Could you please solve it in detail with cleat hand writing? Thanks!

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Could you please solve it in detail with cleat hand writing?Thanks!

Could You Please Solve It In Detail With Cleat Hand Writing Thanks 1 (64.54 KiB) Viewed 11 times

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1 A Strange Dipole Consider the distribution of charges pictured below. In this problem we will calculate the electric field of this distribution on the positive z-axis and approximate its behavior far from the origin. +21+3.5/2 -435/2 (a) Calculate [10pts] Use superposition to find an exact expression for the electric field at an arbitrary point on the z-axis with z > ₂. (b) Simplify [5pts] Pull out a factor from your expression from (a). Your answer should now look like: E-k(...) There should be three terms in the parenthesis.
(c) Approximate [10pts] We will now approximate our answer in the limit that z>> or equivalently<< 1. Consider the binomial approximation, that for x << 1: 1 (1+x) n Apply this approximation to your answer from (b) and simplify. ≈(1- - nx) (d) Unit Check [5pts] Make sense of your answer by checking that the units are correct. (e) Dipole Moment [5pts] In class we found that the electric field (on the z-axis) of a dipole has the form: Ē = 2kp 23³ What would you need to plug in for the dipole moment, p, to get this to match your answer from (c)? (f) Dipole Calculation [5pts] In general, the dipole moment of a distribution of point charges can be calculated as: P = [Q₁³₁ Calculate the dipole moment of this charge distribution and make sure it matches your answer from (e).