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’1", ‘ An inﬁnitely long line charge of uniform linear charge density. +1.. is placed along the axis of
an inﬁnitely long solid conducting cylindrical shell with an inside radius of R, and an outside
radius of R,_ The cylindrical shell has a charge per unit length of 51. Find the magnitude of the electric ﬁeld and its direction. for each of the following regions
(where r is the perpendicular distance from the line charge): a) 0<r<R.
b) Rl<r<Rb
c) Rb<r d) What is the charge per unit length on the inside surface of the cylindrical shell?
e) What is the charge per unit length on the outside surface of the, cylindrical shell? 45 Fit? = gill"? S W57 W C)’)~ S'vr'faeg @ 9+ was Av. E f(2rrrl.)—
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..... GENERAL PHYSICS 11 ~ PRACTICE EXAM I
SPRING QUARTER 2000
' SOLUTIONS J (/5 m3 ;s _
z A mass of 120 g moves up and down on a spring with force constant of 3.0 N/m. At time t= 0 its displacement IS 3!: —+ l 0 cm above equilibrium (y: 0) and it is moving upwards
at a speed of 5.0 cm/s.
a) What is the angular frequency of the motion? i . b) Find the maximum speed of the motion. ! ._  c) What is the amplitude of the motion? Write an expression for the displacement y at time _t_. _‘ _ _ . d)
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’5‘th 'vf’ 5.0/5 ”6;"  A ‘FV‘O'N ”3),. A charge of Q = +104 C is unifomtly distributed around a circular ring of radius R = 30 cm. The ring is in the yz plane with its center at the origin. The axis of the ring is the xaxis. a) What is the linear charge density, 1, of the circular ring? b) Find the magnitude and direction of the electric ﬁeld vector. E, along the axis of the
ring at the point x: 40 cm. c) What point charge 9 could be placed at the center of the ring, it: 0, to make the
electric ﬁeld zero at x: 40 cm?. _,_ ,. at) %=Q/= ’06 =53x20c ZKK jar/ask}
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arm " a) A charge of Q is ﬁxed at each of two opposite comers of a square. across a body
diagonal. A charge q is placed at each of the other two comers. If thénet electrostatic
force on each Q is zero, what is Q in terms of q? (97 to, E1: be m i”? (9 C6; haule Ofraije $2” a, 62 .
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2% 7; 55/? W433 b) A cenain charge Q is divided into two parts, q and ( Q — q ), which are held at a ﬁxed
distance D apart. What must q be in terms of Q so the electrostatic force of repulsion
betweenqand(Q—q) ismaximized? D Q73
_ E = 3(Q‘i2 @ %, , (Q’Q ...
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 Spring '08
 Kogan
 Physics

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