University:
Amherst College
Course:
PHYS 124 | The Maxwellian Synthesis: Dynamics of Charges and Fields
Academic year:

2022
Views:

425

Pages:

11
Author:

Dashawn Mays

Faraday’s and Maxwell-Ampere Laws • A changing magnetic flux produces a curly electric field:    d  Edl   Bnˆ dA dt  • A changing electric flux produces a (curly) magnetic field:    d    Bdl 0  I encl   0 Enˆ dA  dt    A moving “slab” of E and B fields • Thin region in which there are uniform electric and magnetic fields. – – – – No charges or currents in the vicinity of the slab. Outside the slab, both fields are zero. Inside the slab, E and B are perpendicular to each other. Slab moves in a direction perpendicular to both fields. E E B v v E B front view v B top view Does Slab obey Faraday’s Law? E E B v v B front view    d  Edl   Bnˆ dA dt  Does Slab obey Maxwell-Ampere Law? top view E B v E v B    d    Bdl 0  I encl   0 Enˆ dA  dt    Constraints imposed by Faraday’s and Maxwell-Ampere Laws E  Bv B  0 0 Ev c  0  8.85 10 12 C2 Nm2 0  4 10 c  3.00  108 m s 7 Ns 2 C2 1  0 0 Properties of EM Waves • • • • 1 Move at the speed of light (in vacuum): c   0 0 Magnitudes of fields related by E  Bc.   E and B are perpendicular to each other.   Wave moves in direction of E  B , i.e. perpendicular to both fields. E B v Dipole Antenna • To create electromagnetic waves, charges must be accelerating. • Recall that in the steady state, the fields are constant. Figure 31.6b t=0 Later time Figure 31.7 Plane waves • Far from the antenna, the EM waves are well described as plane waves – the fields are uniform within planes perpendicular to the direction of propagation. • Sinusoidal waves – fields are sinusoidal functions of position and time. – E.g. wave moving along x axis:  2 x 2 t ˆ E  E0 sin(  ) j  E0 sin(kx  t )ˆj  T  2 x 2 t ˆ B  B0 sin(  )k  B0 sin(kx  t )kˆ  T Figure 31.9  2 x 2 t ˆ E  E0 sin(  ) j  E0 sin(kx  t )ˆj  T  2 x 2 t ˆ B  B0 sin(  )k  B0 sin(kx  t )kˆ  T c  T f Energy density in EM Waves Electric Field Energy density uE  12  0 E 2 Magnetic Field Energy density uB  1 2 B2 0 E  Bc c 1  0 0 Half of the energy in an EM wave is in the electric field and half is in the magnetic field.

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