Question

A molecule of DNA (deoxyribonucleic acid) is 2.18 μm long. The ends of the molecule become singly ionized: negative on one end, positive on the other. The helical molecule acts like a spring and compresses 1.06% upon becoming charged. Determine the effective spring constant of the molecule.

______N/m

Two small identical conducting spheres are placed with their centers 0.59 m apart. One is given a charge of 12 ✕ 10−9 C, the other a charge of −17 ✕ 10−9 C.
(a) Find the electrostatic force exerted on one sphere by the other.
magnitude_____ N

(b) The spheres are connected by a conducting wire. Find the electrostatic force between the two after equilibrium is reached, where both spheres have the same charge.
magnitude _____N

Rocket observations show that dust particles in Earth's upper atmosphere are often electrically charged.
(a)
Find the distance separating two dust particles (in m) if each has a charge of +e and the Coulomb force between them has magnitude 1.70 ✕ 10−14 N.
______ m
(b)
Calculate the mass (in kg) of one of the dust particles if this Coulomb force would accelerate it at 3.60 ✕ 108 m/s2. (In the upper atmosphere, effects from other nearby charges typically result in a small net force and acceleration.)

_______kg

Answer 1

1)Given,

L = 2.18 x 10^-6 m ; x = 1.06% of L

We know that

F = k q1q2/r^2

q1 = q2 = e = 1.6 x 10^-19 C

F = 9 x 10^9 x (1.6 x 10^-19)^2/(2.19 x 10^-6)^2 = 4.8 x 10^-17 N

Also, F = kx => k = F/x

k = 4.8 x 10^-17/(0.0106 x 2.18 x 10^-6) = 2.08 x 10^-9 N/m

Hence, k = 2.08 x 10^-9 N/m

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