Surface charge, electric fields, and capacitance

In summary: B.) and C.) and finally D.).In summary, the conversation discussed the scenario of two large conducting sheets with positive surface charge density, facing each other and separated by a distance d. The first question (a) asked about the field at a point along the central axis of a smaller sheet, when the left sheet is suddenly shrunk to a square with sides equal to d. The second question (b) involved shrinking both sheets to squares and introducing dielectrics with different constants (K1 and K2) and asking about the relationship between E1 and E2 in a series configuration. The third question (c) explored the E-field relationship for a parallel configuration with equally shared contact area. Finally, question (
  • #1
lookingforhlp
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Homework Statement


Two large conducting sheets are charged with a positive surface charge density. They stand vertically facing each other a distance d apart.

a.) suddenly, we shrink the left sheet to a square with sides equal to d, what is the field at the point along the central axis of the smaller sheet a point directly between the two plates?

b.) By shrinking both sheets to a square with sides equal to d, let each sheet have oppositely charged sufaces with two dielectrics (K1, K2). what is the relationship between E1 and E2 for a series configuration?

c.) Alternatively for b) what is the E-Field relationship for a parallel configuration when the sheet's contact area is shared equally?

d.) what is the equivalent capacitance in each case b) c)?



Homework Equations



C = (K*Epsilon*Area)/d

Efield at a point from a surface charge is = integral of kq/r^2 dq

dq = sigma dA

The Attempt at a Solution



I don't really know where to begin with this...I know in between two parallel plate capacitors the field is uniform and it will change with the change in one plate but the question does not explain what the original dimensions are...and when one shrinks that means the field won't be uniform...

But how do I figure out exactly what that is?
 
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  • #2
I want to take this one step at a time so I want to address A.) first
 

1. What is surface charge and how is it measured?

Surface charge refers to the accumulation of electric charge on the surface of an object or material. It is measured in units of coulombs (C) using an instrument called an electrometer.

2. How are electric fields created and what is their role in surface charge?

Electric fields are created by the presence of electric charges. They exert a force on other charges, causing them to move. In the case of surface charge, electric fields play a crucial role in the attraction and repulsion of charges, leading to the accumulation of charge on the surface of an object.

3. What is capacitance and how does it relate to surface charge?

Capacitance is a measure of an object's ability to store electric charge. It is defined as the ratio of the magnitude of the electric charge on an object to the potential difference (voltage) across it. Surface charge is closely related to capacitance, as the accumulation of charge on a surface can increase the capacitance of an object.

4. How does the shape and material of an object affect its surface charge and capacitance?

The shape and material of an object can greatly affect its surface charge and capacitance. Objects with sharp edges or points tend to have a higher surface charge, while materials with high conductivities have higher capacitance. Additionally, the distance between two charged surfaces also affects capacitance, with closer distances resulting in higher capacitance.

5. How does the application of an external electric field affect the surface charge and capacitance of an object?

The application of an external electric field can change the distribution of charge on an object's surface, leading to changes in surface charge and capacitance. The magnitude and direction of the external field can also affect the strength and direction of the surface charge. Additionally, the presence of an external field can also change the capacitance of an object by altering the potential difference across it.

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