The electric field in a plan a electromagnetic wave is given by :
$$E_{y}=69\sin[0.6\times10^{3}x-1.8\times10^{11}t]V/m$$
The expression for magneticfield associated with this electromagnetic wave is ___ T.

$$E_y = 69\sin[0.6\times10^3 x - 1.8\times10^{11}t]$$ V/m.

Speed: $$c = \omega/k = \frac{1.8\times10^{11}}{0.6\times10^3} = 3\times10^8$$ m/s. ✓

$$B_0 = E_0/c = \frac{69}{3\times10^8} = 2.3\times10^{-7}$$ T.

E is in y-direction, wave propagates in x-direction, so B is in z-direction ($$\hat{y} \times \hat{x}$$... actually $$\hat{E} \times \hat{k}_{wave}$$ should give B direction. $$\hat{y} \times \hat{x} = -\hat{z}$$, but for EM wave $$\vec{E} \times \vec{B} \propto \hat{k}$$, so $$\hat{y} \times \hat{B} = \hat{x}$$, giving $$\hat{B} = \hat{z}$$).

$$B_z = 2.3\times10^{-7}\sin[0.6\times10^3 x - 1.8\times10^{11}t]$$ T.

The answer is Option 4.