Download EP 106 General PhysicsExam

EP 106 General PhysicsExam
Time Duration : 120 Mins.
1) A small test sphere of mass 60 gr is suspended from a string of length 10 cm. At a distance ℓ of 10 cm
from the point of suspension and a distance ℓ/2 from the string is a fixed sphere as shown in figure 1.
The spheres have equal charges of the same polarity. Calculate the charges on each sphere if the
string is deflected by 30 0 ? (25 points)
ℓ
ℓ
ℓ/2
m
m
Figure 1
2) At some instant the velocity components of an electron moving between two charged parallel plates
are vx=2x105 m/sec and vy=0.5x104 m/sec. If the electric field between the plates is given by E =
2.1x104 ĵ N/C. (Neglect the effect of the g)
(a) What is the acceleration of the electron ? (10 points)
(b) When the x-co-ordinate of the electron has changed by 3 cm what will be the velocity of the
electron ? (15 points)
3) (a) Consider two concentric spherical shells of uniform surface charge densities a and b and radii a
and b, b>a. Develop expressions for E in the regions inside the inner shell, between the two shells and
outside the outer shell. What should the ratio of the total charges and their relative signs to be for the
field to be zero outside b. (18 points)
(b) A cone is replaced in a region of uniform electric field E=10 k N/C (Fig.2). Determine the electric
flux for each of the surfaces.(7 points)
z
ℓ=15 cm
x
y
R=10 cm
E
Figure 2
4)
(a)
(b)
(c)
Four charges of 1 C are placed on the corner of a rectangle of sides having length 6 cm and 8 cm.
Find the electric field at the center of the rectangle. (8 points)
Calculate the potential at the center of the rectangle. (8 points)
What is the electric potential energy of the given charge configuration. (9 points)
Inst.Mustafa YILMAZ
Inst.Metin BEDİR
Asst.Prof.Dr.A.Necmeddin YAZICI
Asst.Prof.Dr.Ramazan KOÇ
Useful Constants: k=9x109 Nm2/C2; 1 μC=1x10-6 C me=9.1x10-31 kg, e=-1.6x10-19 C, sin300=1/2; cos300=√3/2;
EP 106 General PhysicsExam
Time Duration : 120 Mins.
1. Two similar charges each have a mass of 10 g. How great a charge should be placed to counter
balance the gravitational force between the charges. The distance between the charges is much
greater than their radii. (G=6.67x10-11 Nm2/kg2)
2. A charge of 8x10-5 C is placed in an electric field by Ex=3x103 N/C, Ey=-600 N/C, and Ez=0.
a-) What are the magnitude and direction of the force on the charged particle.
b-) If the particle starts from rest at the origin, what will be its co ordinates after 3 sec.
(Take mass of the particle m=10 g.)
3. A thick spherical shell has a charge Q, an inner radius a, and an outer radius b. The charge distribution
between a and b is spherically symmetric but varies with distance from the center : ρ=A/r, where A is
a constant. A point charge q is placed at the center of the sphere.
a-) Determine q in terms of Q, a, and b such that the field between a and b is independent of r.
b-) What is the field for r<a ?
c-) What is the field for r>b ?
4. A positive charge q is distributed uniformly throughout a non conducting spherical volume of radius R.
Calculate the potential inside the sphere.
Useful Constants:
k=9x109 Nm2/C2; 1 μC=1x10-6 C me=9.1x10-31 kg, e=-1.6x10-19 C,
Inst.Mustafa YILMAZ
Inst.Metin BEDİR
Asst.Prof.Dr.A.Necmeddin YAZICI
Asst.Prof.Dr.Ramazan KOÇ
EP 106 General PhysicsExam
Time Duration : 120 Mins.
Q-1-) Two uniform line charges, each of length 2l, are replaced parallel to each other.
a-) Determine the magnitude of electric field intensity at point P and then indicate the direction of E
(Fig.1a).
b-) What is the magnitude and direction of force on the suspended pith ball that has charge
Q=260e located at this point P (Fig. 1b). +3
+3
-2
-2
(l=4 cm, x=3 cm, =1x104 C/m)
+
+
l +
+
+
+
+
+
l +
+
+
+
+
+
2l
P
x
x
-
2l
2
Figurex1a
+
+
l +
+
+
+
+
+
l +
+
+
+
+
+
Q
P
x
x
2
Figure
x 1b
-
Q-2-) Consider a solid sphere of radius a=3 cm that carries a negative charge of 2 C distributed
uniformly. The sphere is placed concentrically in a spherical shell of radius b=8 cm that has a positive
charge of 5 C distributed uniformly over it. Calculate the electric field by using the Gauss’s law at the
regions (a) r=1 cm, (b) r=5 cm, and (c) r=10 cm.
