1. The velocity of a simple harmonic oscillator is given by v = -9.35sin(26.6t) (mks
units)
1. What is its angular frequency?
2. What is the amplitude of the motion in Problem 1 in meters to two decimal
places?
3. To the nearest hundredth of a meter where is the mass in Problem 1 at the
time t = 23.07 seconds?
4. If the mass in Problem 3 is 0.69 kg, what is the spring's potential energy to the
nearest tenth of a joule?
5. What is its kinetic energy to the nearest tenth of a joule?
2. A 0.32 kg mass is attached to a spring with spring constant 5.4 N/m and let fall. To
the nearest hundredth of a meter what is the point where it 'stops'?
What is the amplitude of the resulting motion?
3. A sinusoidal wave is moving on a string. If you increase the frequency f of the
wave, the transverse speed
A. increases
B. decreases C. stays the same
4. A sinusoidal wave is moving on a string. If you increase the frequency f of the
wave, the wave speed
A. increases
B. decreases C. stays the same
5. A sinusoidal wave is moving on a string. If you increase the frequency f of the
wave, the wavelength
A. increases
B. decreases
C. stays the same
6. What happens to the fundamental frequency of a string fixed at both ends if the
length of the string is doubled? It
A. doubles.
B. stays same.
C. is cut to 1/2
D. is cut to ¼
7. What happens to the fundamental frequency of a string fixed at both ends if the
mass/length density is doubled? It
A. doubles.
B. stays same.
C. is cut to 1/2
D. is cut to
1/ 2
8. What happens to the fundamental frequency of a string fixed at both ends if the
tension in the string is doubled? It
A. doubles
B. increases by
D. is cut to
2 C. is cut to 1/2
1/ 2
9. An earthquake P wave traveling at 8.0 km/s strikes a boundary within the earth at
an incident angle of 47°. If the angle of refraction is 35°, what is the speed in the
second medium?
A. 10.2 km/s
B. 8.0 km/s
C. 6.27 km/s
D. 5.96 km/s
10 At what displacement from equilibrium is the speed of a SHO half the maximum
value?
11. At what displacement from equilibrium is the energy of a SHO half KE and half
PE?
12. A sound wave travels through wood into aluminum, a stiffer medium than wood.
The wave speed in aluminum will be ____ than the speed in wood.
A. higher
B. the same as
C. lower
13. If the frequency of a periodic wave is doubled while the velocity remains the
same, what happens to the wavelength?
A. It is cut to one fourth.
B. It is cut in half.
C. It stays the same.
D. It doubles.
14. A spring has a spring constant of 200 N/m. What mass is needed to obtain an
oscillation with a period of 0.5 s?
A. 0.314 kg
B. 1.27 kg
C. 2.53 kg
D. 15.9 kg
15. How long should a pendulum be in order to have a period of exactly one
second?
A. 1.56 m
B. 0.248 m
C. 4.03 m
D. 387 m
16. A 0.60 kg mass vibrates according to x = 0.45 cos(6.40t). What are the kinetic
and potential energies when x = 0.30 m?
A. 0.45 J, 6.40 J
B. 2.88 J, 3.52 J
C. 1.38 J, 1.11 J
D. 0.45 J, 2.49 J
17. If a 1.00 m long pendulum on planet Gnuton has a period of 3.26 s, what is the
acceleration due to gravity on Gnuton?
A. 73.0 m/s²
B. 10.6 m/s²
C. 3.71 m/s²
D. 0.00238 m/s²
18. How much time will it take sound from an airplane at 9000 m to reach the ground,
assuming a constant temperature of 15°C?
A. 25.7 s
C. 27.2 s
B. 26.5 s
D. 38.1 s
19. The security alarm on a parked car goes off and produces a frequency of 735 Hz.
The speed of sound is 343 m/s. As you drive toward this parked car, pass it, and
drive away, you observe the frequency to change by 78.4 Hz. At what speed are you
driving?
