Electromagnetic Waves – JEE Main PhysicsPractice Questions & PYQs

The relationship between the electric field vector $\vec{E}$, the magnetic field vector $\vec{B}$, and the velocity of propagation vector $\vec{C}$ is defined by the equation $\vec{E} = \vec{B} \times \vec{C}$. In this scenario, the wave travels in the positive x-direction with a speed of $c = 3 \times 10^8 \,\mathrm{m/s}$, represented by the vector $\vec{C} = 3 \times 10^8 \hat{i} \,\mathrm{m/s}$.

Substituting the given magnetic field $\vec{B} = 2 \times 10^{-7} \hat{j} \,\mathrm{T}$ into the cross product expression yields $\vec{E} = (2 \times 10^{-7} \hat{j}) \times (3 \times 10^8 \hat{i})$. Multiplying the numerical coefficients gives $2 \times 3 \times 10^1 = 60$, while the cross product of the unit vectors $\hat{j} \times \hat{i}$ results in $-\hat{k}$. Consequently, the electric field at the specified point is $-60 \hat{k} \,\mathrm{V/m}$.