Question

2. Dipole-dipole force The charge distribution where two equal but opposite charges are separated by a fixed distance ? is called a dipole and is very common and important in nature. Consider two dipoles, each consisting of charges ±q separated by a distance ?. The axes of two dipoles are parallel and their midpoints are separated by a distance r. One is inverted compared to the other. See the figure. (a) Calculate the force exerted on each dipole by the other. (b) Find an approximate expression for the force that each dipole exerts on the other if r ? ?. The magnitude of the force should be in the form F ? Cr?. Note that n is not necessarily an integer. C is some combination of given quantities and numerical factors that you will have to find. The answer is not zero, but should approach zero as r ? ? (why?). Hint: When |?| ? 1, the two largest terms in the Taylor expansion of (1 + ?)? are (1 + ?)? ? 1 + k? 3. Electric field due to two dipoles Consider the same two dipoles from the previous problem to be fixed in place. This question asks about the electric field at various points in space due to all four charges. (a) What is the electric field at the center of the two dipoles? (b) What is the electric field at the midpoint of the dipole on the left? Don't assume r ? ?.

          2. Dipole-dipole force
The charge distribution where two equal but opposite charges are separated by a fixed distance ? is called a dipole and is very common and important in nature.
Consider two dipoles, each consisting of charges ±q separated by a distance ?. The axes of two dipoles are parallel and their midpoints are separated by a distance r. One is inverted compared to the other. See the figure.
(a) Calculate the force exerted on each dipole by the other.
(b) Find an approximate expression for the force that each dipole exerts on the other if r ? ?. The magnitude of the force should be in the form F ? Cr?.
Note that n is not necessarily an integer. C is some combination of given quantities and numerical factors that you will have to find. The answer is not zero, but should approach zero as r ? ? (why?).
Hint: When |?| ? 1, the two largest terms in the Taylor expansion of (1 + ?)? are
(1 + ?)? ? 1 + k?
3. Electric field due to two dipoles
Consider the same two dipoles from the previous problem to be fixed in place. This question asks about the electric field at various points in space due to all four charges.
(a) What is the electric field at the center of the two dipoles?
(b) What is the electric field at the midpoint of the dipole on the left? Don't assume r ? ?.

2. Dipole-dipole force
The charge distribution where two equal but opposite charges are separated by a fixed distance ? is called a dipole and is very common and important in nature.
Consider two dipoles, each consisting of charges ±q separated by a distance ?. The axes of two dipoles are parallel and their midpoints are separated by a distance r. One is inverted compared to the other. See the figure.
(a) Calculate the force exerted on each dipole by the other.
(b) Find an approximate expression for the force that each dipole exerts on the other if r ? ?. The magnitude of the force should be in the form F ? Cr?.
Note that n is not necessarily an integer. C is some combination of given quantities and numerical factors that you will have to find. The answer is not zero, but should approach zero as r ? ? (why?).
Hint: When |?| ? 1, the two largest terms in the Taylor expansion of (1 + ?)? are
(1 + ?)? ? 1 + k?
3. Electric field due to two dipoles
Consider the same two dipoles from the previous problem to be fixed in place. This question asks about the electric field at various points in space due to all four charges.
(a) What is the electric field at the center of the two dipoles?
(b) What is the electric field at the midpoint of the dipole on the left? Don't assume r ? ?.

Added by Katherine P.

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