b
a
Q-3-) Along the x-axis, indicated by the dashed line on this diagram, the electric field is


E  cx 2 x ,

where c is a positive constant, and x is a unit vector. This minus sign indicates that the field points
“backwards” towards x=0. Ignore gravity. A particle of charge +q 0 and mass m is released from rest at
x=+x0 on the x-axis. What is the particle’s speed when x=0 ? Solve the question in terms of q 0, m , c and x0.
E
x=0
x=x0
q0, m
Q-4-) a-) Prove the capacitance and energy density expressions
for the parallel plate capacitor and the solve the following
problems.
b-) A parallel-plate capacitor having 10 x 20 cm2 dimensions
and the distance between plates is 2 mm and they are
charged with a potential 500 V. Find,
i-) the capacitance C
ii-) the magnitude of charge Q on each plate
iii-) the stored energy U
iv-) the electric field E between the plates
v-) the energy density  between the plates.
d
b
E
a
V
EP 106 General PhysicsExam
Time Duration : 120 Mins.
Q-1-) a-) Prove that the voltage across a capacitor during a charging phase (position 1) in an RC circuit
(in below figure) is given by the relation
VC(t)=V0 (1-exp(-t/RC))
R
S
1
2
C
V
0
b-) Find the mathematical expression of the voltage and current for the capacitor in below figure
and then determine Vc and ic at 100 msec.
10
k
S
5k
1
5 F
10 k
V0=10 V
Q-2-) a-) An automobile battery has a potential difference of 12.0 V and sends current through a circuit
of total resistance 1.5  that contains a copper wire 1. 0 m long with an 0.3 cm 2 cross-sectional
area. Find (a) the current through the wire, (b) the energy lost to heat in the circuit in one hour
and (c) the distance travelled by an electron in the circuit in one hour. (MCu=63.5 gr/mole,
NA=6.02x1023 mole-1, =8.91x103 kg/m3)
Q-3-) A proton is moving in a positive x-direction as it enters a region of uniform magnetic field of 0.4 Tesla
directed vertically down. The proton starts to follow a circular path of a radius 10 cm in this
magnetic field.
a-) Draw path of the proton in this uniform magnetic field.
b-) Determine the momentum and speed of the proton.
c-) If the proton is initially accelerated under the
potential difference 12 kV into the same magnetic
field, what will be radius of the path of the proton.
(mp=1.67x10-27 kg, e=1.6x10-19 C)
+
e
v
B
Q-4-) Two long and thin straight wires carry currents at
P1
a/2
opposite direction as shown in figure. Find the
magnitude of magnetic field and directions at
the points P1 and P2 using Amper’s law.
Inst.Metin BEDİR
Asst.Prof.Dr.A.Necmeddin YAZICI
Asst.Prof.Dr.Güler YILDIRIM
Assoc.Prof.Dr.Zihni ÖZTÜRK
i1=2 A
a=10 cm
x
P2
i2=3 A
a/4
EP 106 General PhysicsExam
Time Duration : 120 Mins.
Q-1-) For the given system (Fig.1)
a-) What is the electric field E at the center of the system.
b-) What is the electric potential at the center of the system.
c-) Assume that you bring a fifth charge (Q5=10 pC) very slowly from infinity to the center of the
system. How much work must you do?
d-) What is the electric force acting on Q5.
e-) What is the potential energy of the charge Q5.
Q1
a
Q2
b
Q3
Q4
Figure 1
Q1=8 pC
Q2=4 pC
Q3=8 pC
Q4=4 pC
a=34 mm
b=17 mm
Q5=10 pC
Q
Q-2-) Consider a spherical uniform volume charge density 
with Q=61 nC and r0=48 mm.
a-) Determine the volume charge density .
b-) Find the electric field E at point r=24, 48, and 96 mm
from the center of the shere.
r0
Figure 2
Q-3-) For the given non conducting system (Fig.3)
a-) What is the electric potential of sphere 2.
b-) What is the electric potential difference
between sphere 2 and 1.
c-) What is the potential of sphere 1.
d-) Assume that a tiny particle of charge
q=4.0 C and mass m=2.0x10-8 kg is released
from rest from the surface of the sphere 2. What
velocity does the particle have when it reaches
a distance 2r3 from the center of sphere 1.
