Halliday, Resnick & Walker — Electric Fields: Problem 47

47 In Fig. 22-42, a “semi-infinite” nonconducting rod (that is, infinite in one direction only) has uniform linear charge density \(\lambda\). (a) Show that the electric field \(\vec{E}_P\) at point \(P\) makes an angle of \(45^\circ\) with the rod and that this result is independent of the distance \(R\). (Hint: Separately find the component of \(\vec{E}_P\) parallel to the rod and the component perpendicular to the rod.) (b) Find the field magnitude for linear charge density \(4.52 \text{ nC/m}\) and \(R = 3.80 \text{ cm}\).