Transcript Magnetism - mjburns.net

Magnetism
Practice Questions
Magnetic I
FM  qvB sin  
r
mv
Bq
Radius of curved path. The radius of the path of a charge
with a given velocity of a given Magnetic field.
FM  ILB sin  
B  o
B  o
Magnetic Force. The magnetic force direction is given by the
right Hand Rule.
I
Force on a Conductor. The force on a wire of length in a
magnetic field.
2 r
Amperes Law. The strength of a magnetic field generated
by a conductor.
NI
L
Magnetic Field Generated by A Solenoid. The magnetic
field by a Solenoid of length L with N loops.
Tm
o  4 10
A
7
Magnetic II
FM 
o I1 I 2 L
2 d
 B  BA cos  
  N

t
Magnetic Force. The magnetic force between two wires of
length L when they are a distance d apart.
Magnetic Flux. The strength of the magnetic flux of a
magnetic field going through an area.
Induced Voltage. The induced emf by a changing flux.
  BLv sin  
Faraday’s Law. The induced emf in a moving conductor.
  NIAB sin  
Magnetic Torque (Force). The magnetic turning force on a
loop of wire.
Tm
o  4 10
A
7
 q  1.6 10
19
C
Question
A beam of protons (q=1.6x10-19C) moves at 3.0x105 m/s through a uniform
magnetic field with magnitude 3.0 T that is directed along the z-axis. The
velocity of each proton lies in the xz-plane at an angle of 300 to the +zaxis.
Determine the force on a proton.
The charge is positive, so the force is in the
same direction as the vector product v x B
which is in the negative y-axis.
F  qvB sin  
m

 1.6 1019 C   3.0 105   3.0T  sin  30 
s

 7.2 1014 N
The direction is down (-y )
Practice Question
An electron accelerates from rest in a horizontally directed electric field through
a potential difference of 52 V. The electron then leaves the electric field,
entering a magnetic field of magnitude 0.30 T directed into the page.
a. Calculate the initial speed of the electron upon entering the magnetic field.
b. Calculate the magnitude and direction of the magnetic force on the electron.
c. Calculate the radius of the electrons circular path.
Practice Question Solution
An electron accelerates from rest in a horizontally directed electric field through a potential difference
of 52 V. The electron then leaves the electric field, entering a magnetic field of magnitude 0.30 T
directed into the page.
a. Calculate the initial speed of the electron upon entering the magnetic field.
b. Calculate the magnitude and direction of the magnetic force on the electron.
c. Calculate the radius of the electrons circular path.
Because the moving particles are electrons
(negatively charged), the direction of the force causes
the electrons to move in a curved path.
U E  EK
The electric potential
energy lost by the
electron in moving
through the electric
potential difference
equals its gain in
kinetic energy.
1
qV  mv 2
2
2 q V
v
m

2 1.6 1019 C   52V 
9.111031 kg
 4.3  106
m
s
Practice Question Solution
An electron accelerates from rest in a horizontally directed electric field through a potential difference
of 52 V. The electron then leaves the electric field, entering a magnetic field of magnitude 0.30 T
directed into the page.
a. Calculate the initial speed of the electron upon entering the magnetic field.
b. Calculate the magnitude and direction of the magnetic force on the electron.
c. Calculate the radius of the electrons circular path.
FM  qvB sin  
m 
kg 

 1.6 1019 C   4.3 106  0.30
 sin  90 
s
C

s



 2.11013 N
B
F
v
Applying the right hand rule
with electrons if the
electron is moving to the
right, the force is down.
Practice Question Solution
An electron accelerates from rest in a horizontally directed electric field through a potential difference
of 52 V. The electron then leaves the electric field, entering a magnetic field of magnitude 0.30 T
directed into the page.
a. Calculate the initial speed of the electron upon entering the magnetic field.
b. Calculate the magnitude and direction of the magnetic force on the electron.
c. Calculate the radius of the electrons circular path.
The electron will go in a uniform circular motion. The
magnetic force is the net centripetal force.
FM  FC
mv 2
qvB sin  90  
r
mv
r
Bq

m

kg   4.3 106 
s

 0.30T  1.6 1019 C 
 9.1110
31
 8.2  105 m
Practice Question
Determine a formula for calculating the mass of a particle of charge q, through
a potential difference of V, into a uniform magnetic field of B when the radius
of the curved path of the deflected mass is r.
EU  EK
FM  Fc
1 2
mv
2
2qV
v
m
qV 
mv 2
qvB sin  90  
r
qBr
v
m
Setting both of
these equations
equal to each other
and solve for m
qBr
2qV

m
m
q 2 B 2 r 2 2qV

m2
m
qB 2 r 2
m
2 V
The electric
potential energy
lost by the particle
moving through the
electric potential
difference equals
its gain in kinetic
energy
Practice Question
A straight conductor 5.0 cm long with a current of 21 A moves through a
uniform 0.40T magnetic field . Calculate the magnitude of the force when the
angle between the current and the magnetic field is 300
F  I  l  B  sin  
  21A 0.05m  0.4T  sin  30
 0.21N
Practice Question
What is the magnitude of a field 3.2 cm from a straight long conductor carrying
a current of 4.1 A?
 I 
B  0 

