PHY2049 Fall 2006
1
Prof. Yasu Takano
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Sep. 25, 2006
Exam 1 Solutions
1. (
New problem
) Four charges each of size
Q
are arranged at the corners of a square of side
L
.
The magnitude of the net electric force (in N) on any of the charges can be written as
22
/
CkQ
L
.
What is the approximate value of
C
?
(1) 1.91
(2) 1.71
(3) 1.41
(4) 0.71
(5) 0
Pick the charge to be in the upper right hand corner (any charge can be used since the situation
is symmetric). The net force from the two adjacent charges is easily seen to be along the 45 de
gree direction with a magnitude
2/
kQ
L (because the charges give equal forces of
/
kQ
L
along the +x and +y direction). The charge across the diagonal is at a distance of
2
L , so it
provides a force of
/2
kQ
L , along the 45 degree direction. Thus the total force is along the 45
degree direction, with a magnitude of
( )
21
/
2
/
kQ
L
+
. Thus
2 1/ 2
1.91
C
=+
±
.
You can also work out the problem directly using components along x and y. The adjacent
charges give a force of
()
/1
,
1
kQ
L
. The opposite charge yields a force of
1/ 2,1/ 2
kQ
L
. Thus the total force is
( )
/
1 1/2 2,1 1/2 2
kQ
L
++
. When you
square and add the components to get the total force you get
1.91
/
kQ
L
.
2. (
WebAssign 22.41
) A uniform electric field of 4.5
×
10
4
V/m is applied to a proton, which is
initially stationary. What speed (in m/s) will the proton attain if the field accelerates the proton
through a distance of 10 cm?
(1) 9.3
×
10
5
(2) 3.0
×
10
8
(3) 4.5
×
10
3
(4) 1.2
×
10
7
(5) 7.4
×
10
6
The force can be written as F
eE
=
. Therefore, the work Fd done by the electric field is eEd,
where d is the distance through which the proton is accelerated.
This work results in the kinetic
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2
energy of the proton increasing from zero to
2
1
2
p
mv
.
From
2
1
2
p
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 Charge, Electrostatics, Force, Electric charge, Fundamental physics concepts

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