The magnetic field of a light wave at given time parallel to y-axis a…

The correct answer is Option (2) → positive direction of z; x-axis

A wave written as \( \sin(kz - \omega t) \) travels along +z: a point of constant phase has \( kz - \omega t = \) constant, so \( z \) increases as \( t \) increases.

In an electromagnetic wave \( \vec{E} \) and \( \vec{B} \) are perpendicular to each other and to the direction of travel, which is the direction of \( \vec{E}\times\vec{B} \). With \( \vec{B} \) along \( \hat{\jmath} \) and travel along \( \hat{k} \), \( \vec{E} \) must be along \( \hat{\imath} \), because

    \( \displaystyle \hat{\imath}\times\hat{\jmath} = \hat{k} \)

So the wave travels in the positive z-direction and the electric field is parallel to the x-axis.

Why the other options are incorrect

• Option (1) positive direction of z; y-axis — Incorrect. The electric field cannot be along the y-axis, because \( \vec{E} \) must be perpendicular to \( \vec{B} \), which is along y.

• Option (3) negative direction of z; y-axis — Incorrect. The sign of \( kz - \omega t \) gives travel along +z, not \( -z \); and \( \vec{E} \) cannot be parallel to \( \vec{B} \).

• Option (4) negative direction of z; x-axis — Incorrect. A wave in \( -z \) would be written \( \sin(kz + \omega t) \); the minus sign here means travel along +z.

NCERT (2026-27):
Nature of Electromagnetic Waves – “… In Fig. 8.3, we show a typical example of a plane electromagnetic wave propagating along the z direction (the fields are shown as a function of the z coordinate, at a given time t). The electric field E_x is along the x-axis, and varies sinusoidally with z, at a given time. The magnetic field B_y is along the y-axis, and again varies sinusoidally with z. The electric and magnetic fields E_x and B_y are perpendicular to each other, and to the direction z of propagation.”