The electric field in a plane electro magnetic wave is given by $E_z=60\sin (0.5 × 10^3x+1.5 × 10^{11} t) V/m$. What is the wavelength and magnetic field amplitude of the wave?

$1.26 cm, 2 × 10^{-7} T$

The correct answer is Option (2) - $1.26 cm, 2 × 10^{-7} T$

The given equation for electric field is -

$E_z=60\sin(0.5×10^3x+1.5 × 10^{11} t) V/m$

and $E_z=E_0\sin(kx+wt)$ [general form]

∴ $E_0$, Amplitude of electric field = 60 V/m

$k$, wave number = $\frac{2\pi}{λ}=0.5×10^3m^{-1}$

$w$, Angular frequency = $2\pi f=1.5×10^{11}rad/s$

$∴λ=\frac{2\pi}{k}=\frac{2×3.14}{0.5×10^3}=0.01256m$

$≃1.26cm$

ans,

$B_0=\frac{E_0}{C}$ [formula]

$∴B_0=\frac{60}{3×10^8}=2×10^{-7}T$