Magnetism
­
a property of certain metals or electric currents that produce magnetic forces
Atomic Reason for Magnetism
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Magnet Facts
2 poles
Poles are defined
Attract / Repel
Break a magnet in half
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Compass
is this compass pointing north
Homemade Compass
3
The earth as a magnet
4
Dynamo
skip :(
Magnetic Declination
True North
Magnetic "North"
5
Pole Reversal
skip :(
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Magnetic Fields
­
The region around a magnetic object where magnetic forces can be detected
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Strength of a Magnetic Field
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Magnetism Hand Rules
­ Used to determine the direction of F, B, I, v
Facts to Know
1) 2) 3)
4) Special Note: Rule 3/4 9
1) Hand rule 1 ­ 'grabby grabby' for a wire
Current flowing through a wire “creates” a magnetic field around the wire
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2A) Hand Rule 2A ­ Flat Hand
Current Wire placed “in” magnetic fields experience force
I
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2B) Hand Rule 2B ­ Flat Hand (same rule)
Charged particle moving in a magnetic field experiences force
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Practice
B
FB ?
I
B
-
FB is out of the
page, which way
is the charge
moving
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I
FB
-I
sketch the
B field
created by
the wire
The wire placed in an
external magnetic field B
experiences force F as
shown. What is the
direction of the external
field
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B
X X X X X X
X X X X X X
+
X X X X X X
v
X X X X X X
FB ?
X X X X X X
X X X X X X
X X X X X X
The B field created
by the wire is
shown. Which way
would electron
current flow in the
wire
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conventional
current
B
FB ?
B
I
FB
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-
FB
Charge moving through external
magnetic field is moving into
the page and experiences force
F. What is the direction of the
field
Wire has conventional current
flowing into the page. Sketch
the magnetic field created by
the wire
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X X X X X X
X X X X X X
X X X X X X
X X X X X X
B
Which way does
the current
carrying loop get
pushed
X X X X X X
X X X X X X
X X X X X X
B
Field B is created
by the wire.
Which way does
electron current
flow in the wire
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Student Practice Sheets
1.) In the diagram below, the electric current (electron flow, negative flow) is going into the page through a wire. Is the field around the wire clockwise or counterclockwise?
2.) As the conventional current flows as shown, what is the direction of the force on the wire?
3.) Find the direction of the force on the proton moving through the magnetic field
4.) Electron Current flows as shown in the diagram. Find the direction of the force on the wire.
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5.) What pole of the bar magnet below is nearest the compass, north or south?
6.) What is the direction of the force on the current carrying wire shown in the diagram?
7.) An electron is projected towards the current carrying wire shown below. What direction will the electron be pushed if the wire carried conventional current (b) What about if the wire carries electron current.
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8.) A proton is moving along the equator of the earth east to west cutting across the earth’s magnetic field. Which direction will the proton be pushed.
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Current Loops and Solenoids
Current Loop
Current loop hand rule
B
Thumb points in the
direction of B field that
the loop creates
Fingers curl in current
direction around loop
Current loops basically create bar magnets
(electromagnets
=
=
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Solenoid - series of loops
Usually wrapped
around an iron
core to intensify
the field
Same hand rule as current loop
B
Acts like a bar magnet:
thumb points to north on
hand rule
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More Practice
1.) Electrons are moving to the left in the wire shown below. In which direction does the North pole of a compass point when it is placed (a) above the wires (b) below the wire
e­
2.) A force of attraction between two parallel wires is shown. The current in the upper wire is flowing from right to left. Which way is the current flowing in the bottom wire.
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3.) When the north pole of a magnet is placed at the right end of the coil shown, it is repelled. What is the direction of current flow in the coil?
4.) Find the direction of the force on the wire
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5.) The direction of the force on a current carrying wire is shown in the diagram below. What is the direction of electron flow?
6.) Which end of the electromagnet shown below is S
7.) As the distance between two opposite magnetic poles increases, the flux density midway between them
(1) decreases
(2) increases
(3) remains the same
8.) What is the direction of the magnetic field in the center of the loop shown below.
9.) The Left side of the electromagnet shown below is N pole. (a) What direction does electron current flow (b) if the proton shown below moved upwards as shown, what would happen to it as it passed by the solenoid.
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10.) The wire shown below has ­ (electron) current running into the page. What direction would the wire be pushed.
11.) The accompanying diagram shows a proton moving through a magnetic field.
If the proton is moving out of the page, in which direction will it be deflected by the magnetic field?
