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An electron gun is composed of hollowed anode and cathode discs. These discs are used to accelerate electron when a high voltage is applied as shown in Figure 1. (1) Using equation of electric field produced by a surface charge density p. show that E at location (0, 0, a) due to a disk charge centered at origin (disc axis is in z- direction) radius a ≤ p≤ 2a is expressed by E(0,0, a) = 2a (ii) Calculate the force experienced by an electron charge of -4 nC at (0, 0, a), where a=0.5 and p= 4 C/m². (iii) Calculate the surface charge density ps2 of a second disc (similar size to the first disc) when it is placed at z = 1 and the force experienced by the -4 nC charge (Question 1 b (ii)) is doubled. Ps √5-√2 2⁹ √10 a Electron Figure 1 -a₂ Cathode Anode