A 2.6 mm-diameter sphere is charged to -4.6 nC . An electron fired directly at the sphere?
from far away comes to within 0.39 mm of the surface of the target before being reflected. a) What was the electron's initial speed? b) At what distance from the surface of the sphere is the electron's speed half of its initial value? c) What is the acceleration of the electron at its turning point? Thank youSee Answer 10 Add Answers
electron's initial kinetic energy = electron's electric potential energy before being reflected
mv^2/2 = (q)(e)/[(4πεo)(b)]
(9.11e-31 kg)(v^2)/2 = (-4.6e-9 C)(-1.602e-19 C)/[(4π)(8.85e-12 C^2/N-m^2)(2.6e-3 / 2 + 3.9e-4 m)]
v = 9.3e7 m/s
electron's initial kinetic energy = (kinetic energy of electron) + (electric potential energy of electron)
mv^2/2 = m(v/2)^2/2 + (q)(e)/[(4πεo)(r)]
3mv^2/8 = (q)(e)/[(4πεo)(r)]
3(9.11e-31 kg)(9.3e7 m/s)^2 / 8 = (-4.6e-9 C)(-1.602e-19 C)/[(4π)(8.85e-12 C^2/N-m^2)(2.6e-3 / 2 m + x)]
x = 9.5e-4 m = 0.95 mm
ma = (q)(e)/[(4πεo)(b)^2]
(9.11e-31 kg)(a) = (-4.6e-9 C)(-1.602e-19 C)/[(4π)(8.85e-12 C^2/N-m^2)(2.6e-3 / 2 + 3.9e-4 m)^2]
a = 2.5e18 m/s^2
the sector can't be a nil dimensional factor by using fact it violates situation variety 4 and a million. a nil dimensional factor has no length, no width, and no intensity, it does not occupy area subsequently it could no longer occupy the two time or area. additionally, if this is 0 dimensional then this violates the mathematical ratio of the sector, that's ?. everywhere on the sector, the ratio of the circumference to the diameter is ? that's impossible for a nil dimensional factor, subsequently this removes this posit as an evidence. to confirm that the sector to be thoroughly flat we nevertheless can no longer violate this mathematical relation while you evaluate that's often around. the only way for the sector to be around and flat is that if an merchandise can trip to the left facet and finally end up on the superb facet, variety of like interior the recreation "asteroids" the place the deliver travels alongside a 2 dimensional airplane, yet in no way falls off while you evaluate that's a 2 dimensional sphere (nicely, the exterior is) and on a sphere you may pass in one direction and finally end up on the comparable factor. that's the only way wherein a sphere could be "flat" at any length different than 0 is that if the facets are by some ability linked via one greater length, yet given the situations one might degree a curvature to the exterior. So, relative to an outdoors observer the exterior might seem to be flat, yet for every person on the exterior, they might degree a curvature. This sphere is hypothetically existent interior the universe and there is no longer something interior the regulations of physics that denies greater effective dimensions or greater dimensional passage techniques which includes wormholes that ought to advantage a 2 dimensional airplane the characteristics of a sphere. Very exciting question via the way, this is probable the 1st question on right here that made me think of this lots. 10 trillion cases greater valuable than the "2012" questions approximately right here. is this superb?