JEE Advanced 2026 — Paper 1 — PHY-II solution

JEE Advanced2026Paper 1PHY-II

The electric field associated with an electromagnetic wave travelling in vacuum is given by $E_{0} sin (3 y + 4 z + ω t) \hat{i}$ , where $ω$ is the angular frequency. All quantities are in SI units. The correct statement(s) about this wave is/are:

[Given: speed of light in vacuum $c = 3 \times 1 0^{8}$ ms $^{- 1}$ .]

A
The wave is travelling in $- \frac{1}{5} (3 \hat{j} + 4 \hat{k})$ direction.
B
The magnitude of the wave vector is $0.5 m^{- 1}$ .
C
The value of $ω$ is $1.5 \times 1 0^{9}$ rad s $^{- 1}$ .
D
The magnetic field associated with this wave is given by $\frac{E _{0}}{c} sin (3 y + 4 z + ω t) (4 \hat{j} - 3 \hat{k})$ .

Solution

Phase analysis. Phase $ϕ = 3 y + 4 z + ω t$ . Wave vector points opposite to the direction of propagation since the time and space terms have the same sign. Writing the spatial part as $k \cdot r$ with $k = 3 \hat{j} + 4 \hat{k}$ , the direction of propagation is $- \hat{k} /∣ k ∣ = - \frac{1}{5} (3 \hat{j} + 4 \hat{k})$ . (A) correct.

Wave-vector magnitude. $∣ k ∣ = 3^{2} + 4^{2} = 5$ m $^{- 1}$ , not $0.5$ m $^{- 1}$ . (B) incorrect.

Angular frequency. $ω = c ∣ k ∣ = 3 \times 1 0^{8} \times 5 = 1.5 \times 1 0^{9}$ rad s $^{- 1}$ . (C) correct.

Magnetic field direction. $B$ must satisfy $B \propto \overset{n}{^} \times E$ , where $\overset{n}{^}$ is the direction of propagation. With $\overset{n}{^} = - \frac{1}{5} (3 \hat{j} + 4 \hat{k})$ and $E \propto \hat{i}$ : $\overset{n}{^} \times \hat{i} = - \frac{1}{5} (3 \hat{j} + 4 \hat{k}) \times \hat{i} = - \frac{1}{5} (- 3 \hat{k} + 4 \hat{j})$ , giving $B \propto (3 \hat{k} - 4 \hat{j}) /5$ . So $B = \frac{E _{0}}{5 c} sin (\dots) (3 \hat{k} - 4 \hat{j})$ , which differs from the expression in option (D) both in sign and magnitude. (D) incorrect.

Correct answers: (A) and (C).

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