physics - giancoli 7e ch 20:...

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PHYSICS - GIANCOLI 7E

CH 20: MAGNETISM

CONCEPT: HOW MAGNETS WORK Forever ago we found metals that would attract each other. First found in island of Magnesia named _____________.

- Most common are iron (Fe), cobalt (Co), nickel (Ni), but not all Fe/Co/Ni are magnetic.

- Electrical Forces only between CHARGED materials Magnetic Forces only between MAGNETIC materials:

_________________ _________________ _________________ Electrical Forces can be ATTRACTIVE or REPULSIVE Same with Magnetic Forces, depending on ENDS:

Because one end behaves differently from another there must be 2 types of ends, aka Magnetic POLES - In Electricity, positive & negative charges In Magnetism, ____________ & ____________ POLES.

_________________

_________________

_________________

_________________ In Electricity, opposites charges ATTRACT In Magnetism, opposite poles [ ATTRACT / REPEL ].

NON-MAGNETIC

NON-MAGNETIC

MAGNETIC

NON-MAGNETIC

MAGNETIC

MAGNETIC

IRON BAR 1

IRON BAR 2

IRON BAR 2

A A

A B

B A

B B


CH 20: MAGNETISM

CONCEPT: MAGNETIC FIELDS AND MAGNETIC DIPOLES Remember: Electric Charges produce ELECTRIC Fields (E) from positive to negative charges:

- Similarly, Magnets produce ________________ Fields (B) directed from _______ to _______ (on the outside): - Everything* is High to Low Positive to Negative AND North to South One KEY difference: Single charges can exist on their own Electric _______________. - Magnets CANNOT have just one Pole Magnetic _______________ cannot exist, only _______________. Therefore, if you CUT a Magnet in half, you get:

EXAMPLE: Suppose both magnets below are fixed in place, but each is able to rotate about its own central axis. They are initially held in the positions shown below.

(a) If you release the bottom magnet only, what would its new orientation look like?

(b) If you release both magnets simultaneously, what would their new orientations look like?

This is how ___________________ work!

S

N

N

S


CH 20: MAGNETISM

CONCEPT: COMPASSES AND EARTH’S MAGNETIC FIELD Remember: Magnets have “ends” or POLES called NORTH and SOUTH. But how do you know which is North/South?

The end of the Magnet that points to the Earth’s NORTH is labeled the _______________ POLE of the Magnet.

- This is how COMPASSES work: The “end” of the Magnetic Needle that points to Earth’s North is labeled NORTH.

Remember: Magnetic Forces only exist between two ______________. Therefore: 1) If the Magnetic Needle in compasses are attracted to the Earth, the Earth must be a ______________. 2) Opposites attract, so if Compass’ North points to Earth’s North, Earth’s North must be its Magnetic __________

Earth’s “North” = GEOGRAPHIC _____________ = MAGNETIC _____________.

- Because of this, the NORTH Pole of a Compass Needle is sometimes called “___________-SEEKING”

ANY Magnet’s North points [ IN DIRECTION OF / OPPOSITE TO ] the Magnetic Field around it. - In the Southern Hemisphere, the Compass’ ____________ Pole will point to the Earth’s ____________.

EXAMPLE: The green magnet below is fixed in place. Many small compasses are placed around it. Draw the approximate orientation of the magnetic needles in the compasses, using an arrow to indicate the North direction.

N S


CH 20: MAGNETISM

CONCEPT: SUMMARY OF MAGNETISM PROBLEMS Remember: Electric Charges and Magnets both (a) PRODUCE A FIELD and (b) FEEL A FORCE:

We will calculate Fields PRODUCED BY and Forces FELT BY Electric (i) ______________, (ii) ______________.

- What about Magnets? No calculations, only directions! KEY Difference: Magnets ALWAYS Produce Fields AND Feel Forces. - Electric CHARGES produce Fields AND feel Forces ONLY IF they are ___________________. - Electric WIRES produce Fields AND feel Forces ONLY IF they have ___________________.

PRODUCING NEW B-FIELDS FEELING FORCE IN B-FIELDS

Most Magnetism problems have to do with calculating the magnitude of:

(1) A(n) _______________ Magnetic Field being PRODUCED; (2) A Force FELT due to a(n) _________________ Magnetic Field.

