EM Waves - Would the bulb glow?

[jlmccart03]

Homework Statement

A long, thin steel wire is cut in half, and each half is connected to a different terminal of a light bulb. An electromagnetic plane wave with E and B moves past the wire as shown.

Part B: Suppose the wire were oriented parallel to the y-axis, as shown above. WOuld the bulb glow in this case? Explain.

Part C: Suppose instead that the wire were positioned as described below. WOuld the brightness of the bulb be greater than, less than, or equal to the brightness that it had in parb b? Explain in each case.
(i):The wire is parallel to the y-axis but with its bottom end located on the x-axis
(ii):The wire is tilted so that it makes an angle of 40 degrees with respect to the y-axis but is still aprallel to the y-z plane.

Homework Equations

Conceptual besides the EM wave equations:
E = E₀sin(kx-ωt)(y-hat)
B = B₀sin(kx-ωt)(z-hat)

The Attempt at a Solution

For part b I said that yes it would light up because it is at a 0 degree angle to the E wave and parallel so that would make it light up. If it were perpendicular then the bulb would not light up.

For part c (i) I said that yes it would light up but it would be less than that of the part b brightness because it is perpendicular to the E wave, but half the length as described.

For part c (ii) I said that the wire would be brighter since it is at a 40 degree angle, but I really don't feel confident with this answer as I was basing it on the degrees only.

Thanks for any help!

 

[TSny]

For part b I said that yes it would light up because it is at a 0 degree angle to the E wave and parallel so that would make it light up. If it were perpendicular then the bulb would not light up.

Good.

For part c (i) I said that yes it would light up but it would be less than that of the part b brightness because it is perpendicular to the E wave, but half the length as described.

You are dealing with a plane wave. If you pick any plane that is perpendicular to the x-axis and you pick some instant of time, how do E and B vary as you move to different points of this plane?

For part c (ii) I said that the wire would be brighter since it is at a 40 degree angle, but I really don't feel confident with this answer as I was basing it on the degrees only.

How should E be oriented relative to the wire in order to produce maximum brightness? You already stated that if the wire is perpendicular to E, then the bulb would not light up. How should the wire be oriented in order for E to be most effective in moving charge in the wire?

 

[jlmccart03]

Good.

You are dealing with a plane wave. If you pick any plane that is perpendicular to the x-axis and you pick some instant of time, how do E and B vary as you move to different points of this plane?How should E be oriented relative to the wire in order to produce maximum brightness? You already stated that if the wire is perpendicular to E, then the bulb would not light up. How should the wire be oriented in order for E to be most effective in moving charge in the wire?

OHHHHH I forgot about the plane wave situation. It doesn't matter where you are in the plane wave as long as you are perpendicular since it is moving at some speed c. So for part c (i) I would say it is equal to that of part b since it is parallel to the y-axis exactly like it is in part b.

For part c (ii) I want to say at a 45 degree angle the bulb is lit the most, but I think that is wrong since wouldn't it be best at 0 degrees as seen in part b? This wway the wave and the wire are exactly parallel and through it the moving charges are most effective in the wire. Because simply put we want the electrons to be moving up and down at their maximum to create a current and if the angle is 0 degrees then that would be the most maximum right? SO in this case we would have a less brightness than that of part b?

 

[TSny]

OK for both c(i) and c(ii), although I don't understand the phrase "as long as you are perpendicular since it is moving at some speed c". The force that drives the charge in the wire is the electric force F = qE. But only the component of this force that is parallel to the wire is effective. So, you want to orient the wire so that the component of E along the wire is maximum. That would clearly be when the wire is parallel to E.

 

[jlmccart03]

OK for both c(i) and c(ii), although I don't understand the phrase "as long as you are perpendicular since it is moving at some speed c". The force that drives the charge in the wire is the electric force F = qE. But only the component of this force that is parallel to the wire is effective. So, you want to orient the wire so that the component of E along the wire is maximum. That would clearly be when the wire is parallel to E.

Oh poor wording. I meant that since the wave is moving at the speed c (light) then your location within the plane doesn't matter but rather your angle. I was referring to the fact that the wave is moving.

 

[Charles Link]

The problem I think is designed to teach the student about the electric field in electromagnetic waves, but in practice, the scenario with a wire and a light bulb and getting it to glow with an electromagnetic wave is not readily achieved. Getting even a 7 watt night light type bulb to glow in this manner would take a tremendous amount of radio frequency or microwave power. The power levels in the radio frequency or microwave beam would need to be so high that it would be unsafe to try to conduct such an experiment. e.g. when an antenna is used to pick up radio waves and convert the signal (voltage) into music, etc., typical power levels received by the radio antenna would be at the nanowatt or microwatt level.

 

[jlmccart03]

The problem I think is designed to teach the student about the electric field in electromagnetic waves, but in practice, the scenario with a wire and a light bulb and getting it to glow with an electromagnetic wave is not readily achieved. Getting even a 7 watt night light type bulb to glow in this manner would take a tremendous amount of radio frequency or microwave power. The power levels in the radio frequency or microwave beam would need to be so high that it would be unsafe to try to conduct such an experiment. e.g. when an antenna is used to pick up radio waves and convert the signal (voltage) into music, etc., typical power levels received by the radio antenna would be at the nanowatt or microwatt level.

Interesting didn't really think about it that way! I find these tutorials ultra useless in helping teach certain topics honestly. I would much prefer doing an actual experiment designed to teach these concepts and then let the student write a report such in a way to convey the ideas through personal interaction rather than conceptual design.

 

[TSny]

For a demonstration using a miniature light bulb, see starting at time 14:33

 

[Charles Link]

@TSny Thank you. A very interesting video. I guess I stand corrected, but in general anyone doing experiments such as these does need to be somewhat careful. At times he is working with some rather high voltages (in his transformers), and is generating some pretty hefty radio waves. In any case very interesting. :) :)