Electric Field Homework Question

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SUMMARY

The discussion centers on calculating the effective spring constant of a DNA molecule that becomes charged, resulting in a compression of 0.6%. The DNA molecule measures 1.061 micrometers in length, and the Coulomb constant is specified as 8.99 x 10^9 N*m^2/C^2. To find the spring constant (k), one must equate the Coulomb force, which causes the DNA to shrink, with the spring-like force of the DNA at equilibrium. This leads to a definitive equation for k based on the compressed length of the molecule.

PREREQUISITES
  • Understanding of Coulomb's Law and electric forces
  • Basic knowledge of spring mechanics and Hooke's Law
  • Familiarity with the concept of equilibrium in physics
  • Ability to perform calculations involving micrometers and N/m units
NEXT STEPS
  • Calculate the Coulomb force using the given parameters
  • Apply Hooke's Law to derive the spring constant k
  • Explore the relationship between electric charge and molecular structure
  • Investigate the implications of molecular elasticity in biological systems
USEFUL FOR

This discussion is beneficial for physics students, molecular biologists, and researchers interested in the mechanical properties of biomolecules, particularly DNA under electric fields.

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I am having difficulty with this homework question. I am not even sure whether to start.

Question:

A molecule of DNA lies along a straight line. It is 1.061 micrometers long. The ends of the molecule become singly ionized; negative on one end, positive on the other. The helical molecule acts as a spring and compresses 0.6% upon becoming charged. The Coulomb constant is 8.99 x 10^9 N*m^2/C^2.

Determine the effective spring constant of the molecule. Take into account the compressed length when calculating the distance between the ends of the molecule. Answer in units of N/m.

Any help would be appreciateid.
 
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Coulomb force make the dna to shrink. Spring like force of the DNA acts opposite to the coulomb force. At the equilibrium point these forces are equal. Use this idea to find an equation and solve for k, the spring constant.
 

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