2. Using conservation of energy, show that the speed v of an electron leaving your "electron gun" can be writtenin terms of the electron accelerating potential V, electron charge e and electron mass me as:v=2eVme(5) be perpendicular to the electron velocity, causing the electrons to move in a circular path. By varying the currentgoing through the Helmholtz coils you will be able to vary the applied magnetic field and thus change the radiusof the electron paths. The magnetic field will be produced using "Helmhotlz coils" that produce a magnetic fieldstrength (at the center of the coil configuration) given by:(4)where R is the radius of the coils, N is the number of turns per coil (N = 124 in your set-up), Po=4π × 10-7 T· A/m,and I is the current flowing though the coils.Helium FilledVacuum tubeElectron Gun(a)Ve-8 POIN5√5 RB =electron's pathDeflection PlatesGrid.Cathode.Heater•●●●●000Anode(b)(+)Deflection PlatesFigure 2: (a) Schematic diagram of the vacuum tube you will use to determine the value of e/me. The circular path of theelectron is shown in blue. Note the direction of the electron's velocity -. For the electron path shown here, the applied Bfield points out of the page. (b) Cathode and anode arrangement of the electron gun in your apparatus.

Question

2. Using conservation of energy, show that the speed v of an electron leaving your &#34;electron gun&#34; can be writtenin terms of the electron accelerating potential V, electron charge e and electron mass me as:v=2eVme(5) be perpendicular to the electron velocity, causing the electrons to move in a circular path. By varying the currentgoing through the Helmholtz coils you will be able to vary the applied magnetic field and thus change the radiusof the electron paths. The magnetic field will be produced using &#34;Helmhotlz coils&#34; that produce a magnetic fieldstrength (at the center of the coil configuration) given by:(4)where R is the radius of the coils, N is the number of turns per coil (N = 124 in your set-up), Po=4π × 10-7 T· A/m,and I is the current flowing though the coils.Helium FilledVacuum tubeElectron Gun(a)Ve-8 POIN5√5 RB =electron's pathDeflection PlatesGrid.Cathode.Heater•●●●●000Anode(b)(+)Deflection PlatesFigure 2: (a) Schematic diagram of the vacuum tube you will use to determine the value of e/me. The circular path of theelectron is shown in blue. Note the direction of the electron's velocity -. For the electron path shown here, the applied Bfield points out of the page. (b) Cathode and anode arrangement of the electron gun in your apparatus.

Accepted Answer

Solution       Given dataUsing conservation of energy show that the speed v of an electron leaving…

2. Using conservation of energy, show that the speed v of an electron leaving your "electron gun" can be written in terms of the electron accelerating potential V, electron charge e and electron mass me as: v= 2eV me (5)