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In the figure below Q1 and Q2 are held fixed at the positions shown and we can position Q3 any place we wish.

Q1 = +200 μC
Q2 = -300 μC
Q3 = +400 μC
m3 = 0.100 kg
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Determine the following:

1
Electric potential at the origin due to Q1
2
Electric potential at the origin due to Q2
3
The total electric potential at the origin due to Q1 and Q2
4
The amount of work required to move Q3 from very far away up to x = 0
5
The change in electrical potential energy of Q3 as it is moved from very far away up to x = 0
6
The electric potential energy of Q3 when it is at the origin
7
The total amount of work done in assembling the collection of charges Q1, Q2 and Q3

If Q3 is now released from rest (at the origin) it will travel along the negative x axis.

Determine the following:

8
The change in Q3's electric potential in traveling from x = 0 to x = -1.00 m
9
The work done on Q3 by the electric field of the two charges (Q1 and Q2) as it moves from x = 0 to x = -1.00 m
10
Q3's kinetic energy when it is at x = -1.00 m
11
Q3's speed at x = -1.00 m

The figure below shows two parallel conducting plates separated by 10 cm and connected to a 20.0 volt battery. It also shows the 5 V, 10 V and 15 V equipotential lines. You also have a test charge Qo = 2.00 C and mo = 2.00 × 10-3 kg

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Determine the following:

12
Magnitude of the electric field at A.
13
The difference in electric potential between A and B
14
The amount of work done to move Qo from A to B
15
The Electric Potential Energy of Qo at point B
16
Magnitude of the electric field at D
17
The amount of work required to move Qo from B to D
18
The electric potential energy of Qo at point D

If Qo is now released from rest at point D determine the following:

19
Work done on Qo by the electric field as it moves from D to C
20
Change in electric potential energy of Qo as it moves from D to C
21
Change in kinetic energy of Qo as it moves form D to C
22
Speed at which Qo slams into the negative plate

The figure below summarizes a sequence of events involving a capacitor, battery, and a slab of dielectric material.

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(a) The capacitor is connected to the battery and charged
(b) While the battery is connected, a dielectric slab is inserted
(c) The battery is disconnected
(d) The dielectric is withdrawn

The following information is known:

A = 1.00 × 10-2 m2 = area of each plate
d = 2.00 × 10-2 m = separation of the plates
Vo = 24 V = voltage of the battery
K = 5.00 = dielectric constant

Determine the following:

23
Capacitance of the capacitor in case (a)
24
Charge on each plate of the capacitor in case (a)
25
Electric field between the plates of the capacitor in case (a)
26
Energy stored in the capacitor in case (a)
27
Capacitance of the capacitor in case (b)
28
Charge on each plate of the capacitor in case (b)
29
Electric field between the plates of the capacitor in case (b)
30
Energy stored in the capacitor in case (b)
31
Capacitance of the capacitor in case (d)
32
Charge on each plate of the capacitor in case (d)
33
Electric field between the plates of the capacitor in case (d)
34
Energy stored in the capacitor in case (d)







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