Please explain thoroughly. Thanks. 2D.9 Consider two identical molecules with pe

Question

Please explain thoroughly. Thanks.

2D.9 Consider two identical molecules with permanent dipole moments separated by a distance r that is much greater than the effective dipole separation s. Imagine that one of the two dipoles has a fixed orientation with its dipole moment pointing directly toward the other molecule. (a) Argue that the forces that the fixed dipole (the left dipole in the drawing below) exerts on the other will (in the absence of other effects) cause the other to align its dipole moment with that of the first, as shown. (Hint: Model the right dipole as a pair of bound but single particles responding to the left dipole's field.) (b) Use the binomial approximation (1 u) 1 au when u s/r 1 to argue that the net force that each dipole in this configuration exerts on the other is attractive and has the magnitude (E2.29) 4 Treo (Hint: Again, consider one dipole to be a pair of bound particles responding to the other dipole's field.)

Explanation / Answer

a) From the definition of dipole as a charge particle shifted from distance its direction is given by =charge*dipoles separation

If we consider the leeft dipole as a function of ditance r then dipole potential P=.r/4pieEpsilon0r^3

From question r>>s

then electric field E in the dipole =1/4pieEpsilon0(3(.r')r/r^5-/r^3)

using the electric field we can get the interaction between these two dipoles (left and right)

is given by the expression -.E

now for two dipoles the directions are 1 and 2

using interaction expression we get that

interaction I= 1/4pieEpsilon0(1.2/r^3 - 3(1.r) (2.r)/r^3)

now for aligned structure we know that 1.2=^2, and 1.r=r.2=.r that means the expression becomes

I=-1/4pieEpsilon0*2^2/r^3

b) now net force on a dipole F= qE(r)

again we consider (1+u)^a= 1+au

using the same and applying value of E in the force F

we get F=q*1/4pieEpsilon0(3(.r')r/r^5-/r^3)

now for aligning of the pole we get

F= 1/4pieEpsilon03modPe/r^4 where mod pe defines the dipole with direction and function of r

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