**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)

2)
At some instant
the velocity components of an electron moving between two charged parallel
plates are v_{x}=2x10^{5} m/sec and v_{y}=0.5x10^{4}
m/sec. If the electric field between the plates is given by **E** = 2.1x10^{4} **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)
5.4.1999

(a) Consider two
concentric spherical shells of uniform

surface charge densities s_{a}
and s_{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)

Figure
2

4) Four charges
of 1 mC 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. (8 points)

(b)
Calculate the
potential at the center of the rectangle. (8 points)

(c)
What is the
electric potential energy of the given charge configuration. (9 points)

*Inst.Metin BEDİR*

*Asst.Prof.Dr.A.Necmeddin YAZICI*

*Asst.Prof.Dr.Ramazan KOÇ*

** Useful Constants**:
k=9x10

**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}
Nm^{2}/kg^{2})

2.
A charge of 8x10^{-5}
C is placed in an electric field by E_{x}=3x10^{3} N/C, E_{y}=-600
N/C, and E_{z}=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=9x10^{9} Nm^{2}/C^{2};
1 μC=1x10^{-6} C m_{e}=9.1x10^{-31}
kg, e=-1.6x10^{-19} C,

*Inst.Metin BEDİR*

*Asst.Prof.Dr.A.Necmeddin YAZICI*

*Asst.Prof.Dr.Ramazan KOÇ*

**Time Duration : 120 Mins.**

** **

** **

** **

**Q-1-)** Two uniform line
charges, each of length 2*l*,

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).

(*l*=4 cm, x=3 cm,
l=1x10^{4}
C/m)

Q-2-)
Consider a solid sphere of radius a=3 cm that carries a

negative charge of 2 mC distributed
uniformly. The sphere

is placed concentrically in a spherical
shell of radius

b=8 cm that has a positive charge of 5 mC 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.

**Q-3-)**
Along the x-axis, indicated by the dashed line on this diagram,

the electric field is _{} , where c is a
positive constant,

and _{} 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=+x_{0} on the

x-axis. What is the particle’s speed when x=0 ? Solve the

question in terms of q_{0}, m , c and x_{0}.

**b-)
**A parallel-plate capacitor having 10 x 20 cm^{2}
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 u between the
plates.

**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

V_{C}(t)=V_{0}
(1-exp(-t/RC))

**b-)**
Find the mathematical expression of the voltage and

current for the capacitor in below figure and then

determine V_{c} and *i _{c}* at
100 msec.

**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 W 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. (M_{Cu}=63.5
gr/mole, N_{A}=6.02x10^{23} mole^{-1}, r=8.91x10^{3} kg/m^{3})

** **

**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.

(m_{p}=1.67x10^{-27} kg, e=1.6x10^{-19}
C)

**Q-4-)** Two long and thin straight
wires carry currents at

opposite direction as shown in figure. Find the

magnitude of magnetic field and directions at

the points P_{1} and P_{2} using
Amper’s law.

*Inst.Metin BEDİR*

*Asst.Prof.Dr.A.Necmeddin YAZICI*

*Asst.Prof.Dr.Güler YILDIRIM*

*Assoc.Prof.Dr.Zihni ÖZTÜRK*

** **

** **

** **

** **

** **

**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 (Q_{5}=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 Q_{5}.

**e-)**
What is the potential energy of the charge Q_{5}.

** **

**Q-2-)** Consider a spherical uniform
volume charge density r

with Q=61 nC and r_{0}=48 mm.

**a-) **Determine
the volume charge density r.

**b-)**
Find the electric field E at point r=24, 48, and 96 mm

from the center of the shere.

**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 mC 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 2r_{3} 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.

*Inst.Metin BEDİR*

*Asst.Prof.Dr.A.Necmeddin YAZICI*

**Time Duration : 120 Mins.**

- 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.

- A very long conducting cyclindrical rod of length L and

radius R_{1} with
a total charge +q is surrounded by a

non-conducting
cyclindrical shell of inner radius

R_{2} outer
radius R_{3} with total charge –2q. Use

Gauss’s law to find the
electric field at

a-) r<R_{1}

b-) R_{1}<r<R_{2}

c-) R_{2}<r<R_{3}

d-) R_{3}<r

- A charged particle is projected between

the opposite charged
parallel plates. The

mass of the particle is
10^{-27}kg and its

charge is 1.2x10^{-9}
C which is fired with an

initial velocity 10^{6}
m/sec and 37^{0} 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.

- a-) A ring of outer radius R and inner radius

r=0.4R; the ring has a
uniform surface charge

density s 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.

- A parallel-plate capacitor has circular

plates of 6 cm radius and is filled with

two dielectric materials
with dielectric

constants k_{1}=0.1
and k_{2}=0.2,
respectively.

The plate seperation
distance is 2 mm.

The system is connected a
potential

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.

**Time Duration : 120 Mins.**

1.
**a-)** The current density across a cylindrical copper wire
of radius *R _{0}* varies according to the equation

_{}

where *r* is the distance from the central axis.
Calculate the current (I) in terms of *J _{0}*, cross sectional
area and radius

**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 *s*, electric field *E* when *J _{0}*=1.33x10

2.
What is the potential difference across the resistance
R_{x} in below Figure.

3.
a-) What is the
current and voltage across the

capacitors and resistor R_{3} 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 R_{3} after the switch

passing position 2 at t=10 msec.

4.
A positively charged particle (q=e, m= 6.7x10^{-27}
kg) is

accelerated by potential difference V_{0}=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 *I _{1}*=10 A and

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?

*Inst.Metin BEDİR*

*Asst.Prof.Dr.A.Necmeddin YAZICI*

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 R_{a} ?

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 6.0W 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 **l****(C/m)**. Find the potential difference

between the two points a and b.

**Q- 3)** A thick
spherical shell has a charge Q, an inner radius

r_{1}
and an outer radius r_{2}. The charge distribution

between
r_{1} and r_{2} is spherically symmetric but

varies
with a radialdistance from the center

**r****=C/r**, where C is a
constant and r is the

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,r_{1} and r_{2} such that the electric field
between r_{1} and r_{2} is to be uniform.

**b)
**What should the value of C be so that the
electric field in the region r_{1}<r<r_{2}
has constant magnitude.

**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 I_{1} along the axis of a metal tube

with
inner radius b and outer radius c. The tube carries a

current
I_{1} in a direction oppposite to that in the wire. Find

the
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.

**03/10/2000**

**EP
106 RETEST EXAM. **

** Duration:100 min**

** **

Q-1) Four charges of 1mC 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 r=r_{0
},

inner radius R_{0} outer
radius R_{1}. Find:

a)- the electric field for r<
R_{0 , }R_{0 }<r<R , r
>R_{1 } .

b)- the work done to move a charge Q
from 4R_{1} to 2R_{1}.

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 distance y (not very

small)
above the origin and 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-2)**
A sphere of radius 6 cm has a volume charge density r= 2x10^{3}C/m^{3},

and
is surrounded by a thin metal shell of radius 8 cm whose surface

charge
density s
= 1x10^{2} C/m^{2}.
Calculate the electric field at

r=3
cm, r=7 cm, and r=10cm.

** **

** **

** **

** **

** **

**Q-3)**
A 20 cm long wire has a uniform charge density, l=3.00
C/m. It 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.

** **

** **

**Q-4)**.Find
the current and voltage across the resistance R_{x} in below figure.