Q-4-) Three identical coaxial cable (cylindrical) capacitor
are connected as shown in figure 4.
a-) Find the capacitance of one capacitor.
b-) Find the equivalent capacitance of the system.
c-) What is the charge on each capacitor.
d-) What is the potential difference across each
capacitor.
2
Q2
Q1
r2
r1
1
r3
Figure 3
L
b
a
V=10 V
a=33 mm
b=45 mm
L=225 mm
Figure 4
Inst.Metin BEDİR
Asst.Prof.Dr.A.Necmeddin YAZICI
r1=3.535 mm
r2=4.4 mm
r3=5.4 mm
Q1=4 pC
Q2=2 pC
EP 106 General PhysicsExam
Time Duration : 120 Mins.
1. A charge Q is fixed at each of two opposite corners of a
rectangular which is the length of long side is three
times longer than short side. A charge q is placed at each
of the other two corners.
a-)If the net electrostatic force on each Q is zero, what is
Q in terms of q ?
b-)What is the total potential energy of the system in
terms of q ?
c-)What is the electric potential on each Q?
d-)Is there any value of q that makes the net electrostatic
force on each of the four charges zero? Explain.
2. A very long conducting cyclindrical rod of length L and
-2q
radius R1 with a total charge +q is surrounded by a
non-conducting cyclindrical shell of inner radius
R2 outer radius R3 with total charge –2q. Use
q
Gauss’s law to find the electric field at
a-) r<R1
R22
b-) R1<r<R2
c-) R2<r<R3
d-) R3<r
3. A charged particle is projected between
the opposite charged parallel plates. The
mass of the particle is 10-27kg and its
charge is 1.2x10-9 C which is fired with an
initial velocity 106 m/sec and 370 with
horizontal direction. When the particle is
taken away 12 cm along the horizontal
direction as shown in figure, determine the
electric field between the parallel plates.
3a
q
a
Q
R1
R3
+++++++++++++++++
++++
V0=106 m/s
=37
- - - -0 - - - - - - - - - - - - - - - - - - - ----L=12 cm
z
P
4. a-) A ring of outer radius R and inner radius
r=0.4R; the ring has a uniform surface charge
density  with V=0 Volt at infinity, find an
expression for the electric potential at point
on the central axis of the ring.
b-) If a point charge is located at point z=2R,
what is the potential energy of the system.
z=2
R
y
5. A parallel-plate capacitor has circular
plates of 6 cm radius and is filled with
two dielectric materials with dielectric
constants 1=0.1 and 2=0.2, respectively.
The plate seperation distance is 2 mm.
0.2
The system is connected a potential
mm
difference of 200 volts. Determine
a-) the capacitance of the system
b-) the magnitude of charge on each plate
c-) the stored energy on each capacitor
d-) the potential difference across each capacitor.
x
0.4
R R

R=6 cm

1
2
0.1
mm
V=200
Volt
EP 106 General PhysicsExam
Time Duration : 120 Mins.
1. a-) The current density across a cylindrical copper wire of radius R0 varies according to the equation
J  J 0 ( R0 
r2
)
2 R0
where r is the distance from the central axis. Calculate the current (I) in terms of J0, cross sectional
area and radius R0 of conductor.
b-) Suppose that cross sectional area and length of the wire is equal to 3.14 mm 2 and 314 m.
Calculate the resistance R, current I, current density J, conductivity , electric field E when J0=1.33x103
A/m and =1.72x10-8 -m.
2. What is the potential difference across the resistance Rx in below Figure.
7.5
40
40
5
20
5
15
10
5
5
Rx=15
S
3. a-) What is the current and voltage across the
capacitors and resistor R3 in below figure at t=20 msec
in position 1.
b-) Assume that after t=20 msec, the switch S is
suddenly passed into position 2, What is the current
and voltage across the resistor R3 after the switch
passing position 2 at t=10 msec.
