b) A magnetic field wave propagating with wave vector, k, and angular frequency, w, may be described by B(r, t) = Boei(k⋅r, wt) By writing B, k and r in terms of their rectangular components, or otherwise, show that OB/at=-i@B, div B=ik B and curl B = ikx B i) Show that the electric field, the magnetic field and the direction of propagation are mutually perpendicular. iii) The Poynting vector S is defined (in free space) to be ii) ¹E Ho What physical property does the Poynting vector represent? S= -ExB
b) A magnetic field wave propagating with wave vector, k, and angular frequency, w, may be described by B(r, t) = Boei(k⋅r, wt) By writing B, k and r in terms of their rectangular components, or otherwise, show that OB/at=-i@B, div B=ik B and curl B = ikx B i) Show that the electric field, the magnetic field and the direction of propagation are mutually perpendicular. iii) The Poynting vector S is defined (in free space) to be ii) ¹E Ho What physical property does the Poynting vector represent? S= -ExB
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Transcribed Image Text:2. a) i) Explain what is meant by the term displacement current.
ii)
By considering Ampere's law and the magnetic field in the vicinity of a
charging capacitor, show that there is a need to introduce the
displacement current.
iii) Show that the displacement current is essential for the derivation of the
propagation of electromagnetic waves by demonstrating that, in free
space, the magnetic field, B, obeys the wave equation.
b) A magnetic field wave propagating with wave vector, k, and angular
frequency, w, may be described by
B(r, t) = Boei(kr- wt)
By writing B, k and r in terms of their rectangular components, or
otherwise, show that
OB/Ot=-i@B, div B=ik B and curl B = ik x B
Show that the electric field, the magnetic field and the direction of
propagation are mutually perpendicular.
iii) The Poynting vector S is defined (in free space) to be
1
i)
ii)
S =
- Ex B
Ho
What physical property does the Poynting vector represent?
c) A magnetic field is given by the expression:
B = (a²xz)+(byz)ŷ +(c³ )î
Determine the relationship between constants a and b.
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