The electric field of a plane electromagnetic wave is given by: E_y = 69 sin [0.6 x 10^3x - 1.8 x 10^11t] V/m. The expression for magnetic field associated with this electromagnetic wave is ______ T.

hat B = hat c x hat E => hat c = hat i because phase of electric field is function of x. => hat E = hat j (given) => hat B = hat i x hat j = hat k |B| = (|E| / c) = frac69 x 0.6 x 10^31.8 x 10^11 = (69 / 3 x 10^8) |B| = 2.3 x 10^-7 vec B_z = 2.3 x 10^-7 sin (0.6 x 10^3x - 1.8 x 10^11t) (phase is same as that of electric field)

The electric field of a plane electromagnetic wave is g... | null (Physics)

JEE Mains 2026 21st January Shift 1

Physics

The electric field of a plane electromagnetic wave is given by:

E_y = 69 \sin[0.6 \times 10^3x - 1.8 \times 10^{11}t]\text{ V/m}.

The expression for magnetic field associated with this electromagnetic wave is ______ T.

B_z = 2.3 \times 10^{-7} \, \sin[0.6 \times 10^3 x - 1.8 \times 10^{11} t]

B_z = 2.3 \times 10^{-7} \, \sin[0.6 imes 10^3 x + 1.8 imes 10^{11} t]

B_y = 69 \, \sin[0.6 imes 10^3 x + 1.8 imes 10^{11} t]

B_y = 2.3 imes 10^{-7} \, \sin[0.6 imes 10^3 x - 1.8 imes 10^{11} t]

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Explanation

\hat{B} = \hat{c} \times \hat{E}

\Rightarrow \hat{c} = \hat{i}

because phase of electric field is function of

x

\Rightarrow \hat{E} = \hat{j}

(given)

\Rightarrow \hat{B} = \hat{i} \times \hat{j} = \hat{k}

|B| = \frac{|E|}{c} = \frac{69 \times 0.6 \times 10^3}{1.8 \times 10^{11}} = \frac{69}{3 \times 10^8}

|B| = 2.3 \times 10^{-7}

\vec{B}_z = 2.3 \times 10^{-7} \sin(0.6 \times 10^3x - 1.8 \times 10^{11}t)

(phase is same as that of electric field)

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