MTW Ch7: Choosing Lagrangian for Scalar Potential

TerryW
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I have managed to get to the end of Chapter 6 and have done almost all of the exercises (I didn't get anywhere with exercise 5.6 (d) and have seen the Cesarth/TSny exchange and still don't feel I have a satisfactory solution...) but I have hit a bit of a wall with Exercise 7.1 (a).First question is 'Why choose eφ instead of just φ in the integral for I ?'Next question 'Can anyone give me a hint as to how I should be approaching this?'
I've attached my manuscript working which achieves a result of 0 = 0 (well at least it is consistent) but no differential equations.
Regards
TerryW
 

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