- #1

arrowface

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## Homework Statement

I solved this problem. I just have a general question at the very end.

I solved this problem. I just have a general question at the very end.

A current flows in a wire that has straight sections on either side of a semicircular loop of radius b. Find the mag and direction of the magnetic field B at point P(center of loop).

......... periods = mag field pointing out

....._____...... x's = mag field pointing in

.../xxxxxxx\.... radius = "b" from point P to any part in the semi circle.

...../xxxxxxxxx\........y

-->--->--| xxxx

**P**xxxx|--->---->--.....|

xxxxxxxxxxxxxxxxxxxxxxxxxxxxx...z(out)|___x

## Homework Equations

Bio-Savart

## The Attempt at a Solution

B = μ/4pi ∫(I(dl x r ))/r^2

I started out by pulling out the constants and everything I knew. Since dl is in the same direction as the current, the magnetic field from the straight pieces of the wire does not contribute to the magnetic field at point P due to the angle between dl and r:

B = μI/(4pi*b^2) ∫(dl x r )

As the current goes around the semi circle, a perfect 90 degrees is maintained between dl and r so r cancels out( sin(90)= 1 )

B = μI/(4pi*b^2) ∫ dl

The next step is finding dl which is the sum of which dl travels around the semi circle. Since it is half of a circle it would be pi multiplied by the radius which is b:

B = μI*pi*b/(4pi*b^2) >>>>>>

**B = -μI/4b in the negative z direction**due to the magnetic field.--------------

My Question

--------------

What if the semicircle was not a semicircle, but a square that was cut in half? How would I deal with finding dl then?