Consider the following model for the electrostatic stretching of DNA. A spring with spring constant kDNA = 250 pN/m is tethered to an immobile surface on one end and a charge of qDNA = −350e on the other. A uniform electric field of magnitude |E| = 2.5 N/C is applied pointing perpendicular to the surface.

Question

a) How far does the spring stretch in response to the field?

b) Now an transcription factor (TF), with charge qRNA = +15e, is introduced at the location specified in the figure. Calculate the electric field due to the TF at the location of the DNA. Remember, biophysics experiments are done in water, which has a dielectric constant K = 80. (hint: the TF is very far from both the DNA and the surface, so you can ignore the string stretching distance in this calculation)

c) What is the angle θ that the spring makes with the x-axis in the presence of both the TF and the external field?

I would love any help with this question, as I do not really know where to start.