Max surface charge of a conductive plate

[Bhope69199]

1. Can I use the surface charge equation:

$$Q = \frac{Vk\epsilon_0A}{d}$$

Where V = Voltage, k = dielectric constant, ϵ0 = permittivity of free space , A = Area of plate and d = distance between plates.

For a conductive plate within an electric field? My thinking is that if the plate is placed within an electric field, then grounded, it essentially becomes the lower potential plate of the electric field generating system. There would no longer be an electric field between the original lower potential plate and the conductive plate placed within the electric field.

2. If this plate is grounded the charge Q will flow to the ground in order to ensure that the plate and ground are at the same potential. If this electric field is constant would there be a continuous flow of charge Q to the ground?

3. If not, how much charge would flow to the ground and is there an equation that relates the size of the plate and the charge that would flow to the ground if it wasn't Q and what effect does the electric field have (i.e does it increase the charge on the surface? or does the need for the potential to be the same as ground negate this effect?)

 

[BvU]

Hi,

the surface charge equation:
$$Q = \frac{Vk\epsilon_0A}{d}$$
Where V = Voltage, k = dielectric constant, ϵ0 = permittivity of free space , A = Area of plate and d = distance between plates.

For a conductive plate within an electric field?

Seems you are asking this for a single plate, so :
What $d$ do you have in mind ?
And what $V$ ?

If you are asking what happens when a single unconnected conducting flat plate is placed in an electric field $\vec E$ (with the surface of the plate $\perp\ \vec E$ ) : make a sketch and ask yourself about the field inside the plate.

 

[Bhope69199]

In both cases where d is larger than A and d is much smaller than A? V is say 1000V.

The field inside the plate of a conductor within an electric field would be zero. So the charge on the plate would be zero in that case. But if it was grounded surely it would become the lower potential plate so therefore it would have a charge associated to it?

 

[BvU]

d is much smaller than A

$d$ and $A$ cannot be compared: they have different dimensions.

So are we talking about ONE or TWO plates now?

For a conductive plate within an electric field?

It becomes a little tiring to write IF single plate then ... else if two plates then ... Still don't see no picture ...

 

[Bhope69199]

I've found an answer to question 1. from this link - https://physics.stackexchange.com/questions/108231/charge-distribution-on-plates

Question 2. Does this charge flow continuously or only once? Am I correct in thinking that it only flows once there is no charge on the outer plates, in order to reach equilibrium.

Question 3. Is there a relationship of plate area to charge? Yes - it is just the original surface charge equation.

 

[BvU]

DId I post in vain ? Or were my questions unclear ?

 

[Bhope69199]

DId I post in vain ? Or were my questions unclear ?

I was going to add a picture then found that link. I think it answers your questions and have thought about my initial questions with regards to that answer. If my thinking is wrong please tell me. If it doesn't answer your question I didn't understand what you were asking for.

 

[BvU]

Ah, so now instead of 1 or 2 plates (still unclear !) we are up to three and we don't worry about $\vec E$ any more. Glad you are happy. Let's assume we saw different things to focus on. Can happen in a forum, so don't worrry.

 

[Bhope69199]

I think I see where I didn't explain it properly, sorry about that.

Would the surface charge equation differ if we had two plates (Say plates B and C in the link and plate C was at 1000V) ?