An electromagnetic wave is transporting energy in the negative $z$ direction At a certain point and certain time the direction of electric field of the wave is along positive $y$ direction What will be the direction of the magnetic field of the wave at that point and instant?
- Positive direction of $z$
- Negative direction of $y$
- Positive direction of $x$
- Negative direction of $x$
The Correct Option is C
Solution and Explanation
1. The energy transport in an electromagnetic wave is given by the Poynting vector: \[ \vec{S} = \vec{E} \times \vec{H}, \] where \(\vec{E}\) is the electric field vector and \(\vec{H}\) is the magnetic field vector.
2. Given: - Energy transport (\(\vec{S}\)) is in the negative \(z\)-direction: \(\vec{S} = -\hat{k}\). - Electric field (\(\vec{E}\)) is in the positive \(y\)-direction: \(\vec{E} = +\hat{j}\).
3. Substituting into the cross-product: \[ \vec{S} = \vec{E} \times \vec{H} \implies -\hat{k} = (+\hat{j}) \times \vec{H}. \]
4. Solving for \(\vec{H}\): \[ \vec{H} = -\hat{i}. \]
Thus, the magnetic field is in the positive direction of \(x\).
In an electromagnetic wave, the directions of the electric field, magnetic field, and energy transport (Poynting vector) are mutually perpendicular, forming a right-handed coordinate system.
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Concepts Used:
Electromagnetic waves
The waves that are produced when an electric field comes into contact with a magnetic field are known as Electromagnetic Waves or EM waves. The constitution of an oscillating magnetic field and electric fields gives rise to electromagnetic waves.
Types of Electromagnetic Waves:
Electromagnetic waves can be grouped according to the direction of disturbance in them and according to the range of their frequency. Recall that a wave transfers energy from one point to another point in space. That means there are two things going on: the disturbance that defines a wave, and the propagation of wave. In this context the waves are grouped into the following two categories:
- Longitudinal waves: A wave is called a longitudinal wave when the disturbances in the wave are parallel to the direction of propagation of the wave. For example, sound waves are longitudinal waves because the change of pressure occurs parallel to the direction of wave propagation.
- Transverse waves: A wave is called a transverse wave when the disturbances in the wave are perpendicular (at right angles) to the direction of propagation of the wave.