 2 r 


4.1A

7 T  m 
  4 10

 
A
2

0.032
m


 
 2.6 105 T
Practice Question
What is the magnitude of the force between two parallel conductors 3.0 m long,
with currents of 5.0 A and 9.0 A, 20 cm apart?
u0 I1I 2l
F2 
2 d

7 T  m 
 4 10
  5.0 A 9.0 A 3.0m 
A 

2  0.20m 
 1.4 104 N
Practice Question
A particle with charge q is injected into a region with a constant magnetic field
having straight, parallel lines of B that are perpendicular to and out of the paper,
as shown. The velocity v at the point of injection is entirely in the y-direction in the
figure. The particle emerges from this region (as shown) a distance S away and
with a velocity that is entirely in the negative-y direction. Ignore gravity (The z-axis
points out of the page).
a) What is the sign of the charge of the particle?
b) What is the mass of the particle?
Practice Question Solution
A particle with charge q is injected into a region with a constant magnetic field
having straight, parallel lines of B that are perpendicular to and out of the paper,
as shown. The velocity v at the point of injection is entirely in the y-direction in the
figure. The particle emerges from this region (as shown) a distance S away and
with a velocity that is entirely in the negative-y direction. Ignore gravity (The z-axis
points out of the page).
a) What is the sign of the charge of the particle?
b) What is the mass of the particle?
B
F
v
Because the
particle is forced to
the left, via the
Right hand Rule, it
must be negatively
charged
Practice Question Solution
A particle with charge q is injected into a region with a constant magnetic field
having straight, parallel lines of B that are perpendicular to and out of the paper,
as shown. The velocity v at the point of injection is entirely in the y-direction in the
figure. The particle emerges from this region (as shown) a distance S away and
with a velocity that is entirely in the negative-y direction. Ignore gravity (The z-axis
points out of the page).
a) What is the sign of the charge of the particle?
b) What is the mass of the particle?
FC  FB
mv 2
 qvB sin  
r
qBr sin  
m
v
qB .5s  sin  

v
Practice Question
A rectangular loop, carrying a current I, is in the plane of the paper. A uniform
magnetic field points directly out of the paper, both inside and out of the loop. The
direction of the current is given in the figure, and three of the sides of the
rectangle are labeled 1, 2, and 3. Which of the following is true.
a) The torque on the loop is such as to push side 1 into and side 3 out of the
paper.
b) The torque on the loop is such as to push side 3 into the paper and side 1 out
of the paper.
c) Sides 1 and 3 of the coil are both pulled out of the plane of the paper.
d) Side 2 is pulled out of the plane of the paper.
e) The forces on sides 1, 2 and 3 are directly away from the center of the loop.
Practice Question
Two long, straight carrying wires (each 15 m in length) are positioned
perpendicular to the paper as indicated in the figure. In wire 1 the current (4 Amp)
is coming out of the paper and in wire 2 the current (2 Amp) is going into the
paper.
a) What is the magnitude of the magnetic field at the location of wire 1 due to
wire 2?
b) What is the direction of this magnetic field at wire 1?
c) What is the magnitude of the force on wire 1?
d) What is the direction of this force on wire 1?
Practice Question
Two long, straight carrying wires (each 15 m in length) are positioned
perpendicular to the paper as indicated in the figure. In wire 1 the current (4 Amp)
is coming out of the paper and in wire 2 the current (2 Amp) is going into the
paper.
a) What is the magnitude of the magnetic field at the location of wire 1 due to
wire 2?
b) What is the direction of this magnetic field at wire 1?
c) What is the magnitude of the force on wire 1?
d) What is the direction of this force on wire 1?
0 I
B
2 d

7 T  m 
4


10

  2 A
A


2  0.7m 
 5.7 107 T
Practice Question
Two long, straight carrying wires (each 15 m in length) are positioned
perpendicular to the paper as indicated in the figure. In wire 1 the current (4 Amp)
is coming out of the paper and in wire 2 the current (2 Amp) is going into the
paper.
a) What is the magnitude of the magnetic field at the location of wire 1 due to
wire 2?
b) What is the direction of this magnetic field at wire 1?
c) What is the magnitude of the force on wire 1?
d) What is the direction of this force on wire 1?
Upward
F  ILB sin  
  4 A15m   5.7 107 T  sin  90 
 3.4 105 N
Practice Question
Two long, straight carrying wires (each 15 m in length) are positioned
perpendicular to the paper as indicated in the figure. In wire 1 the current (4 Amp)
is coming out of the paper and in wire 2 the current (2 Amp) is going into the
paper.
a) What is the magnitude of the magnetic field at the location of wire 1 due to
wire 2?
b) What is the direction of this magnetic field at wire 1?
c) What is the magnitude of the force on wire 1?
d) What is the direction of this force on wire 1?
F  ILB sin  
or
  4 A15m   5.7 107 T  sin  90 
 3.4 105 N
F 0 I1I 2

