A long wire carries a steady current of $5.0\ \text{A}$. It lies flat on a table, bent into the shape in the figure. It comes in from far away along a straight line that touches a circle of radius $4.0\ \text{cm}$ at the point $P$. From $P$ it follows the circle three quarters of the way round, to the point $Q$. From $Q$ it runs straight out, along the line from the centre $O$ through $Q$, to far away. Take $\mu_0 = 4\pi \times 10^{-7}\ \text{T m/A}$. What is the size of the magnetic field at $O$?

Fig. 1: A wire in a plane. It comes in from the far left along a horizontal straight line that touches a circle of radius 4.0 cm, centre O, at its lowest point P. It follows the circle anticlockwise for three quarters of a turn, through the right and the top, to the point Q at the far left of the circle. From Q it runs straight out to the left along the line OQ. The quarter of the circle that it misses is dashed. The current is 5.0 A.