(a) toward the top of the page
(b) toward the bottom of the page
(c) to the left
(d) to the right
12.) Base your answer on the diagram below which represents a beam of electrons entering a magnetic field between the poles of a magnet. As the electrons enter the magnetic field between the poles of the magnet, they will be deflected
(a) toward the south pole
(b) toward the north pole
(c) downward
(d) upward
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Mathematics of magnetism
Constants
Permeability of free space μo = 4 π x 10­7 Magnetic constant
k’ = μo / 4 π * 10­7 FB
X X X
magnetic force F b acting on a charge q moving through a field B with a velocity v. v and B should be perpendicular or perpendicular components should be used
B
v
q
X X X
FB
X X X
X X X
FB = qvB Τ
B
I
FB = BIL Τ
X
X
X
X X X
B
r
Lorentz Force
magnetic force Fb acting on a current carrying wire of length L with a current I flowing through it. The current direction and magnetic field should be perpendicular or perpendicular components used.
I
r B
(T m)/A
(T m)/A
B
B
A magnetic field B is created at various locations "r" located away from a wire with a current I flowing in it. The field is circular around the wire at each radial distance r and gets smaller as moving away from the wire
μoI
B =
2πr
Ampere's Law
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Example Problems
1.) A 3 cm long wire lies perpendicular to a magnetic field of strength 0.40 T. (a) Calculate the force and direction of force on the wire if the current is 5.0 A. (b) If the wire was rotated 90° so that it was parallel to the field, what would the force be?
2.) An electron is moving above the surface the earth. It moves undeflected in a constant horizontal path at a velocity of 5x10 5 m/s through a magnetic field. a) Draw forces acting on the electron (b) State the direction of the magnetic field required to produce the result indicated. (c) Calculate the magnitude of the magnetic force acting on the electron and (d) calculate the magnitude of the magnetic field that the electron is moving through?
­
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STUDENTS DO
3.) A wire carrying a 30 A current has a length of 12 cm and is placed between the poles faces of a magnet at an angle of 60 degrees above horizontal. The magnetic field has a magnitude of 0.90 T. What is the force on the wire?
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4.) The width W of the wire loop shown below is 10 cm and it carries a current of 0.245 A. The magnitude of the force acting on the loop shown in the diagram is 3.48x10 ­2 N. What is the direction of the force on the wire and the magnitude of the magnetic field B at the center of the magnet
I
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5.) An electron travels at 2x10 7 m/s in a plane perpendicular to a 0.01 T magnetic field directed into the page. (a) Draw the path of the electron (b) Determine the distance traveled by the electron when it returns to its original location
X X X X X X
B
X X X X X X
X X X X X X
X X X X X X
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6.) A vertical electric wire in the wall of a building carries a dc current of 25 A upward. An electron is shot at 5x107 m/s upwards from an electron gun 10 cm to the right of the wire. What is the force on the electron when it first leaves the gun
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7.) Two wires 2 m long are 3 mm apart and carry a current of 8 A. Calculate the force between these two wires.
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8.) A 3.60 g bullet moves with a speed of 175 m/s perpendicular to the Earth's magnetic field of 5.00 10 ­5 T. If the bullet possesses a net charge of 8.15 10 ­9 C, by what distance will it be deflected from its path due to the magnetic field only, assuming gravity could be ignored, after it has traveled 0.80 km?
X X X X X X B
X X X X X X
+
v
X X X X X X
X X X X X X
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9.) Two long wires are oriented so that they are perpendicular to each other, and at their closest, they are 20.0 cm apart (Fig. 20­
55). What is the magnitude of the magnetic field at a point midway between them if the top one carries a current of 18.8 A and the bottom one carries 4.7 A?
Figure 20­55.
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10.) (a) What value of magnetic field would make a beam of electrons, traveling to the right at a speed of undeflected through a region where there is a uniform electric field of 8,000 V/m pointing vertically up?
4.1 10 6 m/s, go (b) What is the direction of the magnetic field if it is known to be perpendicular to the electric field? 36
11.) A rectangular loop of wire is sitting next to a straight wire, as shown in Fig. 20­59. There is a current of 2.5 A in both wires. What is the magnitude and direction of the net force on the loop? 37
12.) 2003B3. (15 points)
A rail gun is a device that propels a projectile using a magnetic force. A simplified diagram of this device is
shown above. The projectile in the picture is a bar of mass M and length D, which has a constant current I
flowing through it in the + y direction, as shown. The space between the thin frictionless rails contains a uniform
magnetic field B, perpendicular to the plane of the page. The magnetic field and rails extend for a distance L.
The magnetic field exerts a constant force F on the projectile, as shown.
Express all algebraic answers to the following parts in terms of the magnitude F of the constant magnetic force,
other quantities given above, and fundamental constants.
(a) Determine the position x of the projectile as a function of time t while it is on the rail if the projectile starts
from rest at x = 0 when t = 0.
(b) Determine the speed of the projectile as it leaves the right­hand end of the track.
