Question

The magnetic field in a plane electromagnetic wave is given by By=2×10−7sin(0.5×103x+1.5×1011t)T The wavelength and frequency of the wave are

Answer 1

Answer:

09887765865556.7655

Answer 2

Answer:

The wavelength of wave is 1.25 cm

The frequency of wave 23.8 GHz  

Explanation:

The magnetic field in a plane electromagnetic wave is given as

y = 2 × $10^{-7}$ Sin ( 0.5 × 10³ x + 1.5 × $10^{11}$ t ) T

Comparing the given equation with

$B_y$ = $B_0$  sin [2 π ( (x/ λ) + (t/T) )]

i.e $B_0$ = 2 × $10^{-7}$

And  λ =  $\dfrac{2 \Pi }{0.5\times 10^{3}}$  meters

i.e λ =  0.01256 m

Or, λ = 1.25 cm

So, The wavelength = λ = 1.25 cm

Again

$\dfrac{1}{T}$ =  $\dfrac{1.5\times 10^{11}}{2\Pi }$

∵ frequency = f = $\dfrac{1}{T}$

So, f = $\dfrac{1.5\times 10^{11}}{2\Pi }$  Hz

or, f = 2.38 × $10^{10}$

i.e frequency = f = 23.8 GHz

Hence, The wavelength of wave is 1.25 cm

And  The frequency of wave 23.8 GHz  Answer