- #1
throneoo
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Homework Statement
Find the equation of motion of a chain of atoms in 1D with alternating magnetic dipoles
At stationary equilibrium the atoms of mass m are separated by d , all displacements are small compared to d
Homework Equations
U=μBx=2μ2(μ0/4π)(1/x^3)
F(x)=-dU/dx
The Attempt at a Solution
The net force on particle n due to the dipole interactions
=F(xn-1-xn)-F(xn-xn+1)
However, I've found that if I fix the positions of the adjacent particles, the net force on particle n is a linear restoring force (with small displacement from eq. position). Can I assume that the atomic chain behaves as though they are connected by springs with identical fixed spring constant k? If so, the resultant equation would be
m*d2(xn)/dt2=-k*(2xn-xn-1-xn+1)