You measure the magnetic field strength of a traveling electromagnetic wave to be 8.0×10−7T8.0\times10^{-7}T , oriented along the +x direction. If this EM wave moves in the +y direction, what is the magnitude and direction of the wave's electric field at that same exact spot?

240NC240\frac{N}{C}240CN in the +z direction

You measure the magnetic field strength of a traveling electromagnetic wave to be 8.0 × 10 − 7 T 8.0\times10^{-7}T , oriented along the +x direction. If this EM wave moves in the +y direction, what is the magnitude and direction of the wave's electric field at that same exact spot?

Hey, folks. Let's get some more practice here. So we're told that the magnetic field of a traveling electromagnetic wave is 8 times 10 to the negative 7 Tesla, and it points along this the plus x direction. So I'm actually just gonna go ahead and start drawing this stuff out here. So I've got a sort of three-dimensional coordinate system like this. This is gonna be my plus x. This will be my plus y, plus my plus z. Now we're told that the magnetic field points along the plus x direction, so in other words, it points in this direction here. The strength is 8 times 10 to the minus 7 tesla. Now what we wanna do is we wanna figure out not the direction that the wave is traveling, because we already have that. We're told that the wave is moving in the plus y direction. So in other words, it points in this direction here. What we wanna do is we actually wanna figure out the magnitude and the direction of the electric field here. So in other words, basically, where our fingers are pointing. Alright? So where's the electric field? Now we're gonna go ahead and start off with the direction first because it's a little bit simpler. We just use the right hand rule for that. Alright? So here, I've got my, my my two sort of directions for, the b field and the wave's speed. So how do I figure out which way the electric field is pointing? There's basically just a couple of directions here, but we're a couple of different options, but we're gonna use our right hand rule. So let's for for example, let's just guess that it's pointing off in this direction and use our right hand rule to check. Now what happens is if you point your your hand sort of away from you, your fingers like this, and you curl them towards your magnetic field, what you should see is that your thumb is actually gonna be pointing downwards. So this definitely can't be the right answer because, then our thumb would be pointing downwards, and it's actually pointing upwards here. So let's keep going. Now it definitely can't be in this direction either because remember that the electric field and the magnetic field should always be at right angles to each other. They should always make a 90 degree angle. So definitely can't be in this direction here. So what about in this direction down like this? So let's try that. Now if you were to do this, basically, what happens is you would actually point your fingers downward like this, and you would curl them up towards b. What you should see is that your thumb would be pointing at this direction, which it's definitely not, so therefore, it definitely can't be the right answer. So the only other option is that it points in the plus z direction, and hopefully, you guys got that. Now you can check this again by using your right hand rules. What I want you to do is I want you to sort of point your fingers towards you like this, and then when you curl them by the way, you always wanna do this with your right hand. When you curl them towards you, basically, your thumb should be pointing up, and that exactly makes sense. Alright? So that's the electric field, definitely points in the plus z direction. So this is gonna be the plus z direction. So now that we've taken care of the direction, let's find now the magnitude. Remember that the magnitude, we always solve for the the electric field or the magnetic field by using this equation here that relates the strengths of the fields. Alright? So in other words, we know it's the z direction. Now we just need to calculate e, so we just multiply c times b. Very straightforward. So in the words, this is just gonna be e, equals c b. So in other words, it's just gonna be 3 times 10 to the 8th, then you multiply this by, the magnetic field, which is 8 times 10 to the minus 7. And when you work this out, what you should get is 240 Newtons per Coulomb. So in other words, it's 240, Newtons per Coulomb, and it points in the plus z axis, alright, or z direction. That's it for this one, folks. Let me know if you have any questions.

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You measure the magnetic field strength of a traveling electromagnetic wave to be 8.0×10−7T8.0\(\times\)10^{-7}T , oriented along the +x direction. If this EM wave moves in the +y direction, what is the magnitude and direction of the wave's electric field at that same exact spot?

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You measure the magnetic field strength of a traveling electromagnetic wave to be $8.0 \times 10^{- 7} T$ , oriented along the +x direction. If this EM wave moves in the +y direction, what is the magnitude and direction of the wave's electric field at that same exact spot?