Question

The electric component of a beam of polarized light is

E_y = (5.27 V/m) sin[(1.03 × 10⁶ m^-1)z + ωt].

(a) Write an expression for the magnetic field component of the wave, including a value for ω. What are the (b)wavelength, (c) period, and (d) intensity of this light? (e) Parallel to which axis does the magnetic field oscillate? (f)In which region of the electromagnetic spectrum is this wave?

Answer 1

given

E_y = (5.27 V/m) sin[(1.03 X 10⁶ m^-1)z + ωt]

a )

using equation B_m = E_m / C

B_m = 5.27 / 3 X 10⁸ = 1.756 X 10^-8 T

and K = 1.03 X 10⁶ m^-1

= 1.03 X 10⁶

= 6.097 X 10^-6 m

then f = C / = 3 X 10⁸ / 6.097 X 10^-6

f = 4.92 X 10¹³ H z

ω = 2 X 3.14 X f

ω = 2 X 3.14 X 4.92 X 10¹³

ω = 3.089 X 10¹⁴ rad/sec

B_y = ( 1.756 X 10^-8 ) sin [ ( 1.03 X 10⁶ m^-1 )z + ( 3.089 X 10¹⁴ ) t ]

b )

K = 1.03 X 10⁶ m^-1

= 1.03 X 10⁶

= 6.097 X 10^-6 m

= 6.097 m

c )

ω = 3.089 X 10¹⁴

2 / T = 3.089 X 10¹⁴

T = 2 / 3.089 X 10¹⁴

T = 2.033 X 10^-14 sec

d )

I = C B_o² / 2 _o

I = 3 X 10⁸ X ( 1.756 X 10^-8 )² / 2 X 4 X 3.14 X 10^-7

I = 0.03682 W / m²

e )

Parallel to which X - axis

f )

in the region of Visible light