Here's my solution to the problem of finding the distance of closest approach for two atoms approaching each other in a Lennard-Jones potential, starting with velocities (+/-) v_0:
They start with energy T0 = (1/2)m(2v02) which is conserved. Thus,
E = T + V = (1/2)m(2v2) + A/r12 - B/r6 = T0...
I've been thinking that the potential outside the cavity (radius R) could be written Vout(r) = B_1.r.cos(theta)+B_2.r^-2.cos(theta), then, and the boundary conditions are that Vout(R)=Vin(R) which implies:
A = B_1 + B_2 R^-2
and that e0E_in,radial(R) = eE_out,radial(R) (where e is the...
Hello,
I'm learning EM from Bleaney & Bleaney and got stuck on Ex2.1 (can do Ex2.2-2.7, though...) - If the polarization charge on the surface of a spherical cavity is -s.cos(theta), prove that the field strength at the centre is s/3e0. If I expand V(r) within the cavity as A.r.cos(theta) +...