Electric field at a point close to the centre of a conducting plate

AI Thread Summary
The electric field near the center of a conducting plate is twice that of a plastic plate with the same charge density, resulting in a field strength of 20 volts per meter. When charge is initially spread on one surface of the conducting plate, it redistributes to achieve electrostatic equilibrium, leading to a uniform charge density of approximately Q/(2A) at the center. The charge density on the conducting plate is half that of the plastic plate, which results in an electric field of 10 volts per meter for the plastic plate. The uniform distribution of charge on both sides of the conducting plate is confirmed, especially near the center. Overall, the discussions emphasize the differences in electric fields and charge distributions between conducting and plastic plates.
Pushoam
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Homework Statement
A charge Q is uniformly distributed over a large plastic plate. The electric field at a point P close to the centre of the plate is 10 volt per metre. If the plastic plate is replaced by a copper plate of the same geometrical dimensions and carrying the same charge Q, the electric field at the point P will become ......
Relevant Equations
For conducting plate
$$ E = \frac { \sigma}{\epsilon_0}$$
For plastic plate
$$ E = \frac { \sigma}{2\epsilon_0}$$
Since the electric field due to a conducting plate is twice the electric field due to a plastic plate having same charge density, the electric field at the point P will be twice in case of conducting plate and hence it is 20 volt per metre.

Is that correct?
 
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A plate has two large parallel surfaces. If you somehow start with all of Q spread on one of the surfaces of the conducting plate, does the charge redistribute itself? If so, when electrostatic equilibrium is established, think about ##\sigma## on each of the surfaces of the conducting plate.
 
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TSny said:
A plate has two large parallel surfaces. If you somehow start with all of Q spread on one of the surfaces of the conducting plate, does the charge redistribute itself? If so, when electrostatic equilibrium is established, think about ##\sigma## on each of the surfaces of the conducting plate.
So, charge density of the conducting plate is half of the charge density of plastic plate hence the electric field will be 10 volt per metre. The charge Q on both plates remain same.
 
Pushoam said:
So, charge density of the conducting plate is half of the charge density of plastic plate hence the electric field will be 10 volt per metre. The charge Q on both plates remain same.
Yes, I believe this is correct.

The charge density on each of the surfaces of the conducting plate will not be uniform, especially near the edges of the plate. However, near the center of a large conducting plate, the charge density on each surface will be approximately uniform and approximately equal to ##\frac Q {2A}##, where ##Q## is the total charge on the plate and ##A## is the area of one of the surfaces.
 
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TSny said:
Yes, I believe this is correct.

The charge density on each of the surfaces of the conducting plate will not be uniform, especially near the edges of the plate. However, near the center of a large conducting plate, the charge density on each surface will be approximately uniform and approximately equal to ##\frac Q {2A}##, where ##Q## is the total charge on the plate and ##A## is the area of one of the surfaces.
Would you please know where you got ##\frac Q {2A}## from @TSny?
 
Callumnc1 said:
Would you please know where you got ##\frac Q {2A}## from @TSny?
Two surfaces, each of area A.
It's not clear to me whether the charge on the plastic plate is on one surface or both, but for the same total charge the field is the same. Both sides.
 
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haruspex said:
Two surfaces, each of area A.
It's not clear to me whether the charge on the plastic plate is on one surface or both, but for the same total charge the field is the same. Both sides.
Thank you for your help @haruspex!
 
haruspex said:
Two surfaces, each of area A.
It's not clear to me whether the charge on the plastic plate is on one surface or both, but for the same total charge the field is the same. Both sides.
The question says uniform distribution. So, I think it is uniformly distributed on both sides.
 
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