Question

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. positive y-axis
• B. negative y-axis
• C. positive z-axis
• D. at 45° angle from positive y-axis

Answer 1

The Correct Option is B

The direction of propagation of an electromagnetic (EM) wave is given by the cross product of the electric field vector (\( \vec{E} \)) and the magnetic field vector (\( \vec{B} \)): \[ \text{Direction of propagation} \propto \vec{E} \times \vec{B}. \] Given: \[ \vec{E} \, \text{(electric field)} \, \text{is along the negative z-axis} \quad (\vec{E} = -\hat{k}), \] \[ \vec{B} \, \text{(magnetic field)} \, \text{is along the positive x-axis} \quad (\vec{B} = \hat{i}). \] The cross product \( \vec{E} \times \vec{B} \) is: \[ \vec{E} \times \vec{B} = (-\hat{k}) \times (\hat{i}). \] Using the right-hand rule and the vector cross product rules: \[ \hat{k} \times \hat{i} = \hat{j}. \] Thus: \[ (-\hat{k}) \times (\hat{i}) = -\hat{j}. \] This indicates that the direction of propagation of the EM wave is along the negative y-axis. Hence, the direction of propagation of the electromagnetic wave is \( \boxed{\text{negative y-axis}} \).