In a plane electromagnetic wave, the electric field varies as $E_z = 90\sin(500x + 20 × 10^{10}t) V/m$. The expression of its magnetic field variation is:

$3 × 10^{-7} \sin(500x + 20 × 10^{10}t) T$

The correct answer is Option (4) → $3 × 10^{-7} \sin(500x + 20 × 10^{10}t) T$

Given electric field:

$E_z = 90 \sin(500x + 2.0 \times 10^{11}t)$ V/m

Relation between $E$ and $B$ in an electromagnetic wave:

$\frac{E}{B} = c$

$\Rightarrow B = \frac{E}{c}$

Maximum electric field:

$E_0 = 90$ V/m

So, maximum magnetic field:

$B_0 = \frac{90}{3 \times 10^8} = 3 \times 10^{-7}$ T

Since $E$ is along z-axis and wave is propagating along negative x-axis (from argument $500x + \omega t$), the magnetic field will be along y-axis.

Thus, the magnetic field expression is:

$B_y = 3 \times 10^{-7} \sin(500x + 2.0 \times 10^{11}t)$ T