Download Exam 1 Solutions

Physics 142, Spring 2010
Name: __________________________________
Exam 1
1. [21 points] Two point charges are arranged on the B-axis, as shown in the figure below:
C
T
"& cm
+
−
)Þ! nC
&Þ! nC
"& cm
B
"& cm
(a) [12 pts] Find the electric field vector E at the point T .
(b) [9 pts] Find the electric potential at the point T (assuming that Z œ ! at infinity).
Physics 142, Spring 2010
Exam 1
2
2. [12 points] A proton follows the trajectory shown in the figure below:
E
+
#& V
#! V
F
"& V
Its speed as it passes point E is &Þ! ‚ "!% mÎs. What is its speed as it passes point F ?
Physics 142, Spring 2009
Exam 1
3
3. [8 points] Four capacitors are connected as follows:
"Þ! µF
%Þ! µF
#Þ! µF
$Þ! µF
What is the net capacitance of this combination?
Physics 142, Spring 2009
Exam 1
4
4. [15 points] Two charged metal plates are arranged as shown in the figure below:
+
+
−
+
+
−
#Þ! mm
+
−
+
−
−
Each plate has the shape of a $& cm ‚ $& cm square, and each carries a net charge of %Þ" nC (positive on the
top plate, and negative on the bottom plate).
(a) [9 pts] Find the potential difference between the two plates.
(b) [6 pts] Find the total electric potential energy of the two plates.
Physics 142, Spring 2009
Exam 1
5
5. [17 points] The following picture shows the equipotentials in the vicinity of a charged particle:
#Þ! V
%Þ! V
−
&Þ! cm
'Þ! V
)Þ! V
The particle has a charge of !Þ(! µC and a mass of !Þ% mg.
(a) [5 pts] What is the direction of the force on the particle? Explain.
(b) [12 pts] Find the magnitude of the acceleration of the particle.
Physics 142, Spring 2009
Exam 1
6
6. [15 points] A long insulating cylinder has a radius of &Þ! cm and a uniform volume charge density. The
electric field at the surface of the cylinder points radially inward, with a magnitude of 'Þ& kVÎm.
(a) [3 pts] Is the cylinder positively charged or negatively charged? Explain.
(b) [12 pts] Find the volume charge density of the cylinder.
Physics 142, Spring 2009
Exam 1
7
7. [12 points] On days of fair weather, the electric field in the atmosphere points vertically downwards; its
magnitude varies with height according to the equation
I œ I!  O2
where 2 is the height above ground, I! œ "#! VÎm, and O œ #Þ( ‚ "!# VÎm# .
Based on this information, find the potential difference between the ground and an airplane flying at an
altitude of #Þ! km. Make sure to say whether the airplane or the ground has higher potential.