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)

2) At some instant the velocity components of an electron moving between two charged parallel plates are v_x=2x10⁵ m/sec and v_y=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)

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)

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 m_e=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 E_x=3x10³ 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=9x10⁹ Nm²/C²; 1 μC=1x10^-6 C m_e=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).

(l=4 cm, x=3 cm, l=1x10⁴ 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 +q₀ 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 q₀, m , c and x₀.

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 u between the plates.

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

V_C(t)=V₀ (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 cm² 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=6.02x10²³ mole^-1, r=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.

(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 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

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.

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

with Q=61 nC and r₀=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 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.

Inst.Metin BEDİR

Asst.Prof.Dr.A.Necmeddin YAZICI

EP 106 General PhysicsExam

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 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

Gauss’s law to find the electric field at

a-) r<R₁

b-) R₁<r<R₂

c-) R₂<r<R₃

d-) R₃<r

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.

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 k₁=0.1 and k₂=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.

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

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 mm² and 314 m. Calculate the resistance R, current I, current density J, conductivity s, electric field E when J₀=1.33x10³ A/m and r=1.72x10^-8 W-m.

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 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.

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?

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

r₁ and an outer radius r₂. The charge distribution

between r₁ and r₂ 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,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 r₁<r<r₂ 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 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 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=r₀,

inner radius R₀ outer radius R₁. Find:

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