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

• prslook26
In summary, the conversation discusses the concept of a "hoversuit" which allows the wearer to control the amount of electrical repulsion or attraction between the suit and a large charged sheet on the Earth's surface. The conversation covers how much charge and whether it should be positive or negative in order for the suit to hover, accelerate upward, and fall at the same rate as on the Moon. The solution involves using Gauss's Law to calculate the electric field and then using the formula F=Eq to determine the necessary charge.
prslook26

## 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)?

## 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.

prslook26 said:

## 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)?

## 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.

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!

prslook26 said:
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!

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!

prslook26 said:
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.

## 1. What is electrical repulsion and attraction between a uniform charge density and an object?

Electrical repulsion and attraction is a force that occurs between charged particles. When a uniform charge density and an object have opposite charges, they will attract each other. On the other hand, if they have the same charge, they will repel each other.

## 2. How is the strength of the repulsive or attractive force determined?

The strength of the repulsive or attractive force is determined by the amount of charge on each particle and the distance between them. The greater the charge and the closer the particles are, the stronger the force will be.

## 3. Can the electrical force between a uniform charge density and an object be calculated?

Yes, the electrical force between a uniform charge density and an object can be calculated using Coulomb's Law, which states that the force is proportional to the product of the charges and inversely proportional to the square of the distance between them.

## 4. How does the presence of other charged objects affect the electrical force between a uniform charge density and an object?

The presence of other charged objects can affect the electrical force between a uniform charge density and an object by either increasing or decreasing the force. The force can be increased if there are other charged objects with the same charge as the object, as they will repel each other and add to the overall force. On the other hand, if there are charged objects with the opposite charge, they may weaken or cancel out the force between the uniform charge density and the object.

## 5. What is the significance of understanding electrical repulsion and attraction between a uniform charge density and an object?

Understanding electrical repulsion and attraction is crucial in many fields of science and technology, such as electromagnetism, electronics, and chemistry. It also helps us to understand the behavior of matter at a microscopic level and how different materials interact with each other. Additionally, this knowledge is essential in the development of various devices and technologies, such as batteries, motors, and generators.

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