JEE Main 2026 — Apr 4, Shift 2 — Physics solution

JEE Main2026Apr 4, Shift 2Physics

A magnetic field vector in an electromagnetic wave is represented by, $B = B_{0} sin (2 π ν t - \frac{2 π x}{λ}) \hat{j}$ . Its associated electric field vector is ________.

A
$E = - ν λ B_{0} sin (2 π ν t - \frac{2 π x}{λ}) \hat{k}$
B
$E = - ν λ B_{0} sin (2 π ν t - \frac{2 π x}{λ}) \hat{i}$
C
$E = ν λ B_{0} sin (2 π ν t - \frac{2 π x}{λ}) \hat{k}$
D
$E = ν λ B_{0} sin (2 π ν t - \frac{2 π x}{λ}) \hat{i}$

Solution

For a plane EM wave, $\hat{E} \times \hat{B} = \hat{k}_{p r o p}$ , where the wave propagates along $+ \overset{x}{^}$ (read from the phase $2 π ν t - 2 π x / λ$ ).

With $\hat{B} = \hat{j}$ and $\hat{k}_{p r o p} = \hat{i}$ , we need $\hat{E}$ such that $\hat{E} \times \hat{j} = \hat{i}$ . This gives $\hat{E} = - \hat{k}$ .

Magnitudes are related by $E_{0} = c B_{0} = ν λ B_{0}$ .

$∴ E = - ν λ B_{0} sin (2 π ν t - \frac{2 π x}{λ}) \hat{k}$ .

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