AdvEMpset2.pdf - September 1 2017 Cornell University...

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September 1, 2017 Cornell University, Department of Physics PHYS 3327, Advance E&M, HW # 2, due: 9/6/2017, 11:15 AM Question 1 : The dipole Consider a system as discussed in class and shown in Fig. 2.1 in Heald & Marion. 1. Write down the exact potential and expand it in the appropriate small parameter to obtain the result we showed in class, which is that to leading order Φ( r ) = 2 q‘ cos θ r 2 (1) 2. Derive the electric field from Eq. (1). Show that E φ = 0 and write E r and E θ explicity. 3. Argue that the result E φ = 0 is exact and is not a result of the dipole approximation. 4. Find specific values of θ where you can argue that the result of E r or of E θ are exact. You should not need to do any complicated calculations involving the exact potential. Instead, use general physical arguments. 5. Explain why the relative correction to E r due to higher order terms that we neglected scales like ( ‘/r ) 2 , rather than like ( ‘/r ) as we might naively expect. As an example, while the lowest order term contains ( ‘/r ), the next lowest order term contains ( ‘/r ) 3 rather than ( ‘/r ) 2 . 6. We now move the origin a bit, that is O new = O old + a , so that there are only small corrections to the results we have obtained so far. Please define, in words, what “a bit” means. (It might help to answer the next part of the question first.)
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