l
2 d
F

l 0 I1I 2
2 d
T m 
  4 A  2 A 
A 
2  0.7m 
.15m   4 107

 3.4 105 N
Practice Question
Two long, straight carrying wires (each 15 m in length) are positioned
perpendicular to the paper as indicated in the figure. In wire 1 the current (4 Amp)
is coming out of the paper and in wire 2 the current (2 Amp) is going into the
paper.
a) What is the magnitude of the magnetic field at the location of wire 1 due to
wire 2?
b) What is the direction of this magnetic field at wire 1?
c) What is the magnitude of the force on wire 1?
B
d) What is the direction of this force on wire 1?
F
Away from wire 2
Remember when you apply the Right
Hand Rule, The current is the one which
you are determining the force on.
Practice Question
The diagram shows a positive charge q entering the lower right hand corner of a
region in which there is a uniform magnetic field. The field is perpendicular to the
page. The particle emerges from the upper left hand corner of the region, moving
directly leftward. Ignore gravity. Assume the strength of the field is B = 0.25 T and
that the positive charge moves at v =6000 m/s.
a) Does the field point into or out of the page?
b) Assuming still that a positive charge enters, as shown, in the lower right hand
corner of the region, what change might cause the particle to exit through the
bottom side, directly to the left of where it entered?
c) If the charge is a proton (q = 1.6 x 10-19C, m = 1.673 x 10-27 kg), what is the
area of the shaded region?
Practice Question
The diagram shows a positive charge q entering the lower right hand corner of a
region in which there is a uniform magnetic field. The field is perpendicular to the
page. The particle emerges from the upper left hand corner of the region, moving
directly leftward. Ignore gravity. Assume the strength of the field is B = 0.25 T and
that the positive charge moves at v =6000 m/s.
a) Does the field point into or out of the page?
b) Assuming still that a positive charge enters, as shown, in the lower right hand
corner of the region, what change might cause the particle to exit through the
bottom side, directly to the left of where it entered?
c) If the charge is a proton (q = 1.6 x 10-19C, m = 1.673 x 10-27 kg), what is the
area of the shaded region?
By the Right Hand
Rule, it points into the
page.
Practice Question
The diagram shows a positive charge q entering the lower right hand corner of a
region in which there is a uniform magnetic field. The field is perpendicular to the
page. The particle emerges from the upper left hand corner of the region, moving
directly leftward. Ignore gravity. Assume the strength of the field is B = 0.25 T and
that the positive charge moves at v =6000 m/s.
a) Does the field point into or out of the page?
b) Assuming still that a positive charge enters, as shown, in the lower right hand
corner of the region, what change might cause the particle to exit through the
bottom side, directly to the left of where it entered?
c) If the charge is a proton (q = 1.6 x 10-19C, m = 1.673 x 10-27 kg), what is the
radius of the path?
A Stronger Magnetic
Field, A stronger Charge,
A lower velocity, A smaller
mass.
Practice Question
The diagram shows a positive charge q entering the lower right hand corner of a
region in which there is a uniform magnetic field. The field is perpendicular to the
page. The particle emerges from the upper left hand corner of the region, moving
directly leftward. Ignore gravity. Assume the strength of the field is B = 0.25 T and
that the positive charge moves at v =6000 m/s.
a) Does the field point into or out of the page?
b) Assuming still that a positive charge enters, as shown, in the lower right hand
corner of the region, what change might cause the particle to exit through the
bottom side, directly to the left of where it entered?
c) If the charge is a proton (q = 1.6 x 10-19C, m = 1.673 x 10-27 kg), what is the
radius of the circle path?
FC  FB
mv 2
 qvB sin  
r
mv
r
qB
r
mv
qB
1.673 10