20. Two speakers, one directly behind the other, are each generating a 256-Hz wave.
What is the smallest separation distance between the speakers that will produce
destructive interference at a listener standing in front of them? Take the speed of
sound to be 342 m/s.
21. Pipe A is 30.0 cm long and is closed at one end, open at the other. Pipe B is
open at both ends. How long will pipe B have to be to have the same fundamental
frequency as pipe A?
22. Transverse waves traveling across a rope have a frequency of 12.0 Hz and a
wavelength of 2.40 m. What is the velocity of the waves?
23. How long should an antenna be for a receiver with frequency of 30 MHz?
24. A speeder is pulling directly away and increasing his distance from a police car
that is moving at 29 m/s with respect to the ground. The radar gun in the police car
emits an electromagnetic wave with a frequency of 8.0x109 Hz. The wave reflects
from the speeder\'s car and returns to the police car where its frequency is measured
to be 318Hz less than the emitted frequency. Find the speeder's speed with respect
to the ground.
25. You are driving 8 m/s on a straight road and sounding a horn which you hear at a
frequency of 600Hz. The sound of the horn gets reflected from the high rise building
ahead and you hear the echo.(a)What is the frequency of the echo you hear? (b)
What beat frequency you hear?
26. A 0.824 kg mass attached to a vertical spring of force constant 162 N/m oscillates
with a maximum speed of 0.372 m/s. Calculate
a. the period related to the motion of the mass.
b. the maximum acceleration of the mass.
27. An organ pipe, closed at one end and open at the other, is 34.3 cm long. What is
its fundamental frequency? The speed of sound is 343 m/s
A. 136 Hz
B. 250 Hz
C. 343 Hz
D. 1000 Hz
28. Two identical piano strings are designed to vibrate at 110 Hz but one of them
slips from its normal tension of 600 N to a tension of 540 N. What beat frequency is
now heard?
A. 1.1 Hz
B. 5.6 Hz
C. 7.7 Hz
D. 60 Hz
29. When you drive your car at a constant speed toward a police car, what happens
to the frequency of the radar when it bounces off your car?
A. It is shifted higher.
B. It is shifted lower.
C. It stays the same frequency.
30. What is the frequency you hear when a 500 Hz siren recedes from you at 25
m/s? Assume vsnd = 343 m/s.
A. 432 Hz
B. 500 Hz
C. 466 Hz
D. 534 Hz
31. How long would you make an organ pipe (closed at one end) to produce a
frequency of 440 Hz?
A. 110 cm
B. 77.3 cm
C. 25.8 cm
D. 19.5 cm
32. What would be the beat frequency if radio waves of wavelength 3.141 m and
3.135 m are mixed?
A. 50 GHz
B. 6.0 MHz
C. 609 kHz
D. 183 kHz
45. Three charges, q1 = 4 x 10-6 C, q2 = -2 x 10-6 C, and q3 = 5 x 10-6 C are placed
at the corners of a square with sides 0.30 m. What is the field at at the fourth corner?
46. A charged droplet of mass 5.88 x 10-10 kg is hovering motionless between two
parallel plates. The parallel plates create have a potential difference of 24000 V and
are 2.00 mm apart. What is the charge on the particle? By how many electrons is the
particle deficient?
47. Four point charges form the vertices of a square with sides = L. Two diagonally
opposite charges have a charge of 2.25 C each. The other two charges are identical
to each other and each have a charge, q. If there is no net force on either of the 2.25
C points, what is the value of q?
48.. Two point charges lie on the x-axis. A charge of 9.9 C is at the origin, and a
charge of -5.1 C is at x=10cm.
a. At what position x would a third charge q3 be in equilibrium?
b. Does your answer to part a depend on whether q3 is positive or negative? Explain.
49. Two particles each with a positive charge of q are placed on the vertices of a
square having sides a. A third particle with a positive charge Q is placed at the center
of the square. What is the force on the particle at the center of the square?
50.. A charge of 6.00*10-9 C and a charge of -3.00*10-9 C are separated by a
distance of 60.0 cm. Find the position at which a third charge of 12.0*10-9 C can be
placed so that the net electrostatic force on it is zero.
