∵Give the direction ( ±x, ±y, ±z) of the missing quantity for each of the four electromagnetic w

∵Give the direction ( ±x, ±y, ±z) of the missing quantity...

Key Concepts

Right-Hand Rule

The right-hand rule is a tool used to determine the direction of the missing vector when two perpendicular vectors are known. In the context of electromagnetic waves, pointing the fingers of the right hand in the direction of the electric field and curling them toward the magnetic field results in the thumb pointing in the direction of wave propagation, or vice versa.

Coordinate Systems in Electromagnetism

A coordinate system, typically using x, y, and z axes, is employed to specify the directions of electric and magnetic fields. By assigning positive or negative signs to each axis component, one can precisely indicate the orientation of these vectors in space.

Electromagnetic Waves

Electromagnetic waves consist of oscillating electric and magnetic fields that propagate through space. These fields oscillate perpendicular to each other and to the direction of wave propagation. Understanding the properties of these waves is essential for analyzing how energy is transmitted in various media.

Mutual Orthogonality of Fields and Propagation

One of the fundamental properties of electromagnetic waves is that the electric field, magnetic field, and the direction of propagation are all mutually perpendicular. This means that if two of the directions are known, the third is uniquely determined by their orthogonal relationship.

Transcript

00:01 Alright, this is yet another chance to try out our right -hand rule, and in particular to remember how it applies to electromagnetic waves.

00:11 So right -hand rule, you might remember, means that if we put our pointer finger in the x direction and we point our other fingers along the positive y direction, then our thumb will be pointed in the positive z direction.

00:27 So x, y, z.

00:31 What you can also do with the right hand rule is you can just keep continuing this pattern.

00:37 So for example, if we put our pointer finger in the positive y direction, we put our other fingers in the positive z direction, then our thumb has to be pointed in the positive x direction.

00:50 And i bet you can guess this last example.

00:52 We can just keep going with this.

00:55 If we put our pointer finger in positive x direction, z and our other fingers in positive x, then our thumb has to be in the positive y direction.

01:06 Okay, and we can just keep doing this over and over and over again forever.

01:13 All right, and we can do the same rule with electromagnetic waves.

01:19 We put our pointer in the e direction, and we point our other fingers along the positive magnetic direction, the b direction, then our thumb has to be pointed in the direction of travel, which i like to call v.

01:37 All right? and so we have a table and we can just keep repeating this.

01:43 If we do pointer in e, we do other fingers in b, we do thumb in v, and we can keep repeating this.

01:51 If we do pointer in b, we can do our other fingers in v and our thumb in e.

01:57 All right.

01:59 And similarly, if we put our pointer in v, we can do our other fingers in e and our thumb in the positive b direction.

02:10 So what we've been told for our first problem is that v, the direction of propagation, is positive x.

02:19 And we've been told that the direction of our electric field, e, is positive y.

02:27 And now we need to solve for b.

02:31 Well just like it goes v, e, b, that's a valid direction.

02:36 We can go v, e, b.

02:39 We can just go x, y, z.

02:44 All right.

02:46 Our missing quantity is z.

02:50 Okay, let's see if we can do that again.

02:52 All right.

02:53 In our next problem, we've been told the direction of propagation.

03:00 So we know v, all right and this time we don't know e oops but we do know b so i'm actually going to write this in a different way because we go b and then v and then e so if we go b and then v and then e we'll know our rule so the magnetic field is positive y and the direction of travel is positive x so what is e? well, we don't go y and then x.

03:42 We go x and then y.

03:45 So that means that z can't come in this missing spot.

03:50 Instead, it has to be negative z because we got the order wrong...

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