0.5 k
E=10
20 F
C2
B
z
y
x
V0=20 Volt
q
C
B
I0= 5 A
Iı=10 A
A
Inst.Metin BEDİR
Asst.Prof.Dr.A.Necmeddin YAZICI
C1
0.5 k
4. A positively charged particle (q=e, m= 6.7x10-27 kg) is
accelerated by potential difference V0=20 volt and
allowed to enter a magnetic field as shown in below
figure. In the field it moves in a semicircle path, and
striking a photographic plate at distance x=20 cm
from the entry slit.
a-) Draw the direction of the particle in the magnetic
field region.
b-) Determine the kinetic energy and velocity of the
charged particle.
c-) Find the magnitude of the magnetic field B.
5. In below figure, two long wire which are lying
along the left and right side of a rectangular
loop carrying currents I1=10 A and I2=15 A,
respectively. The rectangular loop carries a
current of 5 A. What must be ratio of a/c to
obtain zero force on the rectangular loop?
0.5 k
20 F
b= 5 cm
a=
5 cm
l=
30 cm
D
c
I2=15 A
EP 105 GENERAL PHYSICS ( SUMMER SCHOOL)
18/07/2001
First Midterm
Duration: 100 min
( Answer only four questions)
Q-1) For the given system, assume that all of
the pulleys and strings are very light and
their frictions are negligible. There are
friction between the blocks m2, m3 and
floor. When system is accelerated to the
positive x direction, a) Find the acceleration
of the blocks. b) Find the tension of the strings.
Q-2) A flatbed truck transports a crate of mass
m as seen below. The crate is not fastened to
the bed and the coefficient of static friction ,
between the crate and the bed is 0.8. When
the track starts out from a red light on a horizontal
street, what is the maximum acceleration it can
have such that the crate will not slide backward.
Q-3) A uniform ladder of weight 300 N
and length 6 m leans against a smooth
wall with the ladder lower end on the
floor 2 m from the wall. The coefficient
of static friction of the floor is 0.25.
A painter weighing 700 N begins climbing
the ladder slowly. How far on the ladder
can the painter climb before the ladder
begins to slide?
Q-4) The velocity of an object moving in a straight line is given by v = t+2t2-4 m/sec.
a)- What is the inital velocity of the object?
b)- Calculate the average velocity for the time interval from 1sec to 2 sec.
c)- What is the objects displacement between 2sec and 4 sec.
d)- Find the instantaneous acceleration at any time of the motion.
Q-5) A ball is thrown from the ground into the air. At a height of 8 m the velocity is observed to be v= 4i+3j
in meters per seconds.
a)- To what maximum height will the ball rise.
b)- What will be the total horizontal distance traveled by the ball.
c)- What is the velocity of the ball the instant before it hits the ground.
11/06/2001
EP106 RETEST EXAM
Duration: 100 min
Q-1) A copper wire and an iron wire of equal length L and diameter d are joined and a
potential difference V is applied between the ends of composite wire. Calculate: a) The
electric field strength in each wire. b)The current density in each wire. c) The potential
difference across each wire. Assume that L=10m, d=2.0 m and V=100 Volts.
Q-2) Two long parallel wires 5.00cm apart carry 20.0 A currents in the same direction.
Determine the magnetic field strength at a point 12.0 cm from one wire and 13.0 cm
from the other. ( Hint: Make a drawing in a plane containing the field lines and recall the
rules for vector addition.)
Q-3) a) What is the total resistance in below circuit ?
b) What is the passing current through the resistance Ra ?
c) Indicate the direction of current in this resistance.
Q-4) For given network; a) What is the RC time constant of this circuit ? b) Calculate the
potential difference across the each capacitor at time t=5 msec.
11/06/2001
EP 106 FINAL EXAMINATION
Duration:110 min
Q-1) A wire with a resistance of 6.0 is drawn out so that its new length is three times its original length.
Find the resistance of the longer wire assuming that the resistivity and density of the material are not
changed during the drawing process.
Q-2) An infinitely a long wire has uniform line charge
distribution and its line charge density is (C/m). Find
rb
(C/m)
the potential difference between the two points a
ra
a
b
and b.
Q- 3) A thick spherical shell has a charge Q, an inner radius
r1 and an outer radius r2. The charge distribution
between r1 and r2 is spherically symmetric but
varies with a radialdistance from the center
=C/r, where C is a constant and r is the
r1
Q
q
r2
variable distance from the center of the
shell. In addition, a point charge q is located
at the center of the shell.
a) Determine q in terms of Q,r1 and r2 such that the electric field between r1 and r2 is to be uniform.
b) What should the value of C be so that the electric field in the region r 1rr2 has constant
magnitude.
