How High Can Electrical Potential Get Near Large Charges?

[Latsabb]

The problem is to find the potential at a point that is 3 meters away from two charges. (one 3 meters above, and the other 3 meters below)

q1=3μC
q2=6μC

I put that Ep=Epq1+Epq2

Epq1=K*q1/r1
Epq2=K*q2/r2

K=1/(4πε₀)=8.988x10⁹

This gives me:

Epq1=8.988x10⁹*(3x10^-6/3)=8988J

Which immediately set some bells off for me. Isnt that quite a bit of energy for a charge three meters away? By the same formula, Epq2 equals 17976J, for a total potential of 26964J. Maybe I am wrong, but it seems like a very high potential. I will admit that I haven't wrapped my head around how large of charge a Coulomb is, so maybe 3μC and 6μC are very large amounts of charge, but something seems wrong to me...

Can someone take a look, and see if I did something wrong? Thank you.

 

[TSny]

Hello, Latsabb.

Note that you are calculating potential, not potential energy. The unit of potential is not J.

A μC is a large amount of charge for a particle. So, a large value of potential in this problem is to be expected.

 

[Latsabb]

Ok, thank you. Being that I am not calculating potential energy, that would make this... Volts? So I should be replacing my Ep's with V?

 

[TSny]

Yes. So, you are getting some "high" voltages because your charges are on the order of a few μC and your distances are on the order of a few meters.

 

[HalfLostAndSearching]

I would like to point out that your calculations are correct. The high potential you have calculated is due to the relatively large values of the charges (3μC and 6μC). It is important to note that electrical potential is directly proportional to the amount of charge present, so the higher the charge, the higher the potential will be. In this case, both charges are relatively close to the point of interest (3 meters away), which also contributes to the high potential.

To put things into perspective, a Coulomb (C) is a unit of electric charge equal to approximately 6.24 x 10^18 elementary charges (e). So 3μC and 6μC would correspond to approximately 1.87 x 10^19 e and 3.75 x 10^19 e, respectively. These are indeed large amounts of charge, which is why the potential is also high.

In conclusion, your calculations are correct and the high potential is a result of the relatively large values of the charges involved. It is important to keep in mind that electrical potential is a measure of the potential energy per unit charge, so a high potential does not necessarily mean a dangerous or harmful situation.