Question

In an EM wave, if \(\vec{B}\) is along z-axis, then direction of \(\vec{E}\) and propagation will be:

• A. In \(xy\)-plane
• B. In \(yz\)-plane
• C. In \(y\)-direction
• D. In \(z\)-direction

Hint:

In electromagnetic waves: \[ \vec{E} \perp \vec{B} \perp \text{Direction of propagation} \] Always use the right-hand rule for vector cross products.

Answer 1

The Correct Option is C

Concept: Electromagnetic waves are transverse waves in which:

• Electric field \(\vec{E}\)
• Magnetic field \(\vec{B}\)
• Direction of propagation

are all mutually perpendicular to each other. The relation between them is given by: \[ \vec{E} \times \vec{B} = \text{Direction of propagation} \] Thus, by applying vector cross product rules, we can determine the direction of electric field and propagation.

Step 1: Write the given information.
Magnetic field is along z-axis: \[ \vec{B} \parallel \hat{k} \] We know: \[ \vec{E} \perp \vec{B} \] Therefore, electric field must lie either along x-axis or y-axis.

Step 2: Apply the right hand rule.
For electromagnetic waves: \[ \vec{E} \times \vec{B} = \text{Propagation direction} \] Using unit vectors: \[ \hat{j} \times \hat{k} = \hat{i} \] This means:

• Electric field is along y-axis
• Magnetic field is along z-axis
• Wave propagates along x-axis

Step 3: Choose the correct option.
Since electric field is along y-direction: \[ \boxed{\text{In y-direction}} \] Hence, the correct answer is: \[ \boxed{\text{(C) In y-direction}} \]