Download Principles of Technology

Principles of Technology
CH 11 MAGNETISM 2
Name________
KEY OBJECTIVES
At the conclusion of this chapter you will be able to:
• Describe the mutual effect of two parallel current-carrying wires.
• Define the term torque, and describe how a torque arises as a result of a current-carrying loop in a magnetic
field.
• Describe the principle upon which a galvanometer operates.
• Describe how a galvanometer may be converted into an ammeter or a voltmeter.
• Describe how a direct-current motor is constructed.
• Use an appropriate hand rule to determine the force on a charged particle moving in an external magnetic
field.
• State the equation that detect the magnitude of the force on a charged particle moving in an external magnetic
field, and use this equation to solve related problems.
• Describe the principle upon which mass spectrometry operates.
Forces Between Current-Carrying Parallel Wires
If each of two parallel wires carries a current, the magnetic fields will interact. If the currents are oriented in
the same direction, they will attract each other; if oriented in opposite directions, they will repel each
other (Fig 1).
Fig 1. Magnetic fields in parallel wires (below)
Fig. 2 The diagram represents a rectangular loop placed in a uniform magnetic field (above).
The diagram shows that the orientation of the magnetic field between the two parallel wires is similar to
the orientation of the magnetic field between the bar magnets. Because the bar magnets attract each other,
we can infer that the wires will attract each other.
The force on either wire is directly proportional to the currents in the two wires and the lengths of the
wires, and is inversely proportional to the distance between the wires. This parallel-wire arrangement is
used to define the ampere as a unit of current: Two parallel wires will each carry a current of I ampere if both
wires are 1 meter in length and 1 meter apart, and a force of 2 x 10-7 newton (exactly) exists between them.
Assessment Question 1
Which set of statements is true:
i. If two parallel wires have currents that are oriented in the same direction, they will attract each other;
ii. If two parallel wires have currents that are oriented in opposite directions, they will repel each other.
iii. The orientation of the magnetic field between the two parallel wires is OPPOSITE to the orientation of the
magnetic field between the bar magnets.
iv. The force on either wire is directly proportional to the currents in the two wires and the lengths of the wires,
and is inversely proportional to the distance between the wires.
v. If bar magnets ATTRACT each other, we can infer that the wires will REPEL each other.
a) i , ii, iv
b) i , iii, iv
c) ii , iii, v
d) i , iii, v
Torque and Electromagnetism
The diagram (Fig. 2) represents a rectangular loop placed in a uniform magnetic field. The portions of the
loop that are parallel to the magnetic field (A and C) will experience no force. If we apply right hand rule 3
to section B of the loop, we find that it experiences a force directly upward out of the page. Similarly,
section D will experience a force directly downward into the page. The net result of these two forces is to
rotate the loop.
Forces that produce rotational motion are called torques. The motion produced by the rotation is the basis
for the electric motor. The torque on the loop is proportional to the current in the loop. The loop will not
rotate continuously, but will stop after a 900 rotation because the net torque on the loop will then be zero.
Assessment Question 2
Which set of statements is true when a rectangular loop is placed in a uniform magnetic field:
i. The portions of the loop that are parallel to the magnetic field will experience INFINITE force.
ii. Some portions of the loop will experience an upward force and other portions a downward force.
iii. The net result of the forces is to rotate the loop.
iv. The motion produced by the rotation of the loop is the basis for the electric motor.
v. The torque on the loop is UNRELATED to the current in the loop.
a) i , ii, iv
b) i , iii, iv
c) ii , iii, iv
d) i , iii, v
Electric Meters
A practical application of the effect described above is the construction of meters for measuring current and
potential difference. The simplest device, the galvanometer, is used to measure small electric currents. A
galvanometer (Fig 3) is constructed by placing a coil of wire in a permanent magnetic field. The coil is
attached to a spring and a calibrated dial. Since the torque is proportional to the current in the coil, the
deflection of the galvanometer needle will depend on this current.
Fig 3. A galvanometer (below)
Fig. 4: An Ammeter (above).
Assessment Question 3
Which set of statements is true?
i. A practical application of the torque caused by electromagnetism is the construction of meters for measuring
current and potential difference.
ii. A galvanometer is used to measure very large electric currents.
iii. A galvanometer is constructed by placing a coil of wire attached to a spring and a calibrated dial in a
permanent magnetic field.
iv. The torque in a galvanometer is UNRELATED to the current in the coil.
v. The deflection of the galvanometer needle will depend on this current.
a) i , ii, iv
b) i , iii, iv
c) ii , iii, iv
d) i , iii, v
An ammeter (Fig. 4) is a galvanometer that has been modified in order to measure larger currents. A lowresistance device, known as a shunt, is placed in parallel with the wires of the galvanometer as shown in the
diagram.