NEW B-Field due to

Moving Charge

B-Force on Moving Charge

in EXISTING B-Field

Charges can also move in Wires

NEW B-Field due to

WIRE with Current

NEW B-Field through center

of Wire LOOP (with i)

Wires can be made into Loops

Really long loops are Solenoids

NEW B-Field inside

Solenoids (LONG loops)

B-Force on WIRE w/ Current

in EXISTING B-Field

B-Torque on Wire LOOP

in EXISTING B-Field

B = µ𝐨 𝐯 𝐪 𝐬𝐢𝐧𝛉

𝟒𝛑𝐫𝟐

B = µ𝐨 𝐈

𝟐𝛑𝐫

B = µ𝐨 𝐈

𝟐𝐑 N

B = µ𝐨 𝐈

𝐋 N

F = v q B sinΘ

F = B I L sinΘ

τ = N B A I sinΘ


CH 20: MAGNETISM

CONCEPT: FORCE ON MOVING CHARGES AND THE RIGHT-HAND-RULE

EXAMPLE 1: When a 2 C charge moves perpendicular to a constant magnetic field with 3 m/s, it feels a force of 4 N. What must the magnitude of the magnetic field be? ALL DIRECTIONS in Magnetism problems will come from variations of the RIGHT HAND RULE (RHR).

- WARNING: Different versions Pick one and stick with it. If different from mine or your professor, double-check!

- In 2D, we have Up/Down and Left/Right. In 3D, we need 2 more:

(1) AWAY from you = [ INTO / OUT OF ] the page/plane Symbol:

(2) TOWARDS you = [ INTO / OUT OF ] the page/plane Symbol:

- Fingers = ______________ - Thumb = ______________ - Palm = ______________

- RHR works for POSITIVE charges. For NEGATIVE charges, we use the LEFT Hand (same rule, different hand).

EXAMPLE 2: Find the direction of the Magnetic Force on a moving charge in each of the following situations:

(a) proton moving left in a B-Field pointing up (b) electron moving down in a B-Field pointing out of page (c) electron moving down in a B-Field pointing left (d) proton moving into the page in a B-Field pointing right

A charge moving through an existing Magnetic Field FEELS a Magnetic FORCE:

- MAGNITUDE _______________________ - AKA Lorentz ______________.

- Angle Θ is between _______ and _______ - UNIT of B-Field is TESLA ( 1 T = 1 N / A m )


CH 20: MAGNETISM

EXAMPLE: FORCE ON CHARGE MOVING AT AN ANGLE

What is the magnitude and direction of the magnetic force on a +3 C charge moving at 4 m/s when it first enters a 5 T magnetic field that is directed along the positive x-axis if the charge is initially moving:

(a) in the positive y axis (b) in the negative x axis (c) in a direction that makes 30o with the +y axis

PRACTICE: SPEED OF ELECTRON MOVING AT AN ANGLE

An electron is moving in a straight line (red line below) when it enters the horizontal 0.2 T magnetic field (blue lines). The angle shown below is 37o. If the electron experiences a 10-12 N force upon entering the field, how fast must it be moving?


CH 20: MAGNETISM

CONCEPT: CIRCULAR MOTION IN MAGNETIC FIELDS

Remember: Magnetic Force on a moving charge is ALWAYS perpendicular (90o) to its velocity (RHR).

EXAMPLE: In an experiment, an electron enters a uniform 0.2 T magnetic field directed perpendicular to its motion. You measure the electron’s deflection to have a circular arc of radius 0.3 cm. How fast must the electron be moving? If a charge moves PERPENDICULAR to the Magnetic Field ________________________ - If a charge moves PARALLEL to the Magnetic Field ________________________ - If a charge moves AT AN ANGLE to the Magnetic Field ________________________ Remember: Work done by ANY Force WF = F ∆x cosΘ - Work done by Magnetic Force on a moving charge WF =

Because of this, moving charges in a Magnetic Field experience CIRCULAR Motion:

∑𝐅 = 𝐦𝐚:


CH 20: MAGNETISM

PRACTICE: FIND MAGNITUDE OF FIELD DEFLECTING CHARGE

A 4 kg, 3 C (unknown sign) charge originally moving in the +x axis with 5 m/s when it enters (red arrow) a small square area that has a constant magnetic field, as shown below. The field causes the charge to be deflected, and it exits the area moving in the +y axis. What is the magnitude of the magnetic field? (Is this charge +3 C or – 3 C?)

2cm

2cm

4cm


CH 20: MAGNETISM

CONCEPT: THE MASS SPECTROMETER

MASS SPECTROMETERS are instruments used to measure the MASS of a known charge. They do this in 4 steps: IONIZATION & ACCELERATION VELOCITY SELECTION DEFLECTION via potential difference to filter desired speeds radius determines mass

EXAMPLE: A +2 C charge is accelerated in the +x axis through an unknown potential difference ∆V. It then passes through

horizontal parallel plates that produce a electric field of 3 N/C that points vertically up. A magnetic field of magnitude 4 T

also exists between the plates, which keeps charges at the desired speed from deflecting while in between the plates. This

magnetic field also exists outside of the plates, and it causes the charge to deflect with a circular arc of radius 5 cm.

