Consider a dipole source made of a proton and an electron separated by 1.0 nm (10-9 m). Find the exact potential (by summing kq/r) at the following locations, check the sign of your answer, and compare to the dipole approximation (equation 22.6 in the text.) You may need to keep an unusual number of digits in intermediary calculations to find the non-zero value of the voltage. I am NOT looking for zero for any of the answers UNLESS the answer is exactly zero! Be careful in the dipole calculation of part e to find the cosine of the angle of r as measured from the MIDPOINT between the sources! And remember it is often simpler to use ratios of sides in a triangle for trig functions than to calculate an angle and then the cosine. (a) 1 nm from the proton, on axis * test point (b) 3 mm from the electron, on axis * test point (not to scale) (c) 1 nm above center, on perpendicular bisector * test point (d) 3 mm above center, on perpendicular bisector (e) 5 nm above the electron (diagram distances NOT to scale!) * test point e p

Consider a dipole source made of a proton and an electron separated by 1.0 nm (10-9 m). Find the exact potential (by summing kq/r) at the following locations, check the sign of your answer, and compare to the dipole approximation (equation 22.6 in the text.) You may need to keep an unusual number of digits in intermediary calculations to find the non-zero value of the voltage. I am NOT looking for zero for any of the answers UNLESS the answer is exactly zero! Be careful in the dipole calculation of part e to find the cosine of the angle of r as measured from the MIDPOINT between the sources! And remember it is often simpler to use ratios of sides in a triangle for trig functions than to calculate an angle and then the cosine. (a) 1 nm from the proton, on axis * test point (b) 3 mm from the electron, on axis * test point (not to scale) (c) 1 nm above center, on perpendicular bisector * test point (d) 3 mm above center, on perpendicular bisector (e) 5 nm above the electron (diagram distances NOT to scale!) * test point e p