Individual electrons or nuclei consisting of 13 protons and 13 neutrons go throu
ID: 1585909 • Letter: I
Question
Individual electrons or nuclei consisting of 13 protons and 13 neutrons go through a capacitor then a uniform magnetic field. Proton mass is 1.673E-27kg with a charge of 1.6022E-19C, neutrons mass is 1.675E-27kg, and electron mass is 9.11E-31kg. Capacitor plates are squares with sides that are 3m long, the charge on one plate is 3C, and the plates are 0.1m apart. After the capacitor is a 3.14159T magnetic field oriented perpendicular to particle motion. The permittivity of free space is 8.85418782E(-12) F/m and the permeability of free space is 1.25663706E(-6) Tm/A.
What is the E-field inside the accelerator? [N/C]
What is the potential difference (voltage) between the plates of the accelerator? [V]
If the nucleus made of protons and neutrons is placed in the center of the accelerator, what will its acceleration be? [m/s^2]
If the nucleus is allowed to accelerate from rest through the entire accelerator, what will its final velocity be? [m/s]
How far would an electron have to be accelerated by a field of the same strength to have the same amount of velocity as a nucleus accelerated through the entire accelerator? [m]
A gaussian surface is the shape of a square box with sides that are half the length of the side of a plate. The gaussian surface is cut exactly in half by the positive plate so two sides of the gaussian surface are parallel to the surface of the plate and four are perpendicular. What is the flux through this gaussian surface? [Nm^2/C]
Explanation / Answer
a) Capacitnace of the capacitor, C = A*epsilon/d
= 9*8.854*10^-12/0.1
= 7.97*10^-10 F
b) E = Q/(A*epsilon)
= 3/(9*8.854*10^-12)
= 3.76*10^10 N/C
c) delta_V = E/d
= 3.76*10^10/0.1
= 3.76*10^11 V
d) a = F/m
= q*E/m
= 13*1.6*10^-19*3.76*10^10/(26*1.67*10^-27)
= 1.801*10^18 m/s^2