I1
c) What is the electric field for ra and rb ?
Q-4 ) In the coaxial cable given in figure, a straight wire of radius
a carries a current I1 along the axis of a metal tube with
inner radius b and outer radius c. The tube carries a current
I1 in a direction oppposite to that in the wire. Find the
I1
magnetic field; a) ra, b) arb, c) rc.
Q-5) Determine the magnetic field at the center of a current carrying
square loop of length a as shown below.
I
I
a
a
03/10/2000
EP 106 RETEST EXAM.
Duration:100 min
Q-1) Four charges of 1C are placed on the corner of a rectangle of sides having length 6 cm
and 8 cm.
a)-Find the electric field at the center of the rectangle.
b)- Calculate the potential at the center of the rectangle.
c)- What is the electric potential energy of the given charge distribution.
Q-2) Prove the capacitance and energy density expressions for the parallel plate capacitor and
the solve following problems. A parallel plate air capacitor has circular plates of 8 cm
radius and spacing of 2 mm is charged to a potential of 200 volts.
Find: a)- the capacitance value of the capacitor,
b)- the magnitude of the charge on each plate,
c)- the stored energy,
d)- the electric field between the plates,
e)- the energy density between the plates.
Q-3) A thick spherical shell of uniform charge density =0 ,
inner radius R0 outer radius R1. Find:
a)- the electric field for r R0 , R0 rR , r R1 .
b)- the work done to move a charge Q from 4R1 to 2R1.
Q-4) A 10 keV electron moving horizontally enters of space in which there is a downward direction
electric field of magnitude 10 kV/m.
a)- What are the magnitude and direction of the magnetic field that will allow the electron to
continue to move horizontally ? ( Ignore the gravitational force ).
b)- Is it possible for a proton to pass through this combination of fields undeflected ?
Q-5) Find the current in each resistor and potential difference between a and b.
EP 106 GENERAL PHYSICS
(Ek Sınav) 25/09/2001
Duration:120 min.
Q-1) The charge -Q shown at the at the right is a
-Q
distance y (not very small) above the origin and
y
moving downward. Find (a) the electric potential it
feels, (b) its potential energy, (c) will it be moving
faster or slower when it reaches the origin.Explain.
q
a
a
q
Q-2) A sphere of radius 6 cm has a volume charge density =
2x103C/m3, and is surrounded by a thin metal shell of radius 8 cm
whose surface charge density  = 1x102 C/m2.
Calculate the electric field at r=3 cm, r=7 cm, and r=10cm.
y
dq
Q-3) A 20 cm long wire has a uniform charge density, =3.00 C/m. It
b
is along the y-axis centered in the origin as shown in figure. Find
the electric potential at a distance a=10 cm from the origin.
r
L=20c
mm
Q-4).Find the current and voltage across the resistance Rx in below figure.
a=10 cm
x
12/07/2004
EP 106 GENERAL PHYSICS
( SUMMER SCHOOL)
First Midterm
Duration: 100 min
1. A positive 27 mC and a negative 35 mC charge is placed 50 cm apart.
a-) Where can a third charge be placed so that it experiences no net force on this
charge?
b-) What must be sign of this charge?
2. A solid sphere of radius R=4 cm has a volume charge distribution of =2x10-4 C/m3.
Determine the electrical potential difference between the surface and center of this
sphere.
3. An electron moving horizontally at a speed of
+++++++++++++++
vo=4x106 m/sec enters the region midway between
two horizontally oriented parallel plates. The distance
vo
E
between parallel plates is 2 cm. The direction of
electric
field
between
the
parallel
plates
---------------------
is
downward and its magnitude is 103 Nt/C.
a-) Determine the deflection direction of the electron between plates?
b-) What must be minimum length of plates for the electron to strike the plate?
4. Two uniform line charges, each of length 2l, are
replaced parallel to each other (see side figure). What
is the magnitude and direction of the electric field at
point P. ( l=4 cm, x=3 cm, =1x104 C/m)
2l
+3
+
+
l +
+
+
+
P
+
+
l +
+
+
+ x
+
+
-2
x
-
Useful Constants: k=9x109 Nm2/C2; o=8.85x10-12 C2/Nt.m2; me=9.1x10-31 kg; e=-1.6x10-19 C