No Current Flow with Negatively Charged Plate & Resistor

• MotoPayton
In summary, in order for electrons to flow in a circuit, there must be a closed path from the positive battery terminal to the negative battery terminal. If just a negatively charged plate is connected with a resistor and a ground connection, electrons will flow until the potentials equalize. However, for a realistically-sized plate, even a large resistance won't give a very impressive time constant. Without a closed circuit, the voltage cannot continuously replenish itself and there will be little to no flow of electrons.

MotoPayton

If you had a negatively charged plate connected to a wire that had a resistor and on the other side of the resistor was a ground connection would electrons not flow?

I tried this at home with one side of a battery and couldn't measure any current on my voltmeter.

MotoPayton said:
If you had a negatively charged plate connected to a wire that had a resistor and on the other side of the resistor was a ground connection would electrons not flow?

I tried this at home with one side of a battery and couldn't measure any current on my voltmeter.

No continuous current will flow unless there is a circuit -- literally a closed path, from the positive battery terminal to the negative battery terminal. Any initial (very) brief current that flows when the wire is first connected to ground would be due to static electric potential difference between the battery as a whole and ground. This is akin to rubbing your feet across a carpet and touching a conductive object at a different static potential (such as a doorknob or your annoying brother). Note that the battery, taken as a whole, is a net neutral object unless you put a static charge on it.

So it must be a closed path for a battery but what if I had just a negatively charged plate(no battery) connected in the same way. Shouldn't current flow to ground through the resistor until the plate is nuetral correct?

MotoPayton said:
So it must be a closed path for a battery but what if I had just a negatively charged plate(no battery) connected in the same way. Shouldn't current flow to ground through the resistor until the plate is nuetral correct?

Current would flow until the potentials equalize, yes. It would have to be an enormous plate for the current to last more than a brief instant (think "spark").

Wouldn't the resistor prevent the charge from distributing instantly? If it was all conducting and 0 resistance I would agree...

MotoPayton said:
Wouldn't the resistor prevent the charge from distributing instantly? If it was all conducting and 0 resistance I would agree...

Sure. But for a realistically-sized plate and the amount of charge you can put on it without it leaking off into the air by corona discharge, even a really large resistance (practically an insulator) won't give you a very impressive time constant.

For example, the self-capacitance of a circular disk is given by $8 \epsilon_o r$. How large must the radius be to give a capacitance of 1μf?

Ok wow that's really helpful. Gonna do some problems related to this and get back to you

So even at 3*10^6 volts the amount of charge on a 1 meter radius disc is microcoloumbs... I had no idea.

So if the circuit is not closed and the voltage cannot continuously replenish itself like in the case of a battery you have nothing.

MotoPayton said:
So even at 3*10^6 volts the amount of charge on a 1 meter radius disc is microcoloumbs... I had no idea.

So if the circuit is not closed and the voltage cannot continuously replenish itself like in the case of a battery you have nothing.

Well, not nothing exactly, but certainly something that comes pretty close to it

Of course, static electric sparks, however brief and however little charge and current involved, can be pretty noticeable on a dry winter's day!