As we described in last week\'s homework, histones are proteins that are positiv

Question

As we described in last week's homework, histones are proteins that are positively charged at physiological pH. Consider two such histones, each of charge +q, located at the locations shown in the figure. Assume that the histones are essentially spherical. Although the histones would actually ex ist in cellular fluid, for now let's just ignore the fluid and treat them as if they are in vacuum. We'll factor in the fluid next week. tq tq (-3d, 0) 3d, 0 (a) Find the electric potential at the location (0, 4d). Express your answer in terms of 4, d, and any necessary constants (b) Now suppose a Cr ion (mass-m, charge =-e) is released from rest at the location (0, 4d). How fast is the ion moving when it reaches the origin? (You may assume that the histones are much more massive than the chloride ion and therefore remain stationary.) Express your answer in terms of q, d, m, and any necessary constants

Explanation / Answer

Given

the potential at (0,4d) due to two charges +q,at (-3d,0) and (+3d,0)

V1 = 2*k*q/r

V1 = 2*k*q/(sqrt(3d)^2+4d^2)

V1 = 2*k*q/5d

adn the potential at origin due to charges is  

V2 = 2*k*q/r

V2 = 2*k*q/(sqrt(3d)^2)

V2 = 2*k*q/3d

the potential difference is  

V2 - V1 = 2*k*q/d(1/3-1/5)

dV = 2*k*q*0.133/d = 0.267*k*q/d

now the cl is of charge q' relleased from rest so initial velocity is zero

the potentail difference = change in kinetic energy /q'

q' = 1.6*10^-19 C

m = 9.1*10^-31 kg

0.267*k*q/d = 0.5*m(v2^2-v1^2)

0.267*k*q/d = 0.5*m(v2^2-0)

0.267*k*q/d = 0.5*m(v2^2)

v2^2 = (0.267*k*q)/(d *2*m)

v2^2 = (0.1335*k*q)/(d*m)

v2 = sqrt((0.1335*k*q)/(d*m))

v2 = sqrt((0.1335*9*10^9)(q/d*m))

v2 = 34662.66 sqrt(q/d*m) m/s

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