The figure to the right shows a head-on view of four long, parallel charged rails (they extend both into and out of the page). The side rails carry a positive charge per unit length +. The top and bottom rails have the same charge density, but with opposite sign (i.e. they are negatively charged). This arrangement forms an ''electrostatic quadrupole''. In the questions below, you will discover why it is useful in devices which contain beams of moving charged particles. ''We will not perform ''any'' calculations in this question …'' all you need is your physical intution.

(a) Sketch the '''electric field lines''' in the interior region of the quadrupole.

(b) Given your sketch, where is the electric field the '''strongest'''? Where is it the '''weakest'''?

(c) Now imagine that a '''beam of moving electrons''' enters the quadrupole, with velocity parallel to the charged rods. When the beam enters the device, its cross-sectional profile is circular. What will the beam look like when it ''exits'' the quadrupole on the other side? (Assume that the force exerted on the electrons is not ''too'' large.)

(d) The cathode ray tube (CRT) in a TV monitor contains a beam of electrons directed towards a fluorescent screen. The screen lights up where the beam hits it. If you were an electrical engineer designing such a CRT, why might you find it useful to pass the electron beam through a quadrupole before it hits the screen? (A little hint: quadrupoles are usually used in ''pairs'' … can you figure out why?)