51. Air breaks down (loses its insulating quality) and sparking results if the field
strength is increased to about 3.0*106 N/C. (a) What acceleration does an electron
experience in such a field? (b) if the electron starts from rest, in what distance does it
acquire a speed equal to 10% of the speed of light?
52. Four point charges, each of magnitude 2.34*10¹ C, are placed at the corners of a
square 40.8 cm on a side. If three of the charges are positive and one is negative,
find the magnitude of the force experienced by the negative charge.
52. Two point charges have a total charge of 560 uC. When placed 1.10m apart, the
force each exerts on the other is 22.8N and is repulsive. What is the charge on each?
53. Calculate the electric field at the center of a square 52.5 cm on a side if one
corner is occupied by a +45.0 x 10-6 C charge and the other three are occupied by 27.0 x 10-6 C charges?
55. Three equal charges, each of +4.6 µC, are spaced along a straight line. Charge
A, is at one end of the line of 1.8 m from the central charge, B. Charge C is the other
side of charge B a distance of 2.2 m from charge B. What is the magnitude and
direction of the total force on each charge?
56. An electric charge Q=4.50 µC is in a region of electric field with a y-component
Ey = 4000 N/C, an x-component Ex = 700 N/C and a z-component Ez = 0. What are
the magnitude and direction of force on the charge Q?
57. .Two free charges, +q and 4q, are placed a distance 1 m apart. A third charge,
Q,is so placed that the entire system is at equilibrium. What is the location,
magnitude and the sign of Q?
58. Find the electric field at a point midway between two charges of +.000000030 C
and +.000000060 C separated by a distance of 30.0 cm.
59. A positive charge of +5.00 µC is placed at the origin. A negative charge of -2.00
µC is placed 20.00 cm away, somewhere in the first quadrant. A third charge of +5.00
µC is placed in the first quadrant, 8.75 cm away from the negative charge. The angle,
going from the original positive charge to the negative charge to the other positive
charge, is 1.396 radians. Find the resultant force exerted on the third charge by the
other two.
60. Two parallel plates 2.1mm apart, are charged so that the potential difference
between the plates is 36V. (i) what is the electric field strength between the plates (ii)
sketch the lines of electric flux between the plates, showing the direction of the field.
(iii) suggest three ways in which the system could be modified to increase its
capacitance. (iv) a small particle charge of +180nC is placed midway between the
plates. find the force on the particle due to the electric field, and the energy required
to move the particle 0.7mm towards the positively charged plate.
61 . How do you calculate the magnitude and direction of the acceleration of a
particle given the electrical field intensity?
62.Two equal, positive charges, q = 2.0 µC are located on the x-axis one at +0.3 m
and the other at -0.3 m. A third charge Q = +4.0 µC is located on the y-axis at +0.4m.
Find
a. the magnitude and direction of the resultant(net) force on Q
b. the electric field at the point (0.0,-0.4m)?
c. the potential at the point (0.0,-0.4m)?
63. A particle (charge 7.5 x 10-6 C)is released from rest at a point on the x-axis, x =
0.1 m. It begins to move due to the presence of a 2.0 x 10-6 C charge which remains
fixed at the origin. What is the kinetic energy of the particle at the instant it passes the
point x = 1.0 m?
64. A charge of uniform density (0.80 nC/m) is distributed along the x-axis from the
origin to the point x = 0.1m. What is the electric potential (relative to zero at infinity) at
a point x=0.18m, on the a-axis?
65. Three equal point charges, each with a charge of 1.50 µC, are placed at the
corners of an equilateral triangle whose sides have a length of 0.200 m. What is the
potential energy of the system? (Take as zero the potential energy of the three
charges when they are infinitely far apart.) Use 8.85×10-12 for the perceptivity of free
space.
66. Two protons and an alpha particle are held at rest at the corners of an equilateral
triangle whose side length is 9.20×10-10 . The particles are released and move
apart. What is their total energy when they are far apart? Use 1.60×10-19 C for the
magnitude of the charge on an electron.
