Questions on electric potentials of systems and electrons.

[LostShadow]

Homework Statement

3 equal point charges, each with charge 1.55 microColoumb, are placed at the vertices of an equilateral triangle whose sides are of length 0.100 m. What is the electric potential energy of the system? (Take as zero the potential energy of the three charges when they are infinitely far apart.)

Homework Equations

Use = 8.85×10−12 F/m or the permittivity of free space.

The Attempt at a Solution

The answer must be in J. I tried finding equivalences in joules. So far I got..

1 J = VC.

Okay, so we have microC.

But I don't have V..

V = J/C = J/FV = Nm/As = Nm/C.

Homework Statement

The electron orbits the proton at a distance of 0.063 nm.
What is the electric potential of the proton at the position of the electron?
What is the electron's potential energy?

Homework Equations

Well, electric potential of a point chage is 1/4(pi)(epsilon 0) * q/r
And the potential energy of a charged particle is qV.

The Attempt at a Solution

For the electric potential energy, the answer must be in V for some reason. I have q.
For the electron's potential energy, the answer must be in joules.

Still can't find a correlation between V = J/C = J/FV = Nm/As = Nm/C. ;/
A joule = VC, but I still don't have V..

Homework Statement

A thin spherical shell of radius R has total charge Q. What is the electric potential at the center of the shell?

Homework Equations

I don't know what the electric potential energy at the center of a shell is. I know for a charged particle it is U = qV.

The Attempt at a Solution

I'm assuming q is not Q. And I don't have a formula to do an attempt with. We were not given the radius of the shell either. The answer must be in terms of Q, R, and appropriate constants.

On my 4th question, is there anything that is infinite in this universe? Meaning, any places where infinity exists? From what I know, the only thing I can think of is a black hole, which has infinite density. I'm not 100% sure on that.

Thanks.

 

[Mindscrape]

1) Use $$V(r) = k \frac{q}{r}$$ and vectors.

2) You just said the potential energy is qV.

3) What is the electric field at the center of a shell? Think easy.

4) Infinity is a concept. What in the universe is negative? Negative is a concept.

P.S. I'm pretty sure black holes don't have infinite density, but I'm no cosmologist.

 

[LostShadow]

Okay thanks for the equation. That should help me with number 1 and 2.

Well I am still a bit clueless at number 3.

Thanks.

 

[LostShadow]

1.Okay, for the 1st, I have..

Electric potential energy of the system:

V(r) = (-8.85*10^−12 F/m)(1.55 microC * 1.55 microC / .1 m)

Since there are 3 points in a triangle, I cube the answer to get the electric potential energy of that system?

2.And the 2nd:

Electric potential of proton at electron's position: V(r) = (-8.85×10−12 F/m)(+1 * -1 / .063 nm) * 1

Where +1 and -1 are charges of proton and electron.

And the electron's potential energy:

qV, so q = 1, just multiple V(r) by 1?

 

[Mindscrape]

Ah, sorry I probably confused electric potential and potential energy, the equation I gave you is for potential energy (and I made a sign error, sorry I'm used to integral form). Electric potential would be

$$V(\mathbf{r}) = \frac{kq}{|\mathbf{r}|}$$

and then all you do is multiply it by the charge to get the potential energy since electric potential is the potential energy per unit charge (similar to electric field being force per unit charge).

For the second one you are almost right, with my correction you should be able to get there.

For the first one, you have to remember that the distance would be the distance to the center. You might be on the right track.

You may want to search for a couple of examples of electric potential to help you along.

Any ideas on the third one? Think about how the electric field varies on the inside, since the electric field is how fast the voltage, electric potential, changes. Gauss's law should be helpful there.

 

[LostShadow]

Mk.

1. V(r) = (8.85*10^−12 F/m)(1.55 microC / .1 m)

2a. V(r) = (8.85×10−12 F/m)(+1 / .063 nm) * 1

Is q in microC?

2b. qV, so above answer * 1, so same answer.

V = J/C, so the q's are measured by the C units, right?

Thanks.

 

[Mindscrape]

Be careful, the k I used is simply a shorthand for \itex[1/(4\pi\epsilon_0)[/itex], approximately 9*10^9. Think about electric potential the same as you would about electric field. It's merely putting a positive test charge a distance r away from your charge, and building up a scalar function based on all the possible r distances away. Does all that terminology make sense?

So for part one you have built the scalar function correctly for one, and in a sense all, of the charges. You need to put them together though.

The second one is almost good, but you've got some multiplicative constant issues. What's the other charge? What is k?

Third one, is the radial electric field varying as you go out from the center of the shell, on the inside?

 

[LostShadow]

Be careful, the k I used is simply a shorthand for \itex[1/(4\pi\epsilon_0)[/itex], approximately 9*10^9. Think about electric potential the same as you would about electric field. It's merely putting a positive test charge a distance r away from your charge, and building up a scalar function based on all the possible r distances away. Does all that terminology make sense?

So for part one you have built the scalar function correctly for one, and in a sense all, of the charges. You need to put them together though.

1. V(r) = 1 / (4)(pi)(8.85*10^−12 F/m) * (1.55 microC / .1 m)

The second one is almost good, but you've got some multiplicative constant issues. What's the other charge? What is k?

+1?

2a. V(r) = 1 / (4)(pi)(8.85×10−12 F/m) * (+1 / .063 nm) * 1

Third one, is the radial electric field varying as you go out from the center of the shell, on the inside?

I guess so.

Thanks.