Question

The magnetic field of an electromagnetic wave is given by B(x,t)=(0.1μT)sin[(6π×106m−1)x−(1.80π×1015s−1)t]

1) Calculate the amplitude of the electric field.
2) Calculate the speed of the wave.
3)Calculate the frequency of the wave.
4) Calculate the period of the wave.
5) Calculate the wavelength

Answer 1

Given that

B(x,t)=(0.1μT)sin[(6π×10⁶ m⁻¹)x−(1.80π×10¹⁵ s⁻¹)t]

We know that standard form of a wave equation given as'

y= A sin ( kx - ωt)

k=6π×10⁶

We know that

2π/λ= k

2π = 6π×10⁶ x λ ⇒ λ= 3.33 x 10⁻⁷ m

ω=1.80π×10¹⁵

We know that

ω=2π f

f= 1.80π×10¹⁵ /2π = 0.9 ×10¹⁵ Hz

1)

Amplitude of e electric field Eo= C Bo

Eo= C Bo

Bo=0.1μ

C=3 x 10⁸ m/s

Eo= C Bo = 3 x 10⁸ x 0.1 x 10⁻⁶

Eo= 30 N/C

2)

Speed of the wave = 3 x 10⁸ m/s

3)

f=0.9 ×10¹⁵ Hz

4)

T=1/f

T=1.15 x 10⁻¹⁵ s

5)

λ= 3.33 x 10⁻⁷ m