- #1

livio

- 11

- 1

- Homework Statement
- I have an underwater dipole (interpole distance is small, probably 1 cm, but cannot be estimated easily so this can only be an approximated measure) generating an electric field which voltage can be measured at 0 cm and is equal to roughly 5 mV. The reading is referred to a reference electrode placed far away at a distance of 100 cm. I would like to estimate the voltage readings at increasing distances for the values 0, 1, 2, 4, 8, 16, 32, 64,…256 cm. According to a simple decay law |E|∼W(t)/d^3 the magnitude of the electric field read at distance d should decay with the distance cube. So based on this, I have estimed these values

voltage drop (2nd column) over distance (1st column)

2 1

4 0,125

8 0,015625

16 0,001953125

32 0,000244141

64 3,05176E-05

128 3,8147E-06

256 4,76837E-07

with the first column being the distance in cm and the second the voltage in mV. However the starting point is kind of arbitrary and it starts from a reading of 2 mV. I would like to start from 5 mV and make sure I am calculating the decay properly (when does the first drop start and how? if for instance I set the first distance at 1 cm is it fair to expect a 8-fold drop already there?). I guess one way would be to resolve the field equation of the dipole at different distances (0 and 1 cm) but I wonder which equation would be correct to use. Would the following be correct

E(R) = [3(p⋅R^)R−p] / [4πε*R^3]

E should be the electric field at the point individuated by the vector R. p is the dipole moment. R is the distance (or the length of the vector).

- Relevant Equations
- E(R) = [3(p⋅R^)R−p] / [4πε*R^3]

If I resolve the equation in 0, imposing a voltage value of 5 mV, it gives a non real solution, therefore I cannot resolve it for R=1 because I do not know which voltage value to impose. I am sure this is simpler than I am putting it :) thanks for any advice!