Question

Write down the equations for the real electric and magnetic fields for a monochromatic plane wave of amplitude E(subscript 0), frequency omega, and phase angle phi=0,that is travelling in the direction from the origin to the point (1,1,1), with polarisation parallel to the xz plane.

Answer 1

The general equation of electric field of a Plane wave is given by

E(r,t)=Eo(r,t)(e^{i(K.r-ωt+φ)}) (here i signifies √-1 )

r denotes position vector

B(r,t) = (K x E)/ω ( x denotes vector cross product)

where K is the wave vector of propagation.

vector along the propagation direction form (0,0,0) to (1,1,1)
K =(k/√3 )(x^+y^{^}+z^{^} )

Polarised along the KZ plane means the electric field oscillates in the KZ plane

∴ E(r,t)= (E_oxx^{^}+E_ozz^)e^i(K.r-ωt)

(E_ox)²+(E_oy)²= E_o²

K.r =( k/√3 )(x+y+z)

Real electric field is given by

E = (E_oxx^{^}+E_ozz^)Cos(( k/√3 )(x+y+z)-ωt)

Real magnetic field is given by

B =(k/ω√3) (E_ozx^{^}+(E_0x -E_oz)y^{^} + E_oxz^{^})Cos(( k/√3)(x+y+z)-ωt)