Consider the electric dipole that you analyzed in problem set 4. It has charges - and q located on the z axis at -d and

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Consider The Electric Dipole That You Analyzed In Problem Set 4 It Has Charges And Q Located On The Z Axis At D And 1 (133.69 KiB) Viewed 44 times

Consider the electric dipole that you analyzed in problem set 4. It has charges - and q located on the z axis at -d and +d, respectively. a. What symmetries does the dipole exhibit? = b. Show that with the usual choice of the zero for the potential, that $(x, y,0) = 0. i.e. that the electric potential is zero on the x - y plane. c. Explain your result from part b using Ap=-SĒ. dĩ and the properties of the electric field. d. Write an exact expression for the electric potential in cylindrical coordinates – i.e. calculate o(r1 ,z). e. Using excel, Mathematica, Wolfram alpha, or whatever mechanism you see fit, plot your result from part d along the z axis. I suggest adding a small constant to the distance factors to regulate the infinities that will occur at z = £d. It is best to actually plot as a function of z/d. f. Applying the same long-distance limit used in problem 2 of problem set 4, show that the electric potential to leading power in d/r is 2zd 2d cos e p3 p2 where r is the usual 3-D distance from the origin and os the angle between r and the z axis. g. Show that if you take the gradient of the first expression for p in the above – expressed in cylindrical coordinates – that you obtain the dipole field you calculated in problem set 4.