Problem 2157 - JEE Physics

Question

If the direction of magnetic field \(\mathrm{B}^{\rightarrow}\) at some instant is along + ve \(Z\) direction and the electromagnetic wave is propagating along + ve \(\mathrm{X}\) direction, then the direction of electric field \(\mathrm{E}^{\rightarrow}\) at that instant is (A) along - ve Y direction (B) along + ve Y direction (C) along + ve \(\mathrm{X}\) direction (B) along - ve \(\mathrm{X}\) direction

Step-by-Step Solution

Answer

The short answer is: The direction of the electric field \(\mathrm{E}^{\rightarrow}\) at that instant is (B) along + ve Y direction.

Step 1: Using the Right Hand Rule

For this problem, we use the right-hand rule to determine the direction of the electric field. First, align your right hand with your thumb pointing in the direction of the magnetic field (along the + ve Z direction) and your fingers pointing in the direction of wave propagation (along the + ve X direction).

Step 2: Determine the Direction of the Electric Field

Now, with your right hand in the position from Step 1, extend your palm. The direction in which your palm is facing is the direction of the electric field (\(\mathrm{E}^{\rightarrow}\)). In this case, your palm will be facing in the + ve Y direction.

Step 3: Identify the Correct Option

We have found that the direction of the electric field is along the + ve Y direction. Comparing this result with the given options, we can see that the correct answer is (B) along + ve Y direction.

Key Concepts

Electromagnetic Waves

Electromagnetic waves are special because they carry energy and travel through space without needing a medium to move. They are a type of wave made up of two components: electric fields and magnetic fields. These fields oscillate, which means they move back and forth in a regular pattern.

One important thing to understand is how these fields are oriented. The electric field and the magnetic field in electromagnetic waves are always perpendicular to each other. Additionally, both fields are perpendicular to the direction in which the wave is moving. This is why electromagnetic waves are classified as transverse waves. Some common examples of electromagnetic waves include sunlight, radio waves, and X-rays.

• Electromagnetic waves don't need a medium to travel through.
• Composed of electric and magnetic fields.
• Fields are perpendicular to each other and to the wave direction.

Electric Field Direction

In the study of electromagnetic waves, knowing the direction of the electric field is crucial. The electric field is a vector which means it has both magnitude and direction. In the context of the Right Hand Rule: when you know the direction of wave propagation and the magnetic field, you can easily find the direction of the electric field.

Here's how it works:

• Point your right thumb in the direction of the magnetic field. In this case, it's the +ve Z direction.
• Next, point your fingers in the direction the wave is traveling. Here, it's the +ve X direction.

Your palm will naturally face the direction of the electric field, which, according to our steps, ends up being the +ve Y direction.

• The electric field's direction is determined using the Right Hand Rule.
• It is always perpendicular to both the magnetic field and the wave direction.
• In our problem, the field is in the +ve Y direction.

Magnetic Field Direction

The direction of the magnetic field is another important aspect of understanding electromagnetic waves. Like the electric field, it is also a vector, having both magnitude and direction. In the example exercise, the magnetic field is aligned along the +ve Z direction.

The Right Hand Rule helps relate the magnetic field to both the wave's direction and the electric field direction. By orienting your hand (as described in previous steps with the thumb in the magnetic field direction), you can figure out how the electric field and wave direction relate to it.

• Magnetic fields have a specific direction in space, dictated by the Right Hand Rule.
• It's always perpendicular to the electric field in electromagnetic waves.
• Plays a key role in determining wave behavior and field interactions.