00:01
This question we are given here a magnetic field so in this question we are given here a magnetic field the component of uniform plane wave propagating in a loose less simple nanomagnetic medium so we can write here a magnetic field b which is equal to invite 0 .25 multiple we can write here sign of 2 pi of multiple we can write 10 to 8 multiple over t plus we can write 0 .5 multiple x minus we can write 0 .125 and here we can write the a y and mu multiply by t now in the first part of this question we want to find find the frequency wavelength and phase velocity so let's find out first in the first sub part we want to find frequency wavelength and then and phase well so first what about frequency so frequency we know that it is 10 to 8 volts from that figure this is our frequency 10 is to 8 holds so frequency is 10 to 8 words now using the equation c which is equal lambda f we know that you want to find value of lambda which is equal we can write c divided by f is a substitute value so we can raise 3 multita by 10 x divided by value of f here is 10 to 8 you simply find we can write here answer is 3 meter this is value of lambda now let's find out the phase velocity so the phase velocity into know w p which is equal to we can write the omega divided by capital r that here we can write omega divided by an omega divided by r which is equal to we can write 2 pi multiple by 10 is to 8 divided by we can write here 2 pi multiple by 0 .5 you just simply find we can write the answer is 2 multiple by 10 to 8 meter per second so this is the value of phase velocity now in the second support of this question we here in the second support what we want to find in the b we want to find relative permeability and interesting patterns of the medium let's find out this two things so here we have relative permittivity permittivity and the relative formativity we want to find er that we want to find and for the er which is equal to we can here c divided by vp c divided by vp square which is equal we can write 3 multiplied by 10 x2 x2 x2 x2 x2 x2 x2.
02:48
Here whole square which is equal we can write answer is 2 .25 now let's find out the ea and here we can write which is equal to square root of mu divided by e which is equal we can write square root of mu modula by mu not divided by we can write e nond multiplied by err which is equal to we can write we can write square root of mu not divided by e nought by we can by square root of er mu r divided by er and here we can write it is substitute of value into this formula so we can write here o pi by 10 x to minus 7 divided by e0 which is equal to we can write 8 .85, more divided by 10 to minus 7, and into the bracket we can write here the er divided by, say, numer divided by er, which is equal, we can write 1 divided by squared.
03:49
Now we are simplifying, we can write here, answer is the eta is equal we can write 1 .920, multiple by we can write here that 1 divided by, the er here is this 2 .25.
04:03
Now you are simply fine we can write your answer is 251.
04:09
251.
04:11
So this is the value.
04:14
Now that is a, you can say, relative pomeability, and this is our interesting impedance.
04:22
So this is our interesting impedance and this is our relative permeability...