Alocalized region of space has a charge density ρ(r). use the general solution of poisson's equation: ρ(r) 4tteo and the expansion of 1/ir -r'| in terms of legendre polynomials p (cos α), tr to calculate the first two terms in multipole expansion for the scalar potential in the region where the charge density is zero. the angle α is the angle between r and r'.you may assume the charge density is azimuthally symmetric about the z- axis. calculate the electric field produced by the first two terms in the multipole expansion. show that the monopole terms for v and e are independent of your choice of origin. follow the argument in sections 3.4.2 - 3.4.4. show that the dipole terms for v and e depend on your choice of origin, except in the case where the total charge in the localized region vanishes

b would be the answer

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: