Question About infinitely large charged plate

[BERGXK]

In my MCAT review book there is a problem that is bugging me.

If the distance between a point charge and an infinitely large charged plate is increased by a factor of 2, t he new force on the point charge will be?

The answer is it will remain the same.

Why is this? Isn't the force on a charged particle dependent on the charges on both the plate and the particle and the distance between them? F=kqq/r^2

Also 2 charged plates can create a potential difference. The mcat book does not provide a way to calculate the electric field without knowing the force. But is the force created by each plate individually acting on the particle in the middle by F=kqq/r^2 and then summing the forces or is the electric field created by the two plates? Can someone also explain how this works?

Thanks a lot!

 

[Doc Al]

F=kqq/r^2

That tells you the force between two point charges--not relevant here. Instead, think of the field produced by the charged plate and the force that field exerts on the point charge. (What's the field from a charged plate?)

 

[tiale11]

this all comes back to the basiscs of calculus. You said that the second charge was infinitely large. That means that the number is so large that there will be no difference in the force exerted on the point charge no matter it's distance from the other.
Ill try to put it in turms of number
q1=9.5*10^100000 google coulombs
q2=1.1micro coulombs
r=5m

now if you double the distance will the force change much?
no, not at all. it will change a bit because q1 has a real value put to it. but in the case of your problem, when q1 is infinitely large it is bigger than any number than you can imagine and really is a limit to itself. therefore it is kinda like saying that if you increase the distance the value of q1 will "also increase" (its infinity) to make the force remain the same again.
did that help you at all?

 

[tiale11]

im sorry BERGXK,
i forgot to answer you second question. To find the electric field, you do not need to know the force acting on the point charge. An electric field is define as the force per point charge. In other words it's F/q1.
On the other and, a votage AKA "potential difference" is expressed as an electric field * the distance between the 2 charges. V=(F*r)/q1
so now, if you want to find the electric field, all you have to do is divide the potential difference by the distance between the two charges. you get this E=V/r
have fun using this.
BTW these equations were derived from Coulombs Law : F= K*q1*q2/(r^2)
have fun!
:)

 

[Nick89]

Just look at the problem from a geometric view. No equations needed at all.

Imagine an non-infinitely large plate. Then imagine that you are a point charge somewhere near the plate.
If you move away from the plate, what will seem to happen to it? It will seem to shrink, because you go further away from it.

Now imagine the same scenario but with an infinitely large plate. If you move away from that, what happens? Nothing! The plate is infinitely large (not just very large, but infinitely large) so it does not matter how far you move away from it, from a geometric point of view, nothing changed.

 

[BERGXK]

Thanks for all your answers guys but i think I understand it Qualitatively but not quantitatively yet.

I keep thinking of charges as mass and electric fields are acceleration is this correct to assume? But I still can't really grasps what voltage is.

Here is the answer in the back of the book:
The electric field above an infinitely large electric plate remains constant with distance. You can visualize this by imagining the electric field lines are perpendicular to the plate and have nowhere to spread. By bending in one direction or another they would increase their distance from one line, only to decrease their distance from another line. Since the lines would remain at an equal distance from one another, the electric field will remain constant.

But doesn't electric field strength vary with distance? If the electric field is the Force divided by the charge at a certain point right what is the force? Isn't the force an attraction or repulsion of the charges? Even though this is a plate the plate has charges on it that repel or attract the charged particle right? The force and the electric field would vary with distance and will vary over time as the charges move right? Does a Charged plate have an electric field if there are no other charges near it?

Is there anything wrong with my reasoning?

I understand the reasoning behind the infinitely large plate but if the plate was limited would 2x the distance change the electric field strength and force on the charge?

 

[Doc Al]

Thanks for all your answers guys but i think I understand it Qualitatively but not quantitatively yet.

Have you studied the field from an infinitely large charged plate? Look it up!

Try this: http://hyperphysics.phy-astr.gsu.edu/Hbase/electric/elesht.html#c1"

Here is the answer in the back of the book:
The electric field above an infinitely large electric plate remains constant with distance. You can visualize this by imagining the electric field lines are perpendicular to the plate and have nowhere to spread. By bending in one direction or another they would increase their distance from one line, only to decrease their distance from another line. Since the lines would remain at an equal distance from one another, the electric field will remain constant.

OK.

But doesn't electric field strength vary with distance?

From a simple point charge, sure--but not from an infinite sheet of charge. You cannot treat all charge configurations as if they were solitary point charges.

If the electric field is the Force divided by the charge at a certain point right what is the force? Isn't the force an attraction or repulsion of the charges? Even though this is a plate the plate has charges on it that repel or attract the charged particle right? The force and the electric field would vary with distance and will vary over time as the charges move right? Does a Charged plate have an electric field if there are no other charges near it?

Of course a charged plate has a field, regardless of any other charges that may be around.

FYI: I would suggest that you disregard tiale11's posts #3 & 4 in this thread; that is not a useful way to understand things.

 

[BERGXK]

Oooo I think i finally understand. Its all about the charge density on the sheet right? In a infinitely large sheet the charge is infinite so to calculate the field they use Gauss' law? Which gives a electric field strength over area ratio right? The amount of charge is infinite but the electric field over area is constant based on density?

My question is if the plate is not infinite and limited could we just do something like center of mass and find center of charge and find the electric field from that? Something tells me we still must consider the charge density but what determines the density of the charges? the strength of the charges? If a charged plate has charges the charges must spread out but how do we calculate how much they spread out? Do you also have to consider the area of the particle?

 

[JaWiB]

Here is the answer in the back of the book:
The electric field above an infinitely large electric plate remains constant with distance. You can visualize this by imagining the electric field lines are perpendicular to the plate and have nowhere to spread. By bending in one direction or another they would increase their distance from one line, only to decrease their distance from another line. Since the lines would remain at an equal distance from one another, the electric field will remain constant.

That last sentence doesn't make sense to me. If the lines were bent, then they would not longer be at equal distance from each other...

I would have thought about it differently. The lines can't be anything other than perpendicular to the plate and parallel to each other, because anything else would give preference to some direction or position. Since the plate is infinite/uniform charge, we shouldn't be able to tell one direction or position from another (for example, if all the lines curved outward that would imply a center to the plate, which doesn't make sense)

My question is if the plate is not infinite and limited could we just do something like center of mass and find center of charge and find the electric field from that? Something tells me we still must consider the charge density but what determines the density of the charges? the strength of the charges? If a charged plate has charges the charges must spread out but how do we calculate how much they spread out? Do you also have to consider the area of the particle?

I'd guess you'd need to set up an integral. You can find the electric field essentially by summing the electric fields from an infinite number of point charges. Or maybe by summing an infinite number of lines of charge?