(a) What must be the direction of the magnetic field?

(b) Sketch the deflection that the charge will experience after leaving the parallel plates.

(c) Calculate the mass of the charge.

(d) Through what potential difference must the charge have been accelerated?


CH 20: MAGNETISM

PRACTICE: FIND DIRECTION OF FIELDS IN SPECTROMETER A negative charge in a spectrometer is accelerated in the negative x-axis. It is later deflected and collides some distance ABOVE velocity selector. What are the orientations of the electric and magnetic fields, respectively, inside the selector?

(a) up and out of the page (b) up and into the page (c) down and out of the page (d) down and into the page

PRACTICE: FIND COLLISION DISTANCE IN SPECTROMETER A 2 kg, – 3 C charge is accelerated through a potential difference of 4 V. The velocity selector has an electric field of magnitude 5 N/C. How far from the velocity selector will the charge collide against the spectrometer “wall”? EXAMPLE: FIND MASS TO CHARGE RATIO IN SPECTROMETER A mass spectrometer has a velocity selector electric field of magnitude 20 N/C. When a certain charge is accelerated to a constant 30 m/s, it collides 40 m away from the velocity selector. What is this charge’s mass-to-charge ratio, m / q?


CH 20: MAGNETISM

CONCEPT: FORCE ON CURRENT-CARRYING WIRES

Charges can move in space, OR inside a WIRE CURRENT

CHARGES IN SPACE CURRENT-CARRYING WIRES

- A moving Charge PRODUCES a NEW B-Field B =

- A Charge moving in an EXISTING Field FEELS a Force F =

- A current-carrying wire PRODUCES a NEW B-Field B =

- A wire in an EXISTING Field FEELS a Force (if i ≠ 0)

F =

Directions are given by the RIGHT HAND RULE Negative charges LHR Currents ALWAYS RHR - The Magnetic Force on a current-carrying wire will cause it to bend slightly: (i) current up: (b) current down:

EXAMPLE: A 2-meter-long wire is passed through a constant magnetic field, as shown below:

(a) If the wire experiences a force of 3 N when it has a current of 4 A, what is the strength of the field?

(b) If the wire experiences a downward force, what must the direction of the current be?

S N S N S N S N


CH 20: MAGNETISM

EXAMPLE: FORCE ON CURRENT-CARRYING WIRE AT AN ANGLE

A 2-m long wire is immersed in a 3 T magnetic field that is directed in the negative y axis. What is the magnitude of the magnetic force on the wire if it has 4 A flowing through it and it is directed:

(a) in the negative y axis (b) in the positive x axis (c) in a direction that makes 53o with the +y axis

PRACTICE: CURRENT ON WIRE AT AN ANGLE

A 5-m current-carrying wire (red line) is ran through a 4 T magnetic field (blue lines), as shown. The angle shown is 30o. What must the magnitude and direction of the current in the wire be when it feels a 3 N force directed into the page?


CH 20: MAGNETISM

CONCEPT: FORCE AND TORQUE ON CURRENT LOOPS

Remember: Current-carrying wires in a Magnetic Field FEEL a Magnetic Force F = _______________

EXAMPLE: A loop with a magnetic moment of 0.5 Am2 carries a current of 0.01 A. If it is placed in the presence of a magnetic field of strength 0.05 T, which points in the plane of the loop, what magnitude torque will the loop experience?

Wires can be arranged to form LOOPS. In SOME cases, you get a TORQUE: - The NET force on a LOOP in an uniform B-Field is ________.

Magnetic Torque τ = ___________________ - Angle Θ is between Normal of _____ and _____.

Magnetic Moment µ = ___________________


CH 20: MAGNETISM

EXAMPLE: TORQUE ON LOOP AT AN ANGLE A wire is arranged as a rectangular 4 m wide and 2 m deep. It is placed in the plane shown below, where a constant 5 T magnetic field exists. The wire loop is parallel to the plane, and the magnetic field is directed 30o above the plane. If the loop experiences a net torque of 10 N m, what must the current running through it be?


CH 20: MAGNETISM

CONCEPT: MAGNETIC FIELD PRODUCED BY MOVING CHARGES

Remember: A charge moving through an existing Magnetic Field FEELS a Magnetic FORCE.

EXAMPLE: A 3 C charge is moving right with a constant 4 m/s. What is the magnitude and the direction of the magnetic field that this charge produces 2 cm directly above itself?

