A closed loop of wire lies flat on a table. It is shaped like a slice cut from a flat ring, as in the figure. It has two circular arcs about the same centre $O$, of radii $3.0\ \text{cm}$ and $6.0\ \text{cm}$, each making an angle of $120^\circ$ at $O$. Two straight radial pieces join the ends of the arcs. A steady current of $6.0\ \text{A}$ flows round the loop, and the leads to it are twisted together so that they add no field. Take $\mu_0 = 4\pi \times 10^{-7}\ \text{T m/A}$. What is the size of the magnetic field at $O$? Give the answer in $\mu\text{T}$, to two decimal places.

Fig. 1: A closed loop in a plane, shaped like a slice of a flat ring. Two arcs about the same centre O, of radii 3.0 cm and 6.0 cm, each make an angle of 120 degrees at O, and two straight radial pieces join their ends. Arrows show the current of 6.0 A going anticlockwise along the outer arc and clockwise along the inner arc. The two leads leave together from one corner, twisted round each other.