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2. Dipole (continued) Consider an electric dipole with charge +q located at x = -D, and charge -q located at x = +D. a. Compute the electric field E(0, y, 0) for points on the y-axis. Justify the direction (sign) of your answer by sketching the field lines of the dipole. b. Examine the limiting case where the dipole is very far away from our point of interest (i.e. y>>D) by writing your answer in terms of a simple formula times a power series in the small quantity D²/y² (keeping terms through 2nd order). c. In a series expansion, higher order terms are often referred to as "corrections." As an example, say E \propto 1+3x². Then, if 3x²=0.05, we would say that the correction is 5% and that the approximation of E is "good" (small correction). What are the first and second order corrections to your approximation of E if D is 10% of y? If D is 50% of y? Would you say the approximation is good or bad in each case? d. Why doesn't E behave like that of a point charge in the limiting case of large y for this situation?

          2. Dipole (continued)
Consider an electric dipole with charge +q located at x = -D, and charge -q located at x = +D.
a. Compute the electric field E(0, y, 0) for points on the y-axis. Justify the direction (sign) of
your answer by sketching the field lines of the dipole.
b. Examine the limiting case where the dipole is very far away from our point of interest (i.e.
y>>D) by writing your answer in terms of a simple formula times a power series in the small
quantity D²/y² (keeping terms through 2nd order).
c. In a series expansion, higher order terms are often referred to as "corrections." As an
example, say E \propto 1+3x². Then, if 3x²=0.05, we would say that the correction is 5% and that
the approximation of E is "good" (small correction). What are the first and second order
corrections to your approximation of E if D is 10% of y? If D is 50% of y? Would you say the
approximation is good or bad in each case?
d. Why doesn't E behave like that of a point charge in the limiting case of large y for this
situation?

2. Dipole (continued)
Consider an electric dipole with charge +q located at x = -D, and charge -q located at x = +D.
a. Compute the electric field E(0, y, 0) for points on the y-axis. Justify the direction (sign) of
your answer by sketching the field lines of the dipole.
b. Examine the limiting case where the dipole is very far away from our point of interest (i.e.
y>>D) by writing your answer in terms of a simple formula times a power series in the small
quantity D²/y² (keeping terms through 2nd order).
c. In a series expansion, higher order terms are often referred to as "corrections." As an
example, say E ∝1+3x². Then, if 3x²=0.05, we would say that the correction is 5% and that
the approximation of E is "good" (small correction). What are the first and second order
corrections to your approximation of E if D is 10% of y? If D is 50% of y? Would you say the
approximation is good or bad in each case?
d. Why doesn't E behave like that of a point charge in the limiting case of large y for this
situation?

Added by Terri M.

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