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MCQEasyJEE 2023Characteristics of EM Waves

JEE Physics 2023 Question with Solution

In an electromagnetic wave, at an instant and at a particular position, the electric field is along the negative z axis and magnetic field is along the positive x-axis. Then the direction of propagation of electromagnetic wave is:

  • A

    negative y-axis

  • B

    at 45∘45^\circ angle from positive y-axis

  • C

    positive y-axis

  • D

    positive z-axis

Answer

Correct answer:A

Step-by-step solution

Standard Method

Given: The electric field E⃗\vec{E} is along the negative zz-axis and the magnetic field B⃗\vec{B} is along the positive xx-axis.

Find: The direction of propagation of the electromagnetic wave.

For an electromagnetic wave, the direction of propagation is given by

E⃗×B⃗\vec{E} \times \vec{B}

Using the given directions,

E⃗=−k^,B⃗=i^\vec{E} = -\hat{k}, \quad \vec{B} = \hat{i}

Therefore,

E⃗×B⃗=(−k^)×(i^)\vec{E} \times \vec{B} = (-\hat{k}) \times (\hat{i})

Using the vector product rule,

k^×i^=j^\hat{k} \times \hat{i} = \hat{j}

So,

(−k^)×(i^)=−j^(-\hat{k}) \times (\hat{i}) = -\hat{j}

Hence, the wave propagates along the negative y-axis.

The correct option is A. The solution lists B, but the working clearly gives negative y-axis, which matches option A.

Common mistakes

  • Using B⃗×E⃗\vec{B} \times \vec{E} instead of E⃗×B⃗\vec{E} \times \vec{B}. This reverses the direction and gives the wrong axis. Always use the propagation direction as E⃗×B⃗\vec{E} \times \vec{B} for an electromagnetic wave.

  • Ignoring the negative sign in E⃗=−k^\vec{E} = -\hat{k}. If the sign is dropped, the direction becomes +j^+\hat{j} instead of −j^-\hat{j}. Keep track of the sign of each vector before taking the cross product.

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