I.The Electric Field Near Sheets and Plates with Charge
Physics Laboratory
Capacitance Tutorial
I.The electric field near sheets and plates with charge
A.A small portion of a large sheet (single layer) of charge is shown to the right. Suppose the sheet of charge has a net charge Q uniformly distributed over an area A. In terms of Q, A, and constants:
- write an expression for the charge density for this sheet.
- write an expression for the electric field to the left and right of the sheet, and indicate the directions of these fields.
B.A small portion of a large thin conductingplate is shown to the right. Eachside of the plate has a charge Q that is uniformly distributed over an area A. In terms of Q, A, and constants, write an expression for the charge density on each side of the conducting plate.
Draw the electric field vectors at point P (inside the conducting plate) due to the charges on the surfaces of the plate, and find the resultant electric field inside the conductor due to the charge on the plate.
Is your answer consistent with your knowledge of the electric field inside a conductor?
Find the resultant electric field on each side of the plate and indicate their directions.
C.A second conducting plate of equal and opposite charge is now held parallel to and near the first. The plates are large and close enough together that fringing effects near the edges can be ignored.
The diagrams below show various distributions of charge on the two plates. Decide which arrangement is physically correct. Explain.
II.Parallel plates and capacitance. We will compare and contrast two different situations for capacitance: one where the charge on the plates is kept constant, and one when the potential difference (voltage) between the plates is kept constant.
Two very large thin conducting plates are a distance D apart. The surface area of the face of each plate is A. A side view of the plates is shown.
A.Charge on plates kept constant
The inner surface of one plate has a constant, uniform charge density of +o and the other of -o.
1.Draw vectors at each labeled point to represent the electric field at that point due to each charged plate.
2.Write expressions for the following quantities in terms of (the surface charge density),A (the area of each plate), D (the distance between the plates, and constants:
- the electric field at points 1, 2, 3, and 4.
1:2:3:4:
- the potential difference between the plates.
3.Now move the right hand plate to the left until the new distance apart is d. Describe how each of the following quantities will change (if at all).
- the charge or charge density on each plate
- the electric field both outside and between the plates
outside:between:
- the potential difference between the plates
4.Write expressions for the following quantities in terms of o (the surface charge density), A (the area of each plate), d (the new distance between the plates), and constants:
- the magnitude of the electric field between the plates
- the potential difference V between the plates
- the charge Q on one of the plates
5.Use the above results to find (the ratio of the charge on one plate to the potential difference between the plates).
If the charge densities on the plates were doubled to +2o and –2o, then what would be?
6.Note how the value of does not depend on the amount of charge on the plates.
- Check your results with the instructor before you continue.
B.Potential difference between the plates is kept constant – the battery remains connected to the plates
Suppose the plates are discharged, then held a distance D apart and connected to a battery whose voltage is Vo.
1.Write expressions for the following quantities in terms of Vo, D, and constants:
- the potential difference V between the plates
- the electric field at points 1, 2, 3, and 4
1:2:3:4:
- the charge density, , on each plate
2.Now move the right handplate to the left until the new distance apart is d. Describe how each of the following quantities change (if at all).
- the potential difference V between the plates
- the electric field both outside and between the plates
outside:between:
- the charge density, , on each plate
3.Write expressions for the following quantities in terms of Vo, A (the area of each plate), and d (the new distance between the plates):
- the magnitude of the electric field between the plates
- the charge density on each plate
- the charge Q on one of the plates
4.Use the above results to find (the ratio of the net charge on one plate to the potential difference between the plates).
If the voltage of the battery were doubled to 2Vo, then what would the value of be?
5.Note how the value of does not depend on the potential difference between (or voltage across) the plates.
- Check your results with the instructor before you continue.
C.From the ratio that you calculated for the two plates in part A and in part B:
- does this ratio depend on whether or not the plates are connected to the battery?
- does this ratio depend on the amount of charge on the plates?
- does this ratio depend on the area of the plates?
- does the ratio depend on the distance between the plates?
The ratio does not depend on the voltage connected across the plates nor the charge on the plates. This ratio is defined as the capacitance of the parallel plate arrangement (). Note that the capacitance C only depends on the physical characteristics of the plates, i.e., the area of the plates, the distance between the plates, and the material (free space) between the plates.
D.Consider only charge Q, voltage V, the electric field between the plates E, and the capacitance C in your results from parts A and B.
1.When the plates have fixed charge densities (part A), which quantity or quantities remain fixed and which quantity or quantities change when the distance between the plates changes?
fixed:changes:
2.When the plates are connected to a battery (part B), which quantity or quantities remain fixed and which quantity or quantities change when the distance between the plates changes?
fixed:changes: