How to calculate electric charge with a given electric potential?

In summary: Thanks for your reply!In summary, the iron plate has a potential of +20 kV and has a capacitance of 8εr.
  • #1
Bobcent
31
0
Hi!

An iron plate with a mass of 1 kg surrounded by vacuum has an electric potential of +20 kV. How do I calculate the charge, Q of the iron plate?

I have all the information I need, right?
 
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  • #2
You also need the shape of the plate (thickness, diameter). And I don't know if you are talking about self capacitance here or if the plate is near another plate.
http://en.wikipedia.org/wiki/Capacitance#Self-capacitance
The charge of the plate is the electric potential times it's capacitance.
 
  • #3
Thanks for your reply!

The iron plate is not near another plate, so I'm talking about self capacitance.

But I don't have the capacitance.

Is the capacitance a value based on the shape and the electric properties of the material? How do I calculate it?

Say that the shape of the 1 kg iron plate is a square with an area of 0.225 m^2. That makes the thickness 0.0025 m since the density of iron is 7874 kg/m^3.
 
  • #4
It is going to be pretty complicated expression because it is not a highly-symmetric object. (For example, a sphere would give a nice answer). But for your problem, there is still an exact answer. Assuming the charges in the object are fixed, we than have the electrostatic equation:
[tex]\nabla^2 \phi = - \frac{\rho}{\epsilon_0} [/tex]
This is the 'exact answer' I was talking about. From here, it gets a bit complicated, because the charge distribution rho does not follow a simple symmetry. Of course, you could take the limit of some point near the surface of the object, in which case, you can get a simple (approximate) answer.
 
  • #5
Thanks for your reply Bruce, and happy Easter!

Is there a difference in charge distribution for a positively charged object compared to a negatively charged object? The iron plate would be positively charged if that makes any difference.
 
  • #6
Did you look at the wikipedia page for self capacitance? For a circular disc it's approximatly 8εr. r is the radius of the disc and ε = 8.85× 10−12 F/m. The thickness doesn't matter as long as the radius is much bigger than the thickness. So a thin big plate will have a larger capacitance than a small thick one.
 
  • #7
the only difference in the potential for a positively or negatively charged plate is that the sign of the potential would be opposite. (using the convention that the potential at infinity is zero). Also, DrZoidberg brings up a good point. (p.s. I'm a futurama fan too). I guess that for a circular disk, you can use a cylindrical coordinate system, and take the approximation that the disk is very flat, then I guess it is not too difficult to do the calculation. I have not done this calculation myself, but I would guess that is the general idea.
 

1. How do you calculate electric charge using electric potential?

To calculate electric charge using electric potential, you can use the formula Q = CV, where Q is the electric charge, C is the capacitance, and V is the electric potential.

2. What is the unit for electric charge?

The unit for electric charge is the Coulomb (C), which is equivalent to the charge of approximately 6.24 x 10^18 protons.

3. Can electric charge be negative?

Yes, electric charge can be negative. An object with an excess of electrons will have a negative charge, while an object with a deficiency of electrons will have a positive charge.

4. How is electric potential related to electric charge?

Electric potential is directly proportional to electric charge. This means that as the electric charge increases, the electric potential also increases.

5. What is the difference between electric potential and electric potential energy?

Electric potential is the electric potential energy per unit charge at a given point, while electric potential energy is the energy that a charged particle possesses due to its position in an electric field.

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