Magnetic field from current-carrying wire with circular bend

[andrew410]

A very long straight wire carries current I. In the middle of the wire a right-angle bend is made. The bend forms an arc of a circle of radius r as shown in the figure below.
Figure: http://east.ilrn.com/graphing/bca/user/appletImage?dbid=1161207397

Lets say the permeability of free space is mu. So I believe the answer is ((mu*I)/(4*pi*r))*(pi/2), which equals to (mu*I)/(8*r).

It says the answer is wrong... Can anyone help?

 

[Parth Dave]

what are you asked to solve? The magnetic field at the dot?

 

[s_a]

I'm assuming you want to find the magnetic field where the black dot is in the diagram. Working out the field due to the straights part of the wire is easy, it is as if there's one infinitely long wire carrying current I and distance r from the point where you want to find the B field. Working out the magnetic field due to the curved part of the wire is a tiny bit trickier, you need to use Biot Savart Law (give it a go). Finally you need to add the resultant B fields due to the straight & curved parts of the wire.

Edit: I noticed your answer is correct only for the curved part of the wire, and I'm assuming you thought that the two straight parts canceled out with each other, right? Well they don't. Use the right hand grip rule to see that they both produce a field in the same direction.