(c) Determine the energy supplied to the projectile by the rail gun.
(d) In what direction must the magnetic field B point in order to create the force F ? Explain your reasoning.
(e) Calculate the speed of the bar when it reaches the end of the rail given the following values.
B = 5 T L = 10 m I = 200 A M = 0.5 kg D = 10 cm
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14.)
2002B5. (10 points) A proton of mass mp and charge e is in a box that contains an electric field E, and the box is located in Earth's magnetic field B. The proton moves with an initial velocity vertically upward from the surface of Earth. Assume gravity is negligible.
(a)
On the diagram above, indicate the direction of the electric field inside the box so that there is no change in the trajectory of the proton while it moves upward in the box. Explain your reasoning.
(b) Determine the speed v of the proton while in the box if it continues to move vertically upward. Express your answer in terms of the fields and the given quantities.
The proton now exits the box through the opening at the top.
(c)
On the diagram above, sketch the path of the proton after it leaves the box.
(d) Determine the magnitude of the acceleration a of the proton just after it leaves the box, in terms of the given quantities and fundamental constants.
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15.)
6 m/s as it passes undeflected 2000B7 (10 points) A particle with unknown mass and charge moves with constant speed v = 1.9 x 10
through a pair of parallel plates, as shown above. The plates are separated by a distance d = 6.0 x 10­3 m, and a constant potential difference V is maintained between them. A uniform magnetic field of magnitude B = 0.20 T directed into the page exists both between the plates and in a region to the right of them as shown. After the particle passes into the region to the right of the plates where only the magnetic field exists, its trajectory is circular with radius r = 0.10 m.
a. What is the sign of the charge of the particle? Check the appropriate space below.
___ Positive
___ Negative ___ Neutral ___ It cannot be determined from this information.
Justify your answer.
b. c. d. On the diagram above, clearly indicate the direction of the electric field between the plates.
Determine the magnitude of the potential difference V between the plates.
Determine the ratio of the charge to the mass (q/m) of the particle.
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13.)
1994B4. In a linear accelerator, protons are accelerated from rest through a potential difference to a speed of approximately 3.1 x 10 6 meters per second. The resulting proton beam produces a current of 2 x 10 ­6 ampere.
a. Determine the potential difference through which the protons were accelerated.
b. If the beam is stopped in a target, determine the amount of thermal energy that is produced in the target in one minute.
The proton beam enters a region of uniform magnetic field B, as shown above, that causes the beam to follow a semicircular path.
c. Determine the magnitude of the field that is required to cause an arc of radius 0.10 meter. d. What is the direction of the magnetic field relative to the axes shown above on the right?
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16.) A rectangular wire loop is connected across a power supply with an internal resistance of 0.50 Ω and an emf of 16 V. The wire has resistivity 1.7 x 10­8 Ω · m and cross­sectional area 3.5 x 10­9 m2 . When the power supply is turned on, the current in the wire is 4.0 A.
(a) Calculate the length of wire used to make the loop.
A magnet is placed on a balance and the 0.020 m long horizontal segment of the loop is fixed midway between the poles and perpendicular
to the direction of the magnetic field as shown. The power supply in the loop is turned on, so that the 4.0 A current is in the direction shown.
(b) In which direction is the force on the magnet due to the current in the wire segment?
____Upward ____Downward
Justify your answer.
(c) The reading on the balance changed by 0.060 N when the power supply was turned on. Calculate the strength of the magnetic field
(d) The length of the loop is changed such that the 0.020 m length shown is doubled but the total length of the wire is still the same. This should produce double the force but slightly less than double force is observed; give a possible reason for this.
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Electromagnetic Induction (induced emf)
­
The creation of a potential difference (emf) by moving a wire through a magnetic field
How it works
similar to a battery
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4 Things that affect the induced potential Formula ­ induced potential (EMF) in a single wire 44
Magnetic Flux
­ Φm
Magnetic flux is a measure of the amount of magnetic field lines that pass through a certain cross sectional area
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Working with wire loops moving in B fields 1) You can "look at" the piece of wire in the loop responsible for generating the emf
X X X X X X X X X
X X X X X X X X X
X X X X X X X X X
X X X X X X X X X
B 2) You can use Faradays law
Faradays law of induction for wire loops
An induced emf (voltage) is created in a loop of wire only when the flux through it changes and this induced emf is proportion to the rate of change of the flux
B X X X X X X X X X B X X X X X X X X X
X X X X X X X X X
X X X X X X X X X
Formula 46
RECAP
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Lenz law for induction
­ used to determine the direction in which an induced current will flow in a wire loop when the flux through it changes.
