Electrical repuls./attract. btwn uniform charge density and object

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Homework Statement


Imagine that you've been invited to try out a new "hoversuit," and here's how it works:

Someone has set up a large flat sheet, many kilometers across, somewhere on the Earth, and they've charged the sheet up to a uniform charge density σ = +2 x 10^-6 C/m^2. You are issued a special suit that you wear, and it has controls on it which allow you to charge the suit up to any number of Coulombs (C), positive or negative, that you might want. The idea is that you can control the amount of electrical repulsion (or attraction) between the suit and the charged sheet below you.

(a) How much charge (and is it positive or negative) must you give the suit if you want to be able to just hover stationary above the charged sheet? Give your answer in Coulombs (C).

(b) How much charge (and is it positive or negative) must you give the suite if you want to "fall up," that is, accelerate upward at the same rate that objects normally accelerate downward due to Earth's gravity.

(c) How much charge (and is it positive or negative) must you give the suit if you want to fall down toward the sheet, but at the same rate as if you were on the Moon (remembering that the gravitational acceleration on the Moon is 1/6 what it is on Earth)?


Homework Equations





The Attempt at a Solution



(a) If this is a parallel plate capacitance problem and the given charge is the bottom plate then the upper plate (the suit), if it is to hover, should have the same charge but negative. This way the two "plates" can remain close without pushing each other away.

-2 x 10^-6 C/m^2

(b) Objects normally accelerate downward toward the Earth at the rate of 9.8 m/sec^2. If the suit is to "fall up", that is, accelerate upward, then it must have a positive charge because then it will be repelled by the positively charged sheet.

(c) On this one, I am totally lost. If the gravitational acceleration on the Moon is 1/6 what it is on Earth, then the rate should be 1.63 m/sec^2.

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
gneill
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2,866

Homework Statement


Imagine that you've been invited to try out a new "hoversuit," and here's how it works:

Someone has set up a large flat sheet, many kilometers across, somewhere on the Earth, and they've charged the sheet up to a uniform charge density σ = +2 x 10^-6 C/m^2. You are issued a special suit that you wear, and it has controls on it which allow you to charge the suit up to any number of Coulombs (C), positive or negative, that you might want. The idea is that you can control the amount of electrical repulsion (or attraction) between the suit and the charged sheet below you.

(a) How much charge (and is it positive or negative) must you give the suit if you want to be able to just hover stationary above the charged sheet? Give your answer in Coulombs (C).

(b) How much charge (and is it positive or negative) must you give the suite if you want to "fall up," that is, accelerate upward at the same rate that objects normally accelerate downward due to Earth's gravity.

(c) How much charge (and is it positive or negative) must you give the suit if you want to fall down toward the sheet, but at the same rate as if you were on the Moon (remembering that the gravitational acceleration on the Moon is 1/6 what it is on Earth)?


Homework Equations





The Attempt at a Solution



(a) If this is a parallel plate capacitance problem and the given charge is the bottom plate then the upper plate (the suit), if it is to hover, should have the same charge but negative. This way the two "plates" can remain close without pushing each other away.

-2 x 10^-6 C/m^2
No, your premise is incorrect. The plates of a parallel plate capacitor attract each other due to the charge difference. They are kept separate by mechanical means, either the plates are restrained or a dielectric between them prevents them from closing together.

(b) Objects normally accelerate downward toward the Earth at the rate of 9.8 m/sec^2. If the suit is to "fall up", that is, accelerate upward, then it must have a positive charge because then it will be repelled by the positively charged sheet.

(c) On this one, I am totally lost. If the gravitational acceleration on the Moon is 1/6 what it is on Earth, then the rate should be 1.63 m/sec^2.

The "large flat sheet" probably appears infinite in extent for all intents and purposes here. Look up (or derive) the electric field produced by an infinite sheet of charge with a given charge density.
 
  • #3
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Thank you so much!

Finally, I have an idea on how to approach this. So, if the "large flat sheet" is infinite in extent, could I find electric field by using Gauss's Law, E=2∏kσ? And since the charge of the sheet is positive, the field would be directed radially out out from the line.

