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repository:charged_particles [2021/02/02 23:06] porcaro1 created |
repository:charged_particles [2021/02/02 23:25] porcaro1 [Answer Key] |
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===Prior Knowledge Required=== | ===Prior Knowledge Required=== | ||
*Coulomb's law | *Coulomb's law | ||
- | *$F=k\dfrac{q_1*q_2}{r^2}$ | + | *$F=k\dfrac{q_1q_2}{r^2}$ |
*Vector mathematics | *Vector mathematics | ||
*Principle of superposition | *Principle of superposition | ||
Line 32: | Line 32: | ||
===Code=== | ===Code=== | ||
<code Python [enable_line_numbers="true"]> | <code Python [enable_line_numbers="true"]> | ||
+ | GlowScript 2.7 VPython | ||
+ | #Created by Meagan Brasseur, Sofia Villanueva, and John Plough on August 9,2019 | ||
+ | #Debugged by Dan Weller August 17,2019 | ||
+ | #Code is still INCOMPLETE | ||
+ | |||
+ | ##Objects## | ||
+ | Charge1 = sphere(pos=vec(0,0,0), radius=0.1, color=color.cyan) | ||
+ | Charge2 = sphere(pos=vec(5,0,0), radius=0.1, color=color.cyan) | ||
+ | Tcharge = sphere(pos=vec(2.5,2.5,0), radius=0.05, color=color.red) | ||
+ | |||
+ | #Coulombic charges of our spheres | ||
+ | |||
+ | q1 = 6.0*10**(-19) | ||
+ | q2 = 6.0*10**(-19) | ||
+ | qt = -1.6*10**(-19) | ||
+ | |||
+ | ##Constants## | ||
+ | k = 9*10**9 | ||
+ | mTest = 9.11*10**(-31) | ||
+ | vTest = vec(0,0,0) | ||
+ | |||
+ | ## Create graphs to track force | ||
+ | Grph1 = graph(title='Force (1) v Distance', xtitle='Distance (m)', ytitle='Force (N)', fast=False, ymin=-1.4E-28, ymax=-1.3E-28) #initialize our graphs. | ||
+ | F1Graph = gcurve(color=color.green, label='Force of Charge 1 on Test Charge') #Make a graph for the force on the test charge with respect to distance from Charge1. | ||
+ | |||
+ | Grph1 = graph(title='Force (2) v Distance', xtitle='Distance (m)', ytitle='Force (N)', fast=False, ymin=1.4E-28, ymax=1.3E-28) #initialize our graphs. | ||
+ | F2Graph = gcurve(color=color.green, label='Force of Charge 2 on Test Charge') #Make a graph for the force on the test charge with respect to distance from Charge2. | ||
+ | |||
+ | #Set up time variables for while loop | ||
+ | t=0 | ||
+ | dt=1*10**(-4) | ||
+ | tf=1 | ||
+ | |||
+ | #While loop to iterate over the time interval | ||
+ | |||
+ | while t < tf: | ||
+ | rate(100) | ||
+ | # Defines the rate at which the program runs # | ||
+ | |||
+ | ##Hint: For the following calculations, break them up into components!## | ||
+ | |||
+ | #Come up with an equation for the force on your test charge from Charge 1 | ||
+ | |||
+ | F1tx = | ||
+ | | ||
+ | if Tcharge.pos.x <= Charge1.pos.x : | ||
+ | F1tx = | ||
+ | | ||
+ | F1ty = | ||
+ | | ||
+ | if Tcharge.pos.y <= Charge1.pos.y : | ||
+ | F1ty = | ||
+ | | ||
+ | F1tz = | ||
+ | | ||
+ | if Tcharge.pos.z <= Charge1.pos.z : | ||
+ | F1tz = | ||
+ | | ||
+ | F1t = vec(F1tx,F1ty,F1tz) | ||
+ | | ||
+ | # print("F1t = ", mag(F1t)) | ||
+ | |||
+ | ##Come up with an equation for the force on your test charge from Charge 2 | ||
+ | |||
+ | F2tx = | ||
+ | | ||
+ | if Tcharge.pos.x <= Charge2.pos.x : | ||
+ | F2tx = | ||
+ | | ||
+ | F2ty = | ||
+ | | ||
+ | Tcharge.pos.y <= Charge2.pos.y : | ||
+ | F2ty = | ||
+ | | ||
+ | F2tz = | ||
+ | | ||
+ | Tcharge.pos.z <= Charge2.pos.z : | ||
+ | F2tz = | ||
+ | | ||
+ | F2t = vec(F2tx,F2ty,F2tz) | ||
+ | # | ||
+ | ##Come up with an equation for the net force on your test charge from both charges | ||
+ | # | ||
+ | Fnetx = | ||
+ | Fnety = | ||
+ | Fnetz = | ||
+ | |||
+ | Fnet = | ||
+ | |||
+ | #Come up with an equation for the net acceleration of your test charge from both charges | ||
+ | |||
+ | at = | ||
+ | |||
+ | at = | ||
+ | |||
+ | #Update the position of the test charge using the equation you came up with for acceleration. | ||
+ | |||
+ | vTest = vTest + at*dt | ||
+ | |||
+ | Tcharge.pos = Tcharge.pos + vTest*dt | ||
+ | |||
+ | |||
+ | #Graph the Net Force on the Test charge with regards to position. | ||
+ | |||
+ | F1Graph.plot(mag(Tcharge.pos),mag(F1t)) | ||
+ | F2Graph.plot(mag(Tcharge.pos),mag(F2t)) | ||
+ | |||
+ | t = t + dt | ||
+ | |||
</code> | </code> | ||
---- | ---- | ||
====Answer Key==== | ====Answer Key==== | ||
===Handout=== | ===Handout=== | ||
+ | - Charge 1 is at the origin (0,0,0), Charge 2 is at (5,0,0), and the Test Charge is at (2.5,2.5,0) | ||
+ | - Charge 1 and Charge 2 are both $6.0*10^{-19}$ C, and the Test Charge is $-1.6*10^{-19}$ C. | ||
+ | - Because Charge 1 is positive and the the Test Charge is negative, the force will be attractive. | ||
+ | - See previous | ||
+ | - The Test Charge is located exactly halfway between Charge 1 and Charge 2 and slightly above both. Because the sign and magnitude of Charge 1 and Charge 2 are the same, the force they exert on the test particle will also be the same. | ||
+ | |||
===Code=== | ===Code=== | ||
<code Python [enable_line_numbers="true", highlight_lines_extra=""]> | <code Python [enable_line_numbers="true", highlight_lines_extra=""]> | ||
GlowScript 2.7 VPython | GlowScript 2.7 VPython | ||
#Created by Meagan Brasseur, Sofia Villanueva, and John Plough on August 9,2019 | #Created by Meagan Brasseur, Sofia Villanueva, and John Plough on August 9,2019 | ||
- | #Debugged by Dan Weller August 17,2019 | ||
- | #Code is still INCOMPLETE | ||
##Objects## | ##Objects## |