Most of the current in the circuit passes through the shunt, not through the galvanometer wires. Nevertheless,
the dial on the ammeter is calibrated to read the current passing through both the shunt and the galvanometer
wires. An ammeter is a low-resistance device connected in series with the circuit it is measuring. The low
resistance of the ammeter causes a minimal effect on the circuit.
Assessment Question 4
Which set of statements is true?
i. An ammeter is a thermometer that has been modified in order to measure very small currents.
ii. An ammeter is a low-resistance device connected in series with the circuit it is measuring.
iii. The high resistance of the ammeter causes a major effect on the circuit.
iv. A low-resistance device, known as a shunt, is placed in parallel with the wires of the galvanometer.
v. Most of the current in the circuit passes through the shunt, not through the galvanometer wires.
a) i , ii, iv
b) i , iii, iv
c) ii , iii, iv
d) ii , iv , v
A voltmeter (Fig. 5) is a galvanometer that has been modified to measure the potential difference across two
points in a circuit. Therefore, the voltmeter must be connected in parallel with
the points of the circuit it is measuring, as shown in the diagram.
For the voltmeter to have a minimal effect on the circuit, it must be a highresistance device so that most of the current will flow through the circuit, not
through the voltmeter. This high resistance is gained by placing a large resistor
in series with the galvanometer coil.
Assessment Question 5
Fig. 5: A Voltmeter (above).
Which set of statements is true?
i. A voltmeter is an ammeter that has been modified to measure the force across two points in a circuit.
ii. A voltmeter must be connected in parallel with the points of the circuit it is measuring.
iii. For the voltmeter to have a minimal effect on the circuit, it must be a high- resistance device so that most of
the current will flow through the circuit.
iv. The high resistance in voltmeters is achieved by placing a large resistor in series with the galvanometer coil.
v. The voltmeter will have the greatest effect on current flow if most of the current flows through the circuit
rather than the voltmeter.
a) i , ii, iv
b) i , iii, iv
c) ii , iii, iv
d) i , iii, v
Electric Motors
Another application of a current-carrying loop in a magnetic
field is the electric motor. The electrical energy supplied by
the circuit is converted by means of the magnetic field into
the mechanical energy of rotation. In a motor a coil is wound
around a soft-iron core that concentrates the magnetic field
and increases the magnitude of the torque.
To continue the rotation past 900, the current in the coil must
be reversed after each half rotation. In a direct current (dc)
motor, this reversal is accomplished by means of a device
called a split-ring commutator.
The diagram (Fig. 5) represents a typical motor.
Fig. 5: An Electric Motor (below)
Free Charges In a Magnetic Field
When a charged particle moves freely, the direction of its velocity is analogous to the direction of the current in
a wire. If the charged particle is introduced into a magnetic field, it will experience a force that is always
perpendicular to the direction of its velocity.
We can derive an expression for the magnitude of the force by using the formula:
F= qvB
Assessment Question 6
Which set of statements is true?
i. In a motor a coil is wound around a soft-iron core that concentrates the magnetic field and increases the
magnitude of the torque.
ii. In an electric motor the electrical energy supplied by the circuit is converted by means of the magnetic field
into the mechanical energy of rotation.
iii. To continue the rotation past 900, the current in the coil must be magnified after each half rotation.
iv. When a charged particle moves freely, the direction of its velocity is analogous to the direction of the
current in a wire.
v. If a charged particle is introduced into a magnetic field, it will experience a force that is always parallel to
the direction of its velocity.
a) i , ii, iv
b) i , iii, iv
c) ii , iii, iv
d) i , iii, v
PROBLEM
Calculate the force (F) on a proton with a charge of 1.6 x 10-19 coulomb (q) moving at a speed of 2.0 x 106 m/s
in a magnetic field of 0.50 tesla (B).
SOLUTION
F = qvB
F =(l.6x 10-19 C)(2.0 x 106 m/s) (0.50 N/A∙m)
F = 1.6 x 10-13 N
Assessment Question 7
Calculate the force (F) on a charged particle with 0.085 coloumbs (q) of charge in a magnetic field whose
induction is 0.015 teslas (B) if the charged particle has a velocity of 300,000 m/s (v).
