Question

An electromagnetic wave is travelling in vertically upward direction. At an instant, its electric field vector points in west direction. In which direction does the magnetic field vector point at that instant?

Hint:

The direction of the magnetic field in an electromagnetic wave is determined by the right-hand rule, which ensures it is perpendicular to both the electric field and the direction of propagation.

Answer 1

Given an electromagnetic wave propagating vertically upward, with its electric field vector oriented westward at a specific moment, the objective is to determine the direction of the magnetic field vector at that same moment.

1. Electromagnetic Wave Field Interrelationships:

In an electromagnetic wave, the electric field (\( \vec{E} \)) and magnetic field (\( \vec{B} \)) vectors are mutually perpendicular. Furthermore, both vectors are perpendicular to the direction of wave propagation. These three vectors—electric field, magnetic field, and propagation direction—form a right-handed coordinate system.

2. Defining Directions of Propagation and Fields:

A standard 3D coordinate system can be used for defining these directions:

• Wave propagation is in the vertically upward direction, corresponding to the \( +y \)-axis.
• The electric field vector (\( \vec{E} \)) is directed westward, corresponding to the \( -x \)-axis.
• By the right-hand rule, the magnetic field (\( \vec{B} \)) must be perpendicular to both the electric field (\( \vec{E} \)) and the direction of propagation (the \( y \)-axis).

3. Application of the Right-Hand Rule:

The direction of the magnetic field vector (\( \vec{B} \)) is determined using the right-hand rule. If the thumb of the right hand indicates the direction of wave propagation (upward, along \( +y \)) and the index finger points in the direction of the electric field (westward, along \( -x \)), the middle finger will then point in the direction of the magnetic field.

Applying this rule, with the electric field pointing west (along \( -x \)) and the wave propagating vertically upward (along \( +y \)), the magnetic field vector is directed northward, along the \( +z \)-axis.

4. Conclusion:

At the instant when the electric field vector is westward, the magnetic field vector points northward.