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[求助]
关于DNA静电势计算的推导，本人生物物理新学者，求助啊
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To model DNA, we assume the charge per unit length is λ, which is about one negative charge per 1.7Åof length. For simplicity,we assume that DNA is a long, charged, cylindrical molecule. The cylinder diameteris about 20 Å. The electrical field of a long strand of DNA in water depends on the perpendicular distance r from the strand and on λ.The electric field lines must point inward because DNA is negatively charged.Denoting the electric field at a distance r from the cylinder by E(r), we observe that it is inversely proportional to the dielectric constant and inversely proportional to some power, say rα, of r, hence we write: E(r) = const k*λ/ε*rα (2.27) In vacuum, the electric field of a monopole of charge Q a distance R away is kQ/R2. Since λ is a charge per unit length, α = 1, hence: E(r) = 2 k*λ/ε*r (2.28) Since E(r) = −dV/dr, we have an equivalent form of Equation (2.28). dV (r)/dr= −2k*λ/ε*r (2.29) Integrating Equation (2.29), we see that: V (r) = −2k*λ*ln r/ε + k0 (2.30) In Equation (2.30), k0 is a constant conveniently chosen to be zero. Suppose a positive monovalent ion moves in from a distance of 1μm to the surface of the DNA. The work done or W will be: W = |e |V (r = 1μm) − |e|V (r = 10Å  (2.31)Hence: W = 10 · 2 · 10−20J (2.32) Using k = 8.99 × 109 m2/C2, = 80.4, λ = −|e| per 1.7 × 10−10m, and e = 1.6 × 10−19C from Equation (2.32) 我想请教下2。27中的那个rα是什么啊，这个是如何在推导的？ |
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