E=2∏(8.99x10^9)(2x10^-6)
=1.13x10^5 N/C

In order for the "suit" to hover, it must experience Electric force, which due to electric field is equal to E*q.

W=mg (but I don't have the weight of the suit, should I come up with a weight, say 100kg?)

Hence, mg=E*q

q=E/mg
= (1.13x10^5)/(100)(9.8)
= +115.3 C

Does this sound right?

Will this charge make the suit "hover" or accelerate upward?


Again, thank you SO MUCH for your help on this! I have spent hours and hours trying to figure this out, you have no idea what a relief it is to have some sort of breakthrough!

Thank you thank you!
 
  • #4
gneill
Mentor
20,925
2,866
Thank you so much!

Finally, I have an idea on how to approach this. So, if the "large flat sheet" is infinite in extent, could I find electric field by using Gauss's Law, E=2∏kσ? And since the charge of the sheet is positive, the field would be directed radially out out from the line.

E=2∏(8.99x10^9)(2x10^-6)
=1.13x10^5 N/C
Good.

In order for the "suit" to hover, it must experience Electric force, which due to electric field is equal to E*q.

W=mg (but I don't have the weight of the suit, should I come up with a weight, say 100kg?)
Sure. I suppose that wouldn't be too far off an estimate of the combined weight of the person + suit.

Hence, mg=E*q

q=E/mg
= (1.13x10^5)/(100)(9.8)
= +115.3 C

Does this sound right?
Watch your algebra! What's q equal to? You can always check your work by keeping track of the units through the math.

Will this charge make the suit "hover" or accelerate upward?
When the forces balance there's no acceleration. So hover it will be (after you get the algebra straightened out).
Again, thank you SO MUCH for your help on this! I have spent hours and hours trying to figure this out, you have no idea what a relief it is to have some sort of breakthrough!

Thank you thank you!

Glad to help!
 
  • #5
6
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Thank you!

I see the mistake I've made:

q=mg/E
=(100)(9.8)/(1.13x10^5)
=8.67x10^-3 C

Would the gravitational acceleration be negative, since it is balancing the Electric Force, which is pointing upward?


In order for the "hoversuit" to accelerate upward, the strength of the Electric Force must be greater than the strength of the Gravitation Force, correct? Which means the charge of the "hoversuit" must be increased but by how much? This is something I'm still struggling with. If Fe must be greater than Fg, and the acceleration upward would equal the acceleration downward, due to Earth's gravity, does this mean that all I have to do is change the charge on the "hoversuit", from negative to positive? This way, the positive suit would be repelled from the positively charged field?

I apologize if I'm overwhelming, this assignment is really important to me.

Thank you so much for your help!
 
  • #6
gneill
Mentor
20,925
2,866
Thank you!

I see the mistake I've made:

q=mg/E
=(100)(9.8)/(1.13x10^5)
=8.67x10^-3 C

Would the gravitational acceleration be negative, since it is balancing the Electric Force, which is pointing upward?
You get to choose by selecting the coordinate system that you employ. If you choose "up" to designate the positive direction, then gravitational acceleration which is downwards will be negative. So when you write out the net force acting on the suited man, the sum would be:

##F_{net} = F_e + F_g##

##F_{net} = q E - m g##

In order for the "hoversuit" to accelerate upward, the strength of the Electric Force must be greater than the strength of the Gravitation Force, correct? Which means the charge of the "hoversuit" must be increased but by how much? This is something I'm still struggling with.
Newton's Laws, and in particular, Newton's 2nd law. A body accelerates due to the net force acting on it.

If Fe must be greater than Fg, and the acceleration upward would equal the acceleration downward, due to Earth's gravity, does this mean that all I have to do is change the charge on the "hoversuit", from negative to positive? This way, the positive suit would be repelled from the positively charged field?
The suit was already positively charged in order to hover. To accelerate you need make the net force be positive (upward). Larger net force upward means larger acceleration upward.
 

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