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1 Physics 171.102 Exam 1 February 26, 2002
Prof. Barnett Write your TA’s name, your name and Section Number on each blue book.
Write everything in ink.
You may utilize material written on both sides of ONE 3”x5” index card. 60 = 8.9 x 10—12N9‘m2 a = 9 x 109 N592 g = 10 m/s2 1. Two tiny conducting balls of identical
mass m and identical charge q hang
from non—conducting massless threads of
length L on earth as shown in the ﬁgure.
The angle 6 is so small that tan(6) can be
approximated as sin(6) if this is convenient. lea.-- \' __,1 A) (10 pts) What are the forces Fl acting on the right hand mass? B) (10 pts) Find the formula relating q to the other relevant
parameters (L, m, :13) in the problem. C) (10 pts) If L : 120 cm, m z 10 grams and :1: = 5 cm, what is q? 2. The adjacent ﬁgure shows a cross section of a if“ 2‘
neutrally charged (uncharged) spherical metal "(X/120
shell of inner radius RI and outer radius R0. %. . R 2
A point charge of Q 2 —9 MO is located a -.~, I/ distance R1/2 from the center of the spherical shell. A) (5 pts) What is the total induced charge on the inner surface of the
spherical shell? Is this charge spread uniformly on the surface? B) (5 pts) What is the total induced charge on the outer surface of the
spherical shell? Is this charge spread uniformly on the surface? C) (5 pts) What is the electric ﬁeld EU?) inside the material of the shell, i.e. for R] < R < R0? D) (10 pts) What is the electric ﬁeld E(R) outside the spherical shell,
i.e. for R > R0? E) (5 pts) If the charge Q : ~9 ,LLC were located at the center of the sphere
instead of at R : RI/ 2 how would the electric ﬁeld E(R) outside the spherical shell, i.e. R > R0, change? 3. A capacitor consists of two oppositely charged ﬂat parallel plates.
Each plate has a square shape with edges of length 10 cm.
One plate has charge 62+ 2 9 X 10~10 C and the other plate has charge Q_ = —9 X 10—10 C.
The plates are 1 mm apart. A) (10 pts) What is the potential difference across the capacitor? B) (10 pts) If an electron with charge 6 = ——l.6 X 10‘19 C and mass
m = 9 X 10"31 kg is released at rest from the surface of the negatively
charged plate how much time passes before it collides with the positively
charged plate? ' C) (10 pts) What is the kinetic energy of this electron when it collides with
the positive plate? 4. The electric potential at the point P ‘P in the adjacent ﬁgure due to a uniform 1 charge density /\ on a uniform rod ' of length L is given by lH;L———>l—_x _ A L+§L2+d2)1/2 V(d) _. 4m) m( d j. A) (5 pts) What is the potential at the P
point P in the adjacent figure showing j
an identical rod of length L except that d
it is split into a right and left half and
where the left and right halves have the PM ﬁL—m 4
same linear charge density A. B) (5 pts) What is the potential at the
point P in the adjacent ﬁgure again p
showing an identical rod split into two i
halves, but this time with the linear
charge densities being +)\ for the “Em"‘mgﬂ‘ma left half and —A for the right half? ...
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