4 An electron emitter will be used to make a beam of electrons for a microscope. Electrons are emitted from a hot wire and accelerated between an anode and cathode plate which can be approximated to a parallel plate capacitor. A voltage of 10 kV is applied across two plates, which are 2 cm apart. (a) What is the electric field between the plates? (b) Ignoring relativistic effects, find the velocity of the electrons after acceleration. (c) The beam is 10 nm in diameter and has a flux of 50,000 electrons/second. On average, what is the distance between electrons? (d) Using the answer for (c) and Coulomb's Law, find the acceleration experienced by an electron due to its nearest neighbour. (e) A magnetic filter (see Figure Q4 below) is used to select electrons based on energy. It comprises a semi-circular chamber 10 cm in diameter. What field will be required to use this lens? B d I Electron Aperture I I beam Figure Q4 Diagram of magnetic filter