·The electric field of an electromagnetic wave points in the positive y direction. At the same t

·The electric field of an electromagnetic wave points in the...

Key Concepts

Right-Hand Rule

The right-hand rule is a mnemonic used in vector physics to determine the direction of resultant vectors from cross products. In the context of electromagnetic waves, it helps in identifying the direction of wave propagation by aligning the fingers of the right hand along the electric field, curling them towards the magnetic field, with the thumb then pointing in the direction of propagation.

Vector Cross Product

The vector cross product mathematically represents the relationship between two vectors, yielding a third vector that is perpendicular to the plane containing the first two. In electromagnetic wave propagation, the cross product of the electric field vector and the magnetic field vector gives the direction in which the wave travels.

Electromagnetic Waves

Electromagnetic waves are forms of energy that travel through space with oscillating electric and magnetic fields. These fields are always oriented perpendicular to each other as well as to the direction in which the wave propagates, ensuring that the wave transfers energy and momentum through space.

Transcript

00:01 All right, so we've been asked if the electric field is pointing in the positive y direction and the magnetic field is pointing in the positive z direction of an electromagnetic wave, then what direction is the wave traveling in? i'm going to call the way it's direction v because i can.

00:29 All right, so what direction is v in? all right, in order to answer this question, we're going to do a quick review of the right hand rule, which you've probably seen before.

00:41 So what the right hand rule says is if i take my hand and i point my pointer finger in the x direction, and then i rotate my hand whatever direction it needs to go in so that my other fingers, when i put them at a 90 degree angle to my pointer finger, point in the y direction, then i will find that my thumb is pointed in the z direction.

01:07 And that's what defines the x, y, z coordinate system.

01:13 We also call it the cartesian coordinate system.

01:16 If you ever pay attention to a math book, it's always drawn just like that.

01:21 It's never going to be drawn, for example, with the y direction pointed this way, where x and z are still the same.

01:29 That doesn't happen.

01:30 We don't do it that way.

01:32 And there's no good reason we don't do it that way.

01:34 It's just the rule.

01:35 It's something called a convention.

01:37 And we all agree that this would be the convention and we stuck with it to make things a whole lot less confusing.

01:45 All right.

01:45 There's actually something really cool about the xyz coordinate system is that you can actually just keep repeating this.

01:52 So it goes x, y, z, and then it's going to go x, y, z again.

02:02 So what does that mean? that means that if i point my pointer finger in the y direction and then i rotate my hand so that all of my other fingers are pointed in the z direction, i'm actually going to find that my thumb is pointed up in the x direction.

02:22 So i went y, z, oops.

02:27 So i went y, z, x, x.

02:31 Similarly, if i start at z so that my pointer finger is pointed in the z direction, and i rotate my hand so that my other fingers can point in the x direction, then i'm going to find that my thumb is pointed in the y direction.

02:52 So i went x from pointer x, from pointer x to my other fingers to my other fingers in y to to my thumb in z.

03:05 I can also go from pointer in z to other fingers in x to thumb in y.

03:11 It works and it keeps doing this forever and ever and ever...

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