11:07 1l 5G IPH115_Lab_E_FILE...more mobile that the ions, results in a charge density distribution that looks like an avalanche (theso-called Townsend avalanche, see Fig. 6 lower panel). This implies that during the moment of thedischarge the flow of electrons towards the anode have greater linear charge density leading to a moreluminous terminal connection.6.1 VDG calculationsAt this point we need to go through a few back-of-the-envelope calculations pertinent to the VDG;Remember that all the charges on an inductor (like the VDG) reside on its surface, therefore “r"stands for the distance from the VDG's surface. The VDG can store charge up toQ = CV (6)where V is the VDG voltage and C is its capacitance. We have not yet covered in class the termcapacitance (discussed in lab 4) however what you need to know for now is that (a) a capacitor is acontraption that "stores" charge and (b) the capacitance is a geometrical property (i.e. depends onthe dimensions of the capacitor). In the VDG's case, it is only dependent on its radius in thatC = 4xe,R (7)where R is the VDG radius. Feel free to think of a bucket storing water as a mechanical analogy. Insection 4 we discussed that dry air cannot sustain electric fields higher than -3-106 V-m-!.Therefore, at its surface, the maximum electric field will also be -3-106 Vm1. This implies that a 40013PH 115-LABORATORY MANUAL, ELECTRIC FIELDS, UAH PHYSICS 2021-2022kV VDG will have a radius of R =EMAXVMAX 4x 1053x 10=-13 cm since the potential is constant insidethe VDG. You should be able to figure out that this value also reflects the maximum spark length thatthis 400 kV VDG can generate. In practice, this length is almost always less than the theoretical sincehumidity does not allow a maximum electric field built-up (Can you think why that is and whatfactors contribute to the humidity around the VDG, especially in a room full of students?). Now it is alsoimportant to know how much charge can the VDG store. If we do not allow the VDG to discharge (nocharge collector in the vicinity) then the maximum charge it can hold will beQMAX = CVMAX = 4x€,RV = 4x€,R²EMAX-This is an interesting relationship and you should easily glean that this is the Gauss' law! Putting inthe numbers we getQUAY = (4)(3.14)(8.85 x 10-12(0.13)(3 x 10°) = 5.6uCIs this dangerous for handling? Well, apparently no, but let's see why that is the case; The maximumenergy storedthe VDG is given byUMAX =QMAXVMAX = 1.2Joules« PreviousNext16DashboardCalendarTo DoNotificationsInbox 8otng[Qs-Lab/Home ·**]Derive an algebraic expression for the charge delivered per unit time as a function of the VDG beltwidth, the pulley radius the revolutions per minute and belt's speed. Caution: If you simply copy asolution from the Internet, this question will get a zero i.e. an explanation that goes with the derivation isnecessary.

Answered: Image /qna-images/answer/21e8aa2e-e0f9-4617-a84b-383a4b477509.jpg

PH115_Lab_E_FILE... Q 2 more mobile that the ions, results in a charge density distribution that looks like an avalanche (the so-called Townsend avalanche, see Fig. 6 lower panel). This implies that during the moment of the discharge the flow of electrons towards the anode have greater linear charge density leading to a more luminous terminal connection. 6.1 VDG calculations At this point we need to go through a few back-of-the-envelope calculations pertinent to the VDG; Remember that all the charges on an inductor (like the VDG) reside on its surface, therefore "r" stands for the distance from the VDG's surface. The VDG can store charge up to Q = CV (6) where V is the VDG voltage and C is its capacitance. We have not yet covered in class the term capacitance (discussed in lab 4) however what you need to know for now is that (a) a capacitor is a contraption that "stores" charge and (b) the capacitance is a geometrical property (i.e. depends on the dimensions of the capacitor). In the VDG's case, it is only dependent on its radius in that C = 4re,R (7) where R is the VDG radius. Feel free to think of a bucket storing water as a mechanical analogy. In section 4 we discussed that dry air cannot sustain electric fields higher than -3-106 V-m, Therefore, at its surface, the maximum electric field will also be -3-106 Vm, This implies that a 400 13 PH 115-LABORATORY MANUAL, ELECTRIC FIELDS, UAH PHYSICS 2021-2022 VMAX 4 x 10 kV VDG will have a radius of R = -13 cm since the potential is constant inside EMAX 3x 10 the VDG. You should be able to figure out that this value also reflects the maximum spark length that this 400 kV VDG can generate. In practice, this length is almost always less than the theoretical since humidity does not allow a maximum electric field built-up (Can you think why that is and what factors contribute to the humidity around the VDG, especially in a room full of students?). Now it is also important to know how much charge can the VDG store. If we do not allow the VDG to discharge (no charge collector in the vicinity) then the maximum charge it can hold will be QMAX = CVMAX = 4xe,RV = 4xc,R²EMAX This is an interesting relationship and you should easily glean that this is the Gauss' law! Putting in the numbers we get QMAX = (4)(3.14)(8.85 x 10-12)(0.13) (3 x 10") = 5.6µC Is this dangerous for handling? Well, apparently no, but let's see why that is the case; The maximum energy stored in the VDG is given by UMAX =OMAX VMAX = 1.2Joules • Previous Next 16 Dashboard Calendar To Do Notifications Inbox