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(phys121)[2009](f)midterm~ma_yxf^_10540.pdf
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PHYS121 Fundamentals of Physics
Fall 2009
Midterm Examination

7:15 C 9:00 pm, LTC, 17 Oct 2008
Name: _____________________________ ID: ________________________________ Section No.: ______________________
Question # Total Points Your Points
1 15
2 15
3 30
4 5
5 25
6 10
Total 100


Important:
1. This exam paper has 6 questions. Answer ALL questions.

2. This is a close book examination. You are not allowed to bring any book or paper to the examination room. An electronic calculator is allowed.

3. Please make your student ID available for checking.

4. Please turn off all paging and telecommunication devices. You will be deducted 10 points if your device beeps or vibrates. You will be disqualified if you use your device any time during the course of the examination.

5. You can find a list of formulae in the next page. Note that not every one of them is needed to answer this exam paper.

6. Anyone caught cheating in this exam will fail this course.


Buena Suerte / Viel Glck / Bonne Chance / Good Luck /\



Formulae


NOTE: not every formula listed here is needed in answering this exam paper.
.12 22-1 1 q1q21 q
= 8.854 10 Cm N, Coulombs Law F = 2, E = 204 0 r 4 0 r
qz
Electric field due to a charge ring E =
2 2 3/2
4 0(z + R ) .. Electric field due to a charge disk E = .1.
.
2
0 .

Electric field just on and above the conductor surface (vacuum) E = 0
An electric dipole in an electric field = p E , U =. p . E
Gauss law 0

E . dA = q and
E . dA = q free
total 0
1 q
Electric potential due to a point charge V = where we define V () = 0.
4 0 r
ab
Potential difference Vab = V . Vb =. E . ds = E . ds
a . . ba
QA
Capacitance C = , A parallel plate capacitor C = 0
Vd A cylindrical capacitor C = 2 0 L / ln( b / a) , A spherical capacitor C = 4 0 ab /( b . a)
12
Energy stored in a capacitor U = CV
2 12
Energy density in an electric field u = 0 E
2
43 2
For a sphere of radius R, volume is R , surface area is 4R
3 As | x |<< 1 . 1/
1+ x 1. x /2,
1+ x 1+ x /2
Magnetic force on a charge: F = qv B , on a current wire F = iL B
a b = (ab . ba )i. + (ab . ba ).j + (ab . ba )k.
yzyz zxzx xyxy
| a b |= ab | sin |
a . b = ab cos
Question 1 [15 points]:

(a)
A ring of radius R has a total charge +Q uniformly distributed on it. Calculate the electric field and potential at the centre of the ring. [8 points]

(b)
Consider a charge -Q constrained to slide along the axis of the ring. Show that the charge will execute simple harmonic motion for small displacements perpendicular to the plane of the ring. [7 points]


Question 2 [15 points]:
(a) An electric charge Q is uniformly distributed over the surface of an isolated
conducting soap bubble of radius r. Show that the electric fo