Consider each of the electric- and magnetic-field...

Consider each of the electric- and magnetic-field orientations given next. In each case, what is the direction of propagation of the wave? (a) $\overrightarrow{\boldsymbol{E}}$ in the $+x$ -direction, $\overrightarrow{\boldsymbol{B}}$ in the $+y$ -direction; (b) $\overrightarrow{\boldsymbol{E}}$ in the $-y$ -direction, $\overrightarrow{\boldsymbol{B}}$ in the $+x$ -direction; (c) $\overrightarrow{\boldsymbol{E}}$ in the $+z$ -direction, $\overrightarrow{\boldsymbol{B}}$ in the $-x$ -direction; (d) $\vec{E}$ in the $+y$ -direction, $\overrightarrow{\boldsymbol{B}}$ in the $-z$ -direction. 32.3 - A sinusoidal electromagnetic wave is propagating in vacuum in

Key Concepts

Electromagnetic Wave Orthogonality

In electromagnetic waves, the electric field, magnetic field, and the direction of propagation are mutually perpendicular. This spatial orthogonality is a defining characteristic that ensures the wave can propagate through space without the fields interfering with each other.

Poynting Vector

The Poynting vector is defined as the cross product of the electric field and the magnetic field vectors (S = E × B). It represents the energy flux or power per unit area of the wave and its direction gives the direction in which the electromagnetic wave is propagating.

Right-Hand Rule

The right-hand rule is a convention used to determine the direction of the cross product vector. When applied to electromagnetic waves, pointing the index finger in the direction of the electric field and the middle finger in the direction of the magnetic field, the thumb will point in the direction of the wave's propagation.

Vector Cross Product

The vector cross product is a mathematical operation that takes two vectors and produces a third vector that is perpendicular to the plane formed by the original vectors. In the context of electromagnetic waves, it provides a method to calculate the direction of energy flow using the electric and magnetic fields.

Transcript

00:03 So in order to find the direction of propagation, we're going to use the right hand rule.

00:08 So imagine taking your right hand and your pointer finger pointing to the left, your thumb perpendicular upward, and then your middle finger pointing towards you.

00:20 So in this case, out of the screen.

00:24 And when we do that, we're going to have our e component, our electric component being your pointer finger, our b magnetic component being the middle finger.

00:34 And then the resulting component, the direction of propagation, cross product, e cross b, is going to be the thumb pointing upwards.

00:44 So if we look at part a, we have our e component pointing in the positive x, so to the right, and we have our b component in the positive y, so upwards.

01:02 So if you take your right hand, without bending your fingers, just rotate your hand to match, is part a, so your pointer finger is going to be pointing to the right, your middle finger is going to be pointing upward, and then you'll see that your thumb is pointing towards you, or in this case, out of the screen, which is the positive z direction.

01:30 Now in part b, we have our e component in the negative y direction, and we have our b component in the positive x direction.

01:48 So again, if you take your pointer finger pointing down, your middle finger pointing to the right, you're going to see again in this case your thumb is pointing towards you or out of the screen.

02:01 So it's going to be positive z direction...

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