67. An electron moving to the right at 1.0% the speed of light enters a uniform
electric field parallel to its direction of motion. If the electron is to be brought to rest in
the space of 4.0 cm, (a) what direction is required for the electric field, and (b) what is
the strength of the field?
68. A charge of 2.75 µC is held fixed at the origin. A second charge of 2.75 µC is
released from rest at the position (1.15 m, 0.490 m) . a) If the mass of the second
charge is 3.30 g, what is its speed when it moves infinitely far from the origin? in m/s
b.)At what distance from the origin does the 2.75 µC charge attain half the speed it
will have at infinity?
69. What is the charge of q if location A is 2.40 m from the charge, location B is 4.5m
away from the charge, and VB-VA=45V?
70. Two point charges of magnitude 4 nC and 5nC are seperated by 39 cm. The
Coulomb constant is 8.98755 x 109. What is the potential difference between a point
inifinitely far away and a point midway between the charges? Answer in units of V.
71. An electron that is initially 53 cm away from a proton is displaced to another
point. The Coulomb constant is 8.98755 x 109 Nm2/C2 and the acceleration of
gravitiy is 9.8 m/s2. If the change in electric potential energy as a result of this
movement is 3 x 10-28 J, what is the final distance between the electron and the
proton? Answer in units of m.
72. To move a charged particle through an electric potential difference of 2.0x10-6 V
requires 4.8x10-6 J of energy. What is the magnitude of the charge?
73. If V=0 at a point in space, must E=0 there? ____
If E=0 at a point in space, must V=0 there? ____
A. yes . . . yes
B. yes . . . no
C. no . . . yes
D. no . . . no
74. Conductors with charges +10µC and -10µC have a potential difference of 10 V.
What is the capacitance?
A. 1 pF
B. 10 pF
C. 1 µF
D. 100 µF.
75. A capacitor has fixed charges on its plates as the separation between the plates
is doubled. What happens to the energy stored in the electric field?
A. PE2 = 4 PE1
B. PE2 = 2 PE1
C. PE2 = 0.5 PE1
D. PE2 = 0.25 PE1
76. A capacitor with A=25 cm2 and d=1.5 cm is charged to 250 V. What is the charge
on its plates?
A. 151 nC
B. 369 pC
C. 519 µC
D. 17.1 mC
77. Calculate the speed of a proton accelerated from rest through 120 V.
A. 23.1 Gm/s
B. 6.49 Mm/s
C. 152 km/s
D. 120 m/s
78. An electron (q = 1.6 x 10-19C; m =9.11 x 10-31 kg) accelerates from rest through a
potential difference of 171.5 V. What is the electron's final speed (in m/s)?
79.Three charges are fixed as shown, with Q1 = - 4.52 ľC, Q2 = 2.99 ľC, and Q3 =
1.29 ľC. How many degrees below the x axis is the force on a proton located at point
P?
80. How much work (in J) is required to move 1.6 mC of charge from a distance of
3.59 m to a distance 1.75 m from a charge of 4.02 µC?
81. The electric field intensity 22.2 m away from a charged sphere is 10.38 N/C.
What charge (in µC) has been added to the sphere?
82. Find the potential difference VB - VA for the configuration of Fig. P25.10.
A. 455 V
C. 325 V
B. 260 V
D. -325 V
83. What is the electric potential at the origin for the charge configuration of Fig.
P25.17?
A. 400 V
B. 800 V
C. 22.5 kV
D. 45.0 kV
84. What field is required to stop electrons having energy 1.60×10-17 J in a distance
of 10.0 cm?
A. 1.0 N/C
B. 10 N/C
C. 100 N/C
D. 1000 N/C
85. Calculate the electric field at Q using the figure if Q = 1 nC and l = 1 m.
A. 53.2 N/C at 121°
B. 14.8 N/C at 68°
C. 105 N/C at 168°
D. 37.6 N/C at -31°
86. The electric field midway between two equal but opposite point charges is 745
N/C, and the distance between the charges is 16.0 cm. What is the magnitude of the
charge on each?
