Download Physics 22 Laboratory

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Physics Laboratory
Capacitance
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.
+
+
+
+
+
+
+
+
+
+
+
+
+
side view of a thin
sheet of charge
B.
A small portion of a large thin conducting plate is shown to the right. Each side 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.
P
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.
side view of a thin
charged 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.
o
+o
(a)
excess charge is on
outside surfaces
II.
 1 o
2
1
 1 o  2 o
2
 o  o
 1 o
2
(b)
excess charge is evenly
distributed on both surfaces
(c)
excess charge is on
the inside surfaces
Parallel plates and capacitance
-o
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
+o
x
x
x
x
1
2
3
4
The inner surface of one plate has a uniform charge density of
+o and the other of -o.
1.
2.
Draw vectors at each labeled point to represent the electric
field at that point due to each charged plate.
D
Write expressions for the following quantities in terms of
A, D, and constants:
the electric field at points 1, 2, 3, and 4.
1:
2:
the potential difference between the plates.
3:
4:
3.
The right plate is moved to the left until the new distance apart
is d. Describe how each of the following quantities will change
(if at all).
-o
+o
the charge density on each plate
the electric field both outside and between the plates
outside:
between:
the potential difference between the plates
4.
d
D
Write expressions for the following quantities in terms of o , 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.
Find
Q
(the ratio of the charge on one plate to the potential difference between the plates).
V
If the charge densities on the plates were doubled to +2o and –2o, then what would

Check your results with the instructor before you continue.
Q
be?
V
B.
Potential difference between the plates is kept constant
Vo
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
x
x
x
x
1
2
3
4
the electric field at points 1, 2, 3, and 4
1:
2:
3:
4:
D
the charge density on each plate
2.
The right plate is moved to the left until the new distance apart
is d. Describe how each of the following quantities change (if at
all).
Vo
the potential difference V between the plates
the electric field both outside and between the plates
the charge density on each plate
d
D
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.
Find
Q
(the ratio of the net charge on one plate to the potential difference between the plates).
V
If the voltage of the battery were doubled to 2Vo, then what would the value of

Check your results with the instructor before you continue.
Q
be?
V
C.
Q
that you calculated for the two plates in part A and in part B:
V
Q
does the ratio
depend on whether or not the plates are connected to the battery?
V
From the ratio
does the ratio
Q
depend on the distance between the plates?
V
For two plates with equal and opposite charge, the ratio of the charge on one plate to the potential
Q
difference between the plates is defined as the capacitance ( C  ). Note that the capacitance C
V
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?
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?