A thin straight rod $AB$, $30\ \text{cm}$ long, carries a charge of $+4.0\ \text{nC}$ spread evenly along it. A point $P$ lies $40\ \text{cm}$ from the end $A$, on the line through $A$ at right angles to the rod, as in the figure. The rod is in empty space, far from other charges. Take $\dfrac{1}{4\pi\varepsilon_0} = 9.0 \times 10^{9}\ \text{N m}^2\,\text{C}^{-2}$. The field at $P$ has a part at right angles to the rod and a part along it. What is the size of the electric field at $P$?

Fig. 1: A thin straight rod AB, 30 cm long, lies horizontally with A on the left, and carries plus 4.0 nanocoulombs. From A a dashed line goes straight up, at right angles to the rod, to a point P 40 cm above A. A small square marks the right angle at A.