(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

an electron (charge -e) is at the origin, and a particle of charge +5e is at x = 17nm, find a point (x = ...nm) where the electric field is zero.

2. Relevant equations

e = 1.6*10^-19 coulombs

electric field E = kq/r^2 where k=9*10^9, q is charge, r is distance

3. The attempt at a solution

kq_1/r^2 = kq_2/(17-r)^2

k(-e)/r^2 = k(+5e)/(17-r)^2

k(-e)(17-r)^2 = k(+5e)(r^2)

k(-e)(28 - 34r + r^2) = k(+5e)(r^2)

(9*10^9)(-1.6*10^-19)(28 -34r + r^2) = (9*10^-9)(8*10^-19)(r^2)

-1.4*10^-9[28 - 34r -r^2] = (9*10^-9)(8*10^-19)(r^2)

(-4.032*10^-8) + (4.896*10^-8)r - (1.6*10^-19)r^2 = (7.2*10^-9)r^2

(-4.032*10^-8) + (4.896*10^-8)r - (7.2*10^-9)r^2 = 0

quadratic formula

r = [-4.032*10^-8 +/- sqrt[(4.896*10^-8)^2 - (4)(-7.2*10^-9)(-4.032*10^-8)] ] / (2)(-7.2*10^-9)

r = [-4.89*10^-8 +/- sqrt(1.237*10^-15)] / -1.44*10^-8

r = 0.957nm or 5.83 nm

are my calculations correct? which one is the correct answer?

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# Homework Help: Where electric field is zero

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