F= qvB
a) 7.75 N
b) 81.25 N
c) 382.5 N
d) 4800 N
We can modify right hand rule 3 as follows:
The thumb of the right hand now represents the direction of the velocity of the positively charged particle. The
fingers in the direction of the magnetic field and the force point away from the palm (for negative particles, use
the left hand).
Fig 7. Right Hand Rule 3 (below)
Fig. 8: Motion of charged particles in a magnetic field (below).
Motion of Charged Particles in a Magnetic Field
Since the particle is free to move, its velocity continually changes direction and the force always remains
perpendicular to the direction of the velocity. This force is a centripetal force; consequently the object moves in
a circular path, as shown in the diagram above (Fig 8).
Mass Spectrometry
A practical application of the effect
described above is a device known as a
mass spectrometer (Fig. 9), which is used
to measure the charge-to-mass ratio of
ions. A beam of charged particles is
introduced into a magnetic field (B). By
measuring the radius (r) of the circular
path and the speed (v) of the particles,
we can calculate the charge-to-mass
(q/m) ratio:
q/m = v/Br
Fig 9. A mass spectrometer (below).
If the charges of the particles are known,
then the particle masses can be
determined.
The mass of a particle is directly
proportional to its radius of curvature in
the magnetic field.
The use of mass spectrometry has helped to demonstrate the existence of the electron and the existence of
atomic isotopes.
Assessment Question 8
Which set of statements is true?
i. The velocity of a charged particle continually changes direction in a magnetic field and the force always
remains perpendicular to the direction of the velocity resulting in a centripetal force and the object
moving in a circular path.
ii. A mass spectrometer is used to measure the charge-to-mass ratio of ions.
iii. If the charges of the particles are known, then the particle masses can be determined.
iv. The length of a particle is directly proportional to its breadth of curvature in the magnetic field.
v. The use of mass spectrometry has not helped to anything scientific as of this moment
a) i , ii, iii
b) i , iii, iv
c) ii , iii, iv
d) i , iii, v
Assessment Question 9
Calculate the charge to mass ratio (q/m) if a charged particle moves in a magnetic field whose induction is
0.33 teslas (B) if the charged particle has a velocity of 15,000 m/s (v) and the radius of curvature of its path is
0.7 m (r).
q/m = v/Br
a) 850 C/kg
b) 3600 C/kg
c) 48,000 C/kg
d) 65,000 C/kg
Electron Beams
A device such as a computer monitor or a television tube depends on the production and control of beams of
electrons. An electron beam is generated when a filament is heated until it ejects electrons. This process, called
thermionic emission, is much like the evaporation of water molecules from the surface of liquid water.
Once the electrons are ejected, they are controlled by both electric and magnetic fields.
The diagram (Fig. 10) shows that the direction of a beam of electrons is dependent on the electrical charges of
the parallel plates above and below the beam.
Fig. 10: An electron beam emitter (below)
We have already seen how magnetic fields can be used to change the direction of a charged particle. Originally,
a device known as a cathode ray tube was used to demonstrate the existence and control of electron beams. The
cathode ray tube is an evacuated glass tube that contains a source of electrons at one end, a fluorescent screen
inside the surface at the other end, and two pairs of deflecting plates in between. When an electron beam strikes
the screen, it produces a fluorescent spot of light. The brightness of the spot is directly related to the intensity of
the electron beam striking the screen, and the location of the spot is controlled by the electric fields.
Assessment Question 10
Which set of statements is true?
i. The process of thermionic emission involves an electron beam being generated when a filament is
heated until it ejects electrons
ii. Ejected electrons are controlled by both electric and magnetic fields in devices involving electron beams.
iii. The direction of a beam of electrons in an electron beam emitter is independent of all factors and controls.
iv. A cathode ray tube is sometimes used to demonstrate the existence and control of electron beams and it is
composed of an evacuated glass tube that contains a source of electrons at one end, a fluorescent screen
inside the surface at the other end, and two pairs of deflecting plates in between.
v. A device such as a radio or hearing aide depends on the production and control of beams of electrons.
a) i , ii, iii
b) i , ii, iv
c) ii , iii, iv
d) i , iii, v
Summary
Magnetic fields exist whenever an electric current is present. The direction of the magnetic field is always
perpendicular to the electric field. Current-carrying wires and charges moving perpendicularly through a
magnetic field experience forces that are perpendicular to both the direction of the magnetic field and the
motion of the charges. If the conductor is a loop, a torque will result; this fact is the basis for electric motors and
meters.