If the magnetic field in a plane progressive | vedclass

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Question

(A) The standard equation for a plane progressive wave is given by $B = B_0 \sin(kx + \omega t)$.Comparing this with the given equation $B_y = 2 	ime

Vedclass · Accepted Answer

$75 	imes 10^9 \ Hz$

Vedclass · Answer

(A) The standard equation for a plane progressive wave is given by $B = B_0 \sin(kx + \omega t)$.Comparing this with the given equation $B_y = 2 	imes 10^{-7} \sin(0.5 	imes 10^3 x + 1.5 \pi 	imes 10^{11} t)$,we identify the angular frequency $\omega$ as $\omega = 1.5 \pi 	imes 10^{11} \ rad/s$.The relationship between angular frequency $\omega$ and frequency $f$ is given by $\omega = 2 \pi f$.Substituting the value of $\omega$,we get $1.5 \pi 	imes 10^{11} = 2 \pi f$.Solving for $f$,we have $f = \frac{1.5 \pi 	imes 10^{11}}{2 \pi} = 0.75 	imes 10^{11} \ Hz$.This can be rewritten as $f = 75 	imes 10^9 \ Hz$.Therefore,the correct option is $A$.

If the magnetic field in a plane progressive wave is represented by the equation $B_{y} = 2 \times 10^{-7} \sin(0.5 \times 10^3 x + 1.5 \pi \times 10^{11} t) \ T$,then the frequency of the wave is (In the equation,time $t$ is in seconds).

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