Question

Q 5. Write mathematical expressions for the vector electric und magnetic field components of a plane electromagnetic wave of wavelength 800 nm travelling along a direction (3.2.1) from the origin and polarized in the xy-plane. What would be results for a dielectric medium with dielectric constant 3.2​

Answer 1

Answer:

Using Maxwell's equation

B

∘

E

∘

=c where c is velocity of light, E

∘

and B

∘

are amplitudes of electric and magnetic field.

given E

∘

=27N/C

The amplitude of magnetic field is B

∘

=

3×10

8

27

=9×10

−8

frequency of wave is given as f=2X10

14

Hz, it's angular frequency is given as ω=2πf=2π×2X10

14

The equation of magnetic field can be given by

B

∘

sin(kx−ωt))=B

∘

sin(2π(

λ

x

−ft))=9×10

−8

sin(2π(

λ

x

−2X10

14

t))(

j

^

or

k

^

)

The direction of electromagnetic wave is given as x axis, the direction of magnetic field will be perpendicular to it, hence option B and C can only be the answer, however, in option B the angular frequency is not as calculated above

Answer 2

$\sf\blue{b(x \: t \: ) = (3 \times 10 {}^{ - 8} t) {}^{} k \: sin(1.5 \times 10 {}^{ - 6} x - 2 \times {10}^{ - 14} t) }$