Example
A
X X X X X X X X X
X X X X X X X X X
X X X X X X X X X
X X X X X X X X X
B
X X X X X X X X X
X X X X X X X X X
X X X X X X X X X
C
X X X X X X X X X
X X X X X X X X X
X X X X X X X X X
X X X X X X X X X
X X X X X X X X X
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Lenz Law Examples
1.) The North pole of a magnet moves towards the ring from above the page
2.) Bar magnet moved towards loop
3.) bar magnet moves towards, thru and then out of the loop
4.) 5.) The loop shrinks
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6.) Loop rotates out of
the page left to right
7.)
(a) Current of increasing magnitude flows up wire
(b) Current becomes constant.
7.) What happens in the 3D loop on right when current first begins to flow.
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Problems
1.) Pull 5cm square loop out of field in 0.10 sec
Loop has 100 turns. Resistance is 100 ohm.
Determine
(a) The emf and current induced
(b) The energy dissipated in the coil
(c) The average force used to pull the coil out
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2.) A 12 ohm resistor is attached to the wire loop below and consumes 5 W of power as the 1.2 m long rod is pulled to the right by an external force and the rod moves with a constant velocity of 3.1 m/s. (a) What is the strength of the magnetic field (b) What external force is required to maintain the rods speed, (c) How much energy is dissipated in 0.58 sec (d) What is the E field in the rod
R = 12 ohm
P = 5 W
L = 1.2 m
V = 3.1 m/s
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3.) A circular loop in the plane of the paper lies in a 0.75 T magnetic field pointing into the paper. If the loops diameter changes from 20 cm to 6 cm in 0.5 seconds (a) What is the direction of the induced current (b) What is the magnitude of the average induced emf, and (c) if the coil resistance is 2.5 ohm, what is the average induced current
before
X X X X
after
X X X X
X X X X
X X X X
X X X X
X X X X
X X X X
X X X X
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4.)
B2004B4. (15 points)
A 20­turn wire coil in the shape of a rectangle, 0.25 m by 0.15 m, has a resistance of 5.0 Ω. In position 1 shown above, the loop is in a uniform magnetic field B of 0.20 T. The field is directed out of the page, perpendicular to the plane of the loop. The loop is pulled to the right at a constant velocity, reaching position 2 in 0.50 s, where B is equal to zero
(a) Calculate the average emf induced in the 20­turn coil during this period.
(b) Calculate the magnitude of the current induced in the 20­turn coil and state its direction.
(c) Calculate the power dissipated in the 20­turn coil.
(d) Calculate the magnitude of the average force necessary to remove the 20­turn coil from the magnetic field.
(e) Identical wire is used to add 20 more turns of wire to the original coil. How does this affect the current in the coil? Justify your answer.
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5.)
1999B3. A rectangular conducting loop of width w, height h, and resistance R is mounted vertically on a noncon­
ducting cart as shown above. The cart is placed on the inclined portion of a track and released from rest at position P1 at a height y0 above the horizontal portion of the track. It rolls with negligible friction down the incline B in the region above the horizontal portion of the track. The conducting and through a uniform magnetic field loop is in the plane of the page, and the magnetic field is directed into the page. The loop passes completely through the field with a negligible change in speed. Express your answers in terms of the given quantities and fundamental constants.
a. Determine the speed of the cart when it reaches the horizontal portion of the track.
b. Determine the following for the time at which the cart is at position P
2, with one­third of the loop in the magnetic field.
i. The magnitude of the emf induced in the conducting loop
ii. The magnitude of the current induced in the conducting loop
c. P..
On the following diagram of the conducting loop, indicate the direction of the current when it is at Position d. i. Using the axes below, sketch a graph of the magnitude of the magnetic flux φ through the loop as a function of the horizontal distance x traveled by the cart, letting x = 0 be the position at which the front edge of the loop just enters the field. Label appropriate values on the vertical axis.
ii. Using the axes below, sketch a graph of the current induced in the loop as a function of the horizontal distance x traveled by the cart, letting x = 0 be the position at which the front edge of the loop just enters the field. Let counterclockwise current be positive and label appropriate values on the vertical axis.
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6.)
An airplane has an aluminum antenna attached to its wing that extends 15 m from wingtip to wingtip. The plane is traveling north at 75 m/s ­5 T is oriented as shown above.
in a region where Earth's magnetic field of 6.0x10
a. On the figure below, indicate the direction of the magnetic force on electrons in the antenna. Justify your answer.
b. Determine the potential difference between the ends of the antenna.
c. i.
The ends of the antenna are now connected by a conducting wire so that a closed circuit is formed.
Describe the condition(s) that would be necessary for a current to be induced in the circuit. Give a specific example of how the condition(s) could be created.
For the example you gave in i. above, indicate the direction of the current in the antenna on the figure below.
ii.
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