A. 3.31×10-9 C
B. 2.65×10-10 C
C. 4.14×10-6 C
D. 3.02×108 C
87. Two resistors of 12.0 ohms and 6.00 ohms are connected in parallel and this
combination is connected in a series with a 6.25 ohm resistor and a battery which
has an internal resistance of .250 ohms. The current in the 6.00 resistor is 8.800 A.
What is the EMF?
88. Two light bulbs are designed for use at 120 V and are rated at 75 W and 150 W.
Which light bulb had the greater filament resistance?
89. Two resistors of 15 and 30 Ohms are connected in parallel. If the combination is
connected in series with a 9 V battery and a 20 Ohm resistor, what is the current
through the 15 Ohm resistor?
90. What field is required to stop electrons having energy 1.60×10-17 J in a distance
of 10.0 cm?
A. 1.0 N/C
B. 10 N/C
C. 100 N/C
D. 1000 N/C
91. Design a voltage divider that would provide one-fifth (0.20) of the battery voltage
across R2. What is the ratio R1 / R2?
A. 5/4
B. 4/5
C. 5
D. 4
92. What is the equivalent capacitance of the configuration below if each capacitor is
identical?
A. C/3
C. 11C/6
B. 2C
D. 6C/7
93. In Fig. P28.6, what is the current
through the 7.00 W resistor if DVab =
34.0 V?
A. 0.835 A
B. 1.17 A
C. 1.74 A
D. 7.72 A
94. Two resistors have Reff = 690 Ohm in series and 150 Ohm in parallel. What are
their values?
A. 180 Ohm, 320 Ohm
B. 250 Ohm, 250 Ohm
C. 136 Ohm, 722 Ohm
D. 220 Ohm, 470 Ohm
95. If the ammeter reads 2.00 A, what is the unknown battery voltage e in Fig.
P28.18?
A. 15.2 V
B. 12.6 V
C. 6.50 V
D. 3.33 V
96. A 75 W @ 120 V lamp is connected to an extension
cord with two wires of 0.800 Ω each. What power is
actually delivered to the lamp?
A. 75.0 W
B. 74.5 W
C. 73.8 W
D. 72.2 W
97. A 9.0-V battery is connected to a bulb whose resistance is 1.6 Ω. How many
electrons leave the battery per second?
A. 5.62 e/s
B. 337 e/s
C. 9.00×1019 e/s
D. 3.51×1019 e/s
98. A 2.0 m long, 0.012 m radius wire carries 3.00 A of current driven by V=240 V.
What is the resistivity of the conductor?
A. 80.0 W·m
B. 3.54×105 W·m
C. 0.112 W·m
D. 0.0181 W·m
99. How much current will a 50-W light bulb draw from a 12-V battery?
A. 0.24 A
B. 4.17 A
C. 12 A
D. 600 A
100. What power does a TV require if it draws 150 mA from the 120-V outlet?
A. 0.80 W
B. 1.25 W
C. 18 W
D. 18 kW
101. A 2.0 m long, 0.012 m radius wire carries 3.00 A of current driven by V=240 V.
What is the resistivity of the conductor?
A. 80.0 W·m
B. 3.54×105 W·m
C. 0.112 W·m
D. 0.0181 W·m
101. A 100-W resistor is attached to a 3-V battery. How much current will flow
through the circuit?
A. 30 mA
B. 3.0 A
C. 33 A
D. 300 A
102. If a 6-V battery provides 0.25 A of current to a light bulb, what is the resistance
of the light bulb?
A. 0.042 W
B. 1.5 W
C. 6.0 W
D. 24 W
103. A jumper cable used to start a stalled vehicle carries a 65 A current. How strong
is the magnetic field 6.0 cm away from it?
