phys documents (dragged) 8

# phys documents (dragged) 8 - Chapter 2 Electricity&...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Chapter 2: Electricity & Magnetism 11 2.5.2 Electromagnetic waves in matter The wave equations in matter, with c mat = ()-1/2 the lightspeed in matter, are: 2 - 2 - t2 t E =0, 2 - 2 - t2 t B=0 give, after substitution of monochromatic plane waves: E = E exp(i(k r -t)) and B = B exp(i(k r -t)) the dispersion relation: i k 2 = 2 + The first term arises from the displacement current, the second from the conductance current. If k is written in the form k := k + ik it follows that: k = 1 2 1+ 1+ 1 and k = ()2 1 2 -1 + 1+ 1 ()2 This results in a damped wave: E = E exp(-k n r ) exp(i(k n r - t)). If the material is a good conductor, . the wave vanishes after approximately one wavelength, k = (1 + i) 2 2.6 Multipoles Because 1 1 = |r - r | r 0 r r l Pl (cos ) the potential can be written as: V = Q 4 n kn rn For the lowest-order terms this results in: Monopole: l = 0, k 0 = Dipole: l = 1, k1 = Quadrupole: l = 2, k 2 = dV r cos()dV 1 2 i 2 2 (3zi - ri ) 1. The electric dipole: dipole moment: p = Qle, where e goes from to , and F = (p W = -p Eout . 3p r Q Electric field: E - p . The torque is: = p Eout 4r3 r2 2. The magnetic dipole: dipole moment: if r A: = I (Ae ), F = ( )Bout 2 mv , W = - Bout || = 2B - 3 r Magnetic field: B = - . The moment is: = Bout 4r3 r2 )Eext , and 2.7 Electric currents The continuity equation for charge is: + t I= J = 0. The electric current is given by: dQ = dt (J n )d2 A For most conductors holds: J = E/, where is the resistivity. ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online