, if we take $r = 2R$ for the top arc and $r = R$ for the bottom arc, and $\alpha = \pi/2$ for both arcs, we get:

$B=(\mu_0I/4)(1/2R - 1/R)$

The answer I'm getting using this equation is wrong. Where is my mistake? Am I going down the correct path for this question?

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closed as off-topic by David Z Apr 3 '15 at 7:43

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    $\begingroup$ Perhaps $\alpha$ should be $\pi$? (I haven't looked closely at this.) $\endgroup$ – garyp Apr 2 '15 at 18:01
  • $\begingroup$ I think @garyp is right - you have 180 degrees, so $\pi$. $\endgroup$ – Floris Apr 2 '15 at 18:04
  • $\begingroup$ So then the equation would change to $B = (\mu_0I/2)(1/2R - 1/R)$ ? If I have my math right. $\endgroup$ – Kommander Kitten Apr 2 '15 at 18:06
  • $\begingroup$ I think your starting equation is wrong, too. $\endgroup$ – garyp Apr 2 '15 at 19:56
  • $\begingroup$ What should it be instead? $\endgroup$ – Kommander Kitten Apr 2 '15 at 20:23
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The way I would do this: calculate the field due to a complete "outer" loop (radius $2R$). Subtract from it the field due to the complete "inner" loop (radius $R$).

Divide the number you get by two (because you only have half a loop). It makes the whole process a little more transparent - easier to follow.

Finally you need to take a look at the diagram to decide what the direction of the net flux should be. The inner loop has a clockwise current and (being closer) should give the strongest field. Looks to me like that means the field is into the page. Make sure that your sign matches.

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