A. 2.17×10-4 T
B. 6.90×10-5 T
C. 3.45×10-5 T
D. 1.38×10-6 T
104. A horizontal conductor is carrying 5.0 A of current to the east. A magnetic field
of 0.20 T pointing straight up cuts across 1.5 m of the conductor. What is the force
acting on the conductor?
105. Find the magnetic flux density 3.1 mm away from a long straight wire carrying a
current of 1.2 A.
b. What force per metre would another long wire feel if it was 3.1mm away from the
wire in part (a) and carrying a current of 4.5A.
c. What force would a 37 µC charged particle feel if it was moving away from the wire
in part (a) from the distance of 3.1mm at a speed of 6.5 m/s?
106. A conducting wire 85 cm long passes through a magnetic field of flux 520 mT at
2.2m/s. What emf will be generated in the wire if it is: (a) perpendicular to the lines of
flux, (b) at 45 degrees to the lines of flux, (c) parallel to the lines of the flux?
107. A conducting rod of 25 cm is pushed across a magnetic field along a U-shaped
wire at a constant speed of 2.0 m/s. The field is directed away from the observer and
is 4.00 T. A current of 8.00 A is induced in the circuit.
108. A conducting rod of 25 cm is pushed across a magnetic field along a U-shaped
wire at a constant speed of 2.0 m/s.
a. What is the potential difference induced in the circuit?
b. What is the resistance of the circuit?
c. What is the force used to push the rod?
d. In what direction is current flowing in the rod?
109. The force on a wire carrying 8.75 A is a maximum
of 1.28 N when placed between the pole faces of a magnet that are 55.5 cm in
diameter. What is the approximate strength of the magnetic field?
A. 1.28 T
B. 0.875 T
C. 0.379 T
D. 0.264 T
110. A proton moving in a circular path has a period of 1.00 µs. What is B?
A. 1.00 µT
B. 55.2 µT
C. 33.3 mT
D. 65.6 mT
111. Determine the magnitude and direction of the force between two parallel wires
35 m long and 6.0 cm apart, each carrying 25 A in the same direction.
A. 0.0729 N attractive
B. 0.0729 N repulsive
C. 2.92 N attractive
D. 2.92 N repulsive
112. Current is produced in a loop when a magnet is moved into the loop. Where
does the electrical energy come from?
A. Energy stored in the wire atoms.
B. Energy stored in the magnet
C. Energy in the magnet's motion.
D. Energy in electric waves.
113. In what time must a 0.20 T magnetic field be turned off in order to induce a 10
kV emf in a solenoid of 500 turns and 10 cm diameter?
A. 5.33 µs
B. 78.5 µs
C. 335 µs
D. 22.2 ms
114. A 1.2 m frictionless bar slides in a 2.5 T magnetic field as shown. If R = 6.0 W,
what force is needed to keep the bar sliding
at 2.0 m/s?
A. 3.00 N
B. 1.00 N
C. 0.500 N
D. 0.025 N
115. In what time must a 0.20 T magnetic field be turned off in order to induce a 10
kV emf in a solenoid of 500 turns and 10 cm diameter?
A. 5.33 µs
B. 78.5 µs
C. 335 µs
D. 22.2 ms
116. An electric field is produced by
A. a constant magnetic field
B. a changing magnetic field
C. either a constant or a changing magnetic field
D. an electric current
117. What is Bmax for an EM wave emitted by a 10 kW radio station 5 km away?
A. 33.3 µT
B. 338 nT
C. 0.516 nT
D. 19.5 mT
118. Electric Dipole: a pair of charges lies in the x-y plane. The charge +q is at
coordinate x = d,
y = 0; the charge -q is at coordinate x = -d, y = 0.
(a) Evaluate the electric field magnitude and direction) at point (0,a).
Show that for a>>d
E ∝
1
a3
What is the direction in this limit? (suppose a>0)
(b) Evaluate the electric field at the point (a, 0). Find also the magnitude and direction
for a>>d (suppose a>0)
(c) How much work does it need to move a particle with charge q’ from (a, 0) to (0, a).
