# A plane electromagnetic wave having a frequency $\nu =23.9 GHz$ propagates along the positive z-direction in free space. The peak value of the Electric Field is 60 V/m. Which among the following is the acceptable magnetic field component in the electromagnetic wave? Option 1) $\vec{B}=2\times 10^{7}\sin (0.5\times 10^{3}z+1.5\times 10^{11}t)\hat{i}$       Option 2) $\vec{B}=2\times 10^{-7}\sin (0.5\times 10^{3}z+1.5\times 10^{11}t)\hat{i}$ Option 3) $\vec{B}=60\sin (0.5\times 10^{3}x+1.5\times 10^{11}t)\hat{k}$ Option 4) $\vec{B}=2\times 10^{-7}\sin (1.5\times 10^{2}x+0.5\times 10^{11}t)\hat{j}$

Relation between Eo and Bo -

$E_{o}=c.B_{o}$

- wherein

$E_{o}$= Electric field amplitude

$B_{o}$ = Magnetic field amplitude

C= Speed of light in vacuum

Electromagnetic wave propagate in =z-direction

Let $B=B_{0}\sin (kz-wt)$

$B=B_{0}=\frac{E}{C}=\frac{60}{3\times 10^{8}}=2\times 10^{^{-7}}T$

$k=0.5\times 10^{3}$

$w=1.5\times 10^{11}$

so correct option is

$\vec{B}=2\times 10^{-7}\sin (0.5\times 10^{3}z+1.5\times 10^{11}t)\hat{i}$

Option 1)

$\vec{B}=2\times 10^{7}\sin (0.5\times 10^{3}z+1.5\times 10^{11}t)\hat{i}$

Option 2)

$\vec{B}=2\times 10^{-7}\sin (0.5\times 10^{3}z+1.5\times 10^{11}t)\hat{i}$

Option 3)

$\vec{B}=60\sin (0.5\times 10^{3}x+1.5\times 10^{11}t)\hat{k}$

Option 4)

$\vec{B}=2\times 10^{-7}\sin (1.5\times 10^{2}x+0.5\times 10^{11}t)\hat{j}$

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