How to Determine the Magnetic Field at the Center of a Partially Open Loop?

[slayer1337]

1. An electric circuit consists of two long straight sections connecting a loop of radius r. The gap in the loop where the straight sections are connected subtends an angle of theta=60d, as shown in this figure (http://imgur.com/tseDHL6). Determine the magnetic field B at the point P in the centre of the loop, if a current I is flowing through the circuit.

See the diagram here - http://imgur.com/tseDHL6

2. Biot-Savart Law
3. The Attempt at a Solution - http://imgur.com/QFrlSn7

I have found the equation relating to the full loop but don't know how to do it for the missing segment.

 

[BvU]

What's wrong with integrating $d l\over r^2$ ?

 

[maajdl]

You need to use the Biot-Savart law:

 

[BvU]

Ma is right, but the next step is to convert to integrating $d l\over r^2$ because there is only one component left over; the others cancel.

 

[Rellek]

\int rd θ/r^2/

 

[rude man]

Consider finding the field as though the circular section wasn't there, but the wire was continuous from -infinity to +infinity: B1. Can use ampere's law.

Then, use Biot-Savart to compute the field due to a short section of wire connecting the loose ends of the loop: B2.

Then, use Biot-Savart to compute the field due to the loop: B3.

B = B1 - B2 + B3.