(Do not assume a>>d)
119. Energy of a radial charge distributions. A spherically symmetric charge
distribution has charge density r
ρ
=
ρ0 , r < a
=
0, r ≥
(a)Findthe electric field E everywhere.
(b)Findthe electrostatic potential V everywhere.
120. A.Hollow spherical shell carries charge density
region a≤ r≤ b.(figure 1)
ρ=
k
r2
in the
Figure 1: Concentric sphere shell with inner radius a,
outer radius b.
(a)Findthe electric field Eeverywhere in space.
(b)Findt he potential V everywhere in space.
120. Two 256.5 m long wires run parallel to each other separated by 26.27 mm and
with a force between them of 0.0204101355919 N. If one of them carries a currents
of 2.636 A, what is the current in the other?
121. There is a 0.00410821440469 N force between two 817.6 m wires which run
parallel to each other carrying currents of 0.316 A and 4.884 A. What is the
separation between the wires?
122. Two 465.3 m long wires run parallel to each other separated by 26.3 mm and
with a force between them of 0.0423177965589 N. If one of them carries a currents
of 2.715 A, what is the current in the other?
123. A small charge of 503 C is at the center of a ball. If the flux 5.588 E-8 N.m2/C
passes through the ball's surface, what is the radius of the ball (if it matters)?
124. Electric charge is distributed uniformly along a semicircle of radius a with a total
charge Q. calculate the potential at the center of curvature if the potential is assumed
to be zero at the infinity.
125. The vacuum paralell plate capacitor of capacitance C= 0,47 nF is connected
permanently to the voltage 3V. How the energy stored in the capacitor changes when
the distance between the plates is increased two times.
126. The vacuum paralell plate capacitor of capacitance C= 0,47 nF has been
charged by connection to the voltage 3V and disconnected. How the energy stored in
the capacitor changes when the capacitor is filled with the mateial of dielectric
constant ε= 5.
127. Find the electrical capacitance of the parallel plate capacitor of area S and
separation d filled with the dielectric material which dielectric constant is є.
128. Find the magnetic field B of the segment of straight wire (length L ) carrying the
current i at the point placed on the bisector line of the segment at distance D from
it. (Use the Biot-Savart's law)
129. Find the capacitance of the spherical capacitor of radii R1 and R2 with the
dielectric material which dielectric constant is ε .
130. Find the magnetic induction B on the axis of the circular ring of radius r with
current i.
131. Find the electric field and potential difference between two points placed at
distances D1 and D2 from the infinite plane of charge . Assume constant surface
charge density.
132. Using the Biot Savart Law find the magnetic induction at the point A placed on
the axis of symmetry of a straight segment of wire (length L) with current i .Point A is
placed at a distance D from the centre of the segment.
133. Find the electrical capacitance of the cylindrical capacitor of area length L and
radii x y filled with the dielectric material of dielectric constant is є.
134. Find the magnetic field B due to the circular loop of radius R with the current I .
Consider point placed at a distance d from the plane of the loop, on the axis of the
loop, perpendicular to its plane.
135. Find the electric potential in the field of spherical surface charge of radius R ,
charged with surface charge density σ at points inside and outside the sphere.
136. Find the electric energy change of parallel plate vacuum capacitor of plate area
S and separation d due to the increase of the distance between the plates up to 3d.
Consider and compare two cases.
1.
Capacitor was permanently connected to the battery of voltage U.
2.
Capacitor was initially fully charged due to the connection to the battery U,
then disconnected from the battery and subsequently the distance between the
plates has been changed.
137. Find the electric potential in the field of spherical charge of radius R , charged
with volume charge density f at points inside and outside the sphere.
138. Find electric potential in the plane of symmetry of a electric dipole of dipole
moment p at a distance x from it.
139. Find the electic field in the plane of symmetry of a electric dipole of dipole
moement p at a distance x from it.
140. Find the torque on an electric dipole with dipole moment p placed in a uniform
electric field E when the angle between the electric field vector and the dipole
moment is 30 degrees.