You and your team are tasked with designing an “electron gun” that operates in a vacuum chamber, the purpose of which is to direct a beam of electrons toward a tiny metallic plate in order to heat it. The electrons in the beam have a speed of 3.50 × 107 m/s and travel in the positive x direction through the center of a set of deflecting plates (a parallel-plate capacitor) that sets up a uniform electric field in the region between the plates. The target is located 22.0 cm along the x-axis from the trailing edge of plates (i.e., the edge closest to the target), and 11.5 cm above the horizontal (i.e., in the +y direction). The length of the plates (in the x direction) is 2.50 cm.

(a) In which direction should the electric field between the plates point in order to deflect the electrons towards the target?

(b) To what magnitude should you set the electric field so that the electron beam hits the target?

(c) After successfully striking the target using your results from (a) and (b), you realized that the target is not heating up to the required temperature.

Since the degree of heating depends on the speed of the electrons, you increase the electron speed to 5.20 × 10⁷ m/s. With the electric field setting from (b), will the electrons still be on target? If not, to what value should you set the electric field?