Three spin-1/2 particles are fixed in position on the vertices of an equilateral triangle. the interaction amongst themselves and with a uniform external magnetic field, b, is described by the hamiltonian where s, i 1,3, are spin operators, and a is a constant (in units of energy/12). (a) obtain the eigenvalues and eigenvectors of h (b) discuss the degeneracies of the spectrum when b-0. (c) discuss the nature of the ground state when a 0 and when a < 0, still for b 0. (d) discuss the effect the magnetic field causes to the degeneracies when it is switched on.

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation:

i am pretty sure it is c because when people are closer together, they cannot move as freely. picture being in a mostly full elevator, for instance. the people are right next to you, and you can barely move.