1.6 10
m

kg   6000 
s

19
C   0.25T 
27
 2.5095 104
Practice Question
The diagram shows three wires, the first 15 cm directly above the second, and the
second 10 cm directly above the third. The top wire carries current I1 = 4 A to the
right, the second carries I2 = 2 A to the left.
a) Assuming for this question only that I3 = 0, where between the first and
second wires is the magnetic field zero?
b) Assume that the third wire carries I3 = 3 A to the left. What are the magnitude
and direction of the force exerted by the other two wires on a 20 cm length of
the third wire?
Practice Question
The diagram shows three wires, the first 15 cm directly above the second, and the
second 10 cm directly above the third. The top wire carries current I1 = 4 A to the
right, the second carries I2 = 2 A to the left.
a) Assuming for this question only that I3 = 0, where between the first and
second wires is the magnetic field zero?
b) Assume that the third wire carries I3 = 3 A to the left. What are the magnitude
and direction of the force exerted by the other two wires on a 20 cm length of
the third wire?
No Where
The magnetic field
between the two wires
is always pointing into
the screen
Practice Question
The diagram shows three wires, the first 15 cm directly above the second, and the
second 10 cm directly above the third. The top wire carries current I1 = 4 A to the
right, the second carries I2 = 2 A to the left.
a) Assuming for this question only that I3 = 0, where between the first and
second wires is the magnetic field zero?
b) Assume that the third wire carries I3 = 3 A to the left. What are the magnitude
and direction of the force exerted by the other two wires on a 20 cm length of
the third wire?
F 0 I1I 2

L
2 d

7 T  m 
 4 10
  3 A 2 A
A

F2  
 .2m
2  0.1m 
 2.4 106 N up 

7 T  m 
 4 10
  3 A 4 A
A

F1  
 .2m
2  0.25m 
 1.92 106 N [down]
F2  F1  2.4 106 N  1.92 106 N
 4.8 107 N [up]
Practice Question
A metal ring falls downward inside this region of uniform magnetic field that
points into the page. In which direction will the induced current flow within the ring
at the instant shown in the diagram?
a) Clockwise
b) Counter Clockwise
c) No current will flow
Practice Question
Charged nuclei (mass 6.64 × 10-27 kg) travel at 6 × 105 m/s towards a magnetic
field (shaded region) of strength 0.08 T. This field only extends a distance L = 0.25
meters in the forward direction.
a) What range of charges q will be turned around and sent backward towards
their source (and not escape out the top)? Answer in terms of |q|, the absolute
value of charge.
b) Assume the field points out of the page. True or false: the trajectory shown
would be for a positive charge.
Practice Question
Charged nuclei (mass 6.64 × 10-27 kg) travel at 6 × 105 m/s towards a magnetic
field (shaded region) of strength 0.08 T. This field only extends a distance L = 0.25
meters in the forward direction.
a) What range of charges q will be turned around and sent backward towards
their source (and not escape out the top)? Answer in terms of |q|, the absolute
value of charge.
b) Assume the field points out of the page. True or false: the trajectory shown
would be for a positive charge.
FC  FB
mv 2
 qvB sin  
r
mv
q
rB
q

mv
rB
m

kg   6 105 
s

 0.25 0.08T 
 6.64 10
27
 1.99 1019 C
Therefore |q|, is greater
than this value
Practice Question
Charged nuclei (mass 6.64 × 10-27 kg) travel at 6 × 105 m/s towards a magnetic
field (shaded region) of strength 0.08 T. This field only extends a distance L = 0.25
meters in the forward direction.
a) What range of charges q will be turned around and sent backward towards
their source (and not escape out the top)? Answer in terms of |q|, the absolute
value of charge.
b) Assume the field points out of the page. True or false: the trajectory shown
would be for a positive charge.
False, this is for a
negative charge.
Practice Question
Two wires are parallel to the z-axis, which lies perpendicular to the plane of the
page. The wires pass through the points (-4, 0) meters and (+4, 0) meters. Each
carries 1.2 A coming out from the sheet of the paper.
What is By, the y component of the magnetic field at the origin?
By=0T
Practice Question
Now a third wire C, carrying some unspecified current coming out of the page, is
placed somewhere along the positive y-axis (that is, the wire lies in the z-direction
and passes through the point (0,y) for y>0). What can we say about the magnetic
force it experiences?
The third wire is pulled down
Practice Question
A loop carrying current in the counter-clockwise direction sits in a magnetic field
pointing downward along the page. What effect does the magnetic field have on
the loop? Assume only magnetic forces act on the loop.
Rotates it so that the top side
comes out of the page and the
bottom goes in.
Practice Question
A point charge of +1 uC moves with velocity v into a uniform magnetic field B
directed to the right. What is the direction of the magnetic force on the charge?
a)
b)
c)
d)
e)
To the right and up the page
Directly out the page
Directly into the page
To the right and into the page
To the right and out of the page
Via the Right Hand Rule
Practice Question
A uniform magnetic field B points up. A loop of wire carrying a clockwise current is
placed at rest in this field. Which of the following describes the motion of the wire
when it is released.
a)
b)
c)
d)
e)
The wire will
The wire will
The wire will
The wire will
The wire will
expand slightly in all directions
contract slightly in all directions
rotate, with the top part coming out of the page
rotate, with the left part coming out of the page
rotate clockwise, remaining in place
Via the Right Hand Rule