# Physics 1304/1404 - Spring 1999

# Homework Assignment #2

**Due:** Thursday 4 February 1999

### READING

Chapters 25 and 26.
### QUESTIONS

Chapter 25 - 1, 2, 4, 6, 8, 10, 14, 15, 16.

Chapter 26 - 1, 4, 10, 11.
### PROBLEMS

Chapter 25 - 2, 6, 12, 23, 24, 26, 32, 39, 42, 45, 50, 53, 54A, 54,
Review Problem.

Chapter 26 - 3, 6, 8, 10, 15, 20, 24, 28, 29, 33, 46, 53, 58.
### ANSWERS

These are the ANSWERS only, not the SOLUTIONS. It is not sufficient to
copy these and turn them in as homework. You must show your work.
**Q 25-1)** They are fundamentally different quantities; electric
potential (or voltage) is the electric potential energy per unit charge.
The MKS unit of potential is the volt (=joule/coulomb) and the MKS unit
of potential energy is the joule.

**Q 25-2)** The potential energy U increases. It moves to a position of
lower potential V.

**Q 25-4)** In a direction perpendicular to the electric field (along the
y or z directions).

**Q 25-6)**
- concentric cylinders
- concentric spheres

**Q 25-8)** No, it implies only that the potential V is a constant.

**Q 25-10)** The smaller sphere has the greater charge density.
(Although the larger sphere has the greater total charge.)

**Q 25-14)** For a given voltage V applied to a conductor, the electric
field E is larger in the vicinity of sharp corners. If the electric
field grows large enough, sparks may emerge from the corners. The
charge may then drain away from the conductor. Notice that the collecting
sphere at the top of the van de Graaff generator is very smooth.

**Q 25-15)** Put the circuit to be shielded in a closed conducting box.
Such a device is called a "Faraday cage". If there are no charges inside
the box, then there is no electric field inside the box. (See pages 722-3.)

**Q 25-16)** (See previous question.)

**Q 26-1)** The charge is also doubled. Q=CV --> 2Q=C(2V)

**Q 26-4)** The pair connected in parallel is more dangerous because it
holds 4 times the charge of the pair in series (and twice as much charge
as a single capacitor).

**Q 26-10)** The factor of 1/2 comes from integrating the infinitesimal
work dW required to move an infinitesimal charge dq from one plate to
the other. (See page 750.)

**Q 26-11)** By a factor of four. energy stored = 1/2 C V^{2}

**P 25-2)** 7.8 x 10^{-4} J = 4.88 x 10^{15} eV

**P 25-6)** 0.502 V

**P 25-12)** 6.67 x 10^{4} V/m (volt/meter = newton/coulomb)

**P 25-23)** q = 1.19 x 10^{-7} C; r = 2.67 m

**P 25-24)**
- 0
- 0
- 45,000 V

**P 25-26)**
- -4.83 m
- +0.67 m and -2 m

**P 25-32)** -3.96 J

**P 25-39)**

E_{x} = -5 + 6xy

E_{y} = 3x^{2} - 2z^{2}

E_{z} = -4yz

E=7.08 V/m

**P 25-42)**
- 0
- kQ/r
^{2} radially outward

**P 25-45)** 0.553 kQ/R

**P 25-50)** k lambda [pi + 2 ln(3)]

**P 25-53)**
- E=0; V=1.67 x 10
^{6} V
- E=5.85 x 10
^{6} V/m; V=1.17 x 10^{6} V
- E=11.9 x 10
^{6} V/m; V=1.67 x 10^{6} V

**P 25-54A)** none on the inner sphere, Q on the outer sphere

**P 25-54)** none on the inner sphere, 10 microcoulombs on the outer sphere

**P 25-Review Problem)**
- kQ/r
^{2}
- kQr/R
^{3}
- kQ/r
- kQ/R + kQ/2R
^{3}(R^{2} - r^{2})
- (Graphs required)
- kQq/r
^{2} toward the center of the sphere
- -kQq/r
- sqrt[2kQq/m (1/R - 1/r)]

**P 26-3)**
- 1 microfarad
- 100 V

**P 26-6)** 3^{1/3} = 1.44

**P 26-8)**
- 5 microcoulombs on the larger sphere;
2 microcoulombs on the smaller sphere
- 90,000 V

**P 26-10)** 43.6 square miles

**P 26-15)**
- 1.11 x 10
^{4} V/m
- 9.83 x 10
^{-8} C/m^{2}
- 3.74 x 10
^{-12} F
- 74.8 x 10
^{-12} C

**P 26-20)** 1.07 x 10^{-2} m

**P 26-24)** 7.08 x 10^{-4} F
(corrected by Angela Watson)

**P 26-28)** 6 pF and 3 pF

**P 26-29)**
- 4 microfarads
- On the 2 microfarad capacitor: 12 V and 24 microcoulombs

On the 3 microfarad capacitor: 8 V and 24 microcoulombs

On the 6 microfarad capacitor: 4 V and 24 microcoulombs

**P 26-33)**

initial charge on C_{1} is 120 microcoulombs

final charge on C_{1} is 80 microcoulombs

final charge on C_{2} is 40 microcoulombs

**P 26-46)** both Q and V are doubled.

**P 26-53)** (Proof required.)

**P 26-58)** 21.9 pF

Please report any corrections to
Professor Scalise.

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