Question

The magnetic field in a plane electromagnetic wave is given by B_(y) = 2xx10^7 T sin (0.5xx10^3x+1.5xx10^11 t) T (a) What is the wavelength and frequency of the wave? (b) Write an expression for the eletric field.

Answer 1

(a) frequency = 2.4 × 10^10 Hz , wavelength = 1.256 × 10^-2 m (b) equation of electric field , $E=(2\times10^{-7}Tsin(0.5\times10^3y+1.5\times10^{11}t)$

given, The magnetic field in a and

electromagnetic wave is given by $B_y=2\times10^{-7}Tsin(0.5\times10^3x+1.5\times10^{11}t)$

we know standard equation of electromagnetic wave of magnetic field $B=B_0sin(kx+\omega t)$

on comparing both equations we get,

angular fequency, ω = 1.5 × 10¹¹

⇒2πη = 1.5 × 10¹¹

⇒η = (1.5/6.28) × 10¹¹ Hz ≈ 0.24 × 10¹¹ Hz

= 2.4 × 10^10 Hz

hence frequency of wave = 2.4 × 10^10 Hz

also k = 2π/λ = 0.5 × 10^3

⇒λ = 2π/(0.5 × 10³) = 4 × 3.14 × 10-³

= 1.256 × 10-² m

wavelength of wave = 1.256 × 10-² m

as we know, electric field and magnetic field are perpendicular to each other.

here magnetic field is propagated along x - axis so electric field is propagated along y - axis.

$E=(2\times10^{-7}Tsin(0.5\times10^3y+1.5\times10^{11}t)$