An electromagnetic wave is traveling in the negative...

An electromagnetic wave is traveling in the negative direction of a $y$ axis. At a particular position and time, the electric field is directed along the positive direction of the $z$ axis and has a magnitude of $100 \mathrm{~V} / \mathrm{m}$. What are the (a) magnitude and (b) direction of the corresponding magnetic field?

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Key Concepts

Poynting Vector

The Poynting vector, defined as the cross product of the electric field and the magnetic field, indicates the direction of energy flow in an electromagnetic wave. It reinforces that the wave’s energy propagation is perpendicular to both the electric and magnetic fields.

Right-Hand Rule

The right-hand rule is a fundamental tool used to determine the mutual orientation of the electric field, magnetic field, and the wave’s direction of propagation. By pointing the thumb along the propagation direction and the index finger in the direction of the electric field, the middle finger naturally points in the direction of the magnetic field.

Electromagnetic Wave

An electromagnetic wave consists of oscillating electric and magnetic fields that are perpendicular to each other and to the direction of propagation. This concept is central to understanding how energy is transmitted through space without the need for a medium.

Relationship Between Electric and Magnetic Fields

In a free-space electromagnetic wave, the magnitudes of the electric and magnetic fields are connected by the relation E = cB, where c is the speed of light. This relation is derived from Maxwell's equations and ensures the balance of energy distribution between the two fields.

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