ALSO: A moving charge __________________________________________ (much less popular question): - MAGNITUDE ______________________ - Remember µ𝐨 = 4π*10-7 N/A2 = 1.26*10-6 N/A2

- Angle Θ is between _____ and _____, which is a vector between charge and location of produced field - DIRECTION comes from RIGHT HAND RULE, by “grabbing” the LINE OF MOTION.


CH 20: MAGNETISM

CONCEPT: MAGNETIC FIELD PRODUCED BY STRAIGHT CURRENTS

Remember: Moving Charges PRODUCE A NEW FIELD B = ___________________

EXAMPLE 1: What is the direction of the magnetic field produced by a current on a very long wire if the current is oriented:

(a) up (b) left (c) into the page EXAMPLE 2: The two wires shown below are 4 m away from the other. What is the magnitude and direction of the magnetic field that is produced at a point in the center of the two wires?

Currents are just charges moving in a wire. So currents ALSO produce new Magnetic Fields:

- MAGNITUDE ______________________ (for very long wire) - Remember µ𝐨 = 4π*10-7 N/A2 - DIRECTION RIGHT HAND RULE: GRAB wire, with THUMB in direction of ___________________. - TWO Fields at same location: Same Direction _______________ Opposite _______________

. i = 3 A i = 5 A


CH 20: MAGNETISM

EXAMPLE: FIND MAGNETIC FIELD DUE TO TWO PERPENDICULAR CURRENTS

The very two long, perpendicular wires below intersect at (0, 0). The vertical wire carries 2 µA up, while the the horizontal

wire carries 3 µA to the left. What is the net magnetic field at point P located at (-4, -9) cm?

EXAMPLE: FIND ZERO MAGNETIC FIELD Two long, horizontal wires are 6 m away from each other. The bottom and top wires carry currents of 4 A and 5 A, respectively, both to the right. How far from the bottom wire is the NET magnetic field due to these currents zero?


CH 20: MAGNETISM

CONCEPT: MUTUAL MAGNETIC FORCE ON PARALLEL CURRENTS

Remember: Current-carrying wires PRODUCE NEW Magnetic Fields B = ______________ - A current-carrying wire in an EXISTING Field FEELS A FORCE F = ______________

EXAMPLE: Two horizontal wires 10 m in length are parallel to each other, separated by 50 cm. The top wire has current 2 A

to the right, and the bottom wire has current 3 A to the left. What is the magnitude and direction of the force exerted on the:

(a) top wire?

(b) bottom wire?

So if you have two PARALLEL currents, you get a MUTUAL Force between them: - MAGNITUDE: - Force per unit length = - DIRECTION: Same Direction _______________ Opposite _______________


CH 20: MAGNETISM

PRACTICE: FORCE PER UNIT LENGTH ON PARALLEL WIRES Two very long wires of unknown lengths are a parallel distance of 2 m from each other. If both wires have 3 A of current flowing through them in the same direction, what must the force per unit length on each wire be?

BONUS: Is the mutual force between the wires attractive or repulsive?


CH 20: MAGNETISM

CONCEPT: MUTUAL MAGNETIC FORCE ON PARALLEL CHARGES

Remember: Parallel currents FEEL A MUTUAL FORCE F =

EXAMPLE: An electron is moving right with 1.0 x 108 m/s when a proton passes it moving left with 2.0 x 108 m/s.

(a) What is the magnetic force between them when they pass each other, if at that moment they are 3 µm apart?

(b) What is the electric force between them at that moment?

Currents are just charges moving in a wire. So parallel moving charges ALSO feel a mutual Magnetic force: - MAGNITUDE _______________ - Same Direction & Charge _______________

- Opposite Direction & Charge _______________

- All Others Combinations _______________


CH 20: MAGNETISM

CONCEPT: MAGNETIC FIELD PRODUCED BY LOOPS AND SOLENOIDS

Remember: Current-carrying wires PRODUCE NEW B-Fields B = ______________ - In STRAIGHT wires: Current is STRAIGHT _______________ B is CURVED ______________ - In wire LOOPS: Current CURVES _______________ B is STRAIGHT ______________ (1) Single or Multiple Loops B = _______________

(2) Solenoid (very long loop) B = _______________

- Solenoids produce magnetic fields similar to ________________!

Remember: TWO Fields at same location: Same Direction ADD Opposite SUBTRACT

EXAMPLE: A wire is twisted into 5 tight loops 4 m in radius. A 3 A current is ran through the wire in the counter-clock direction. Find the magnitude and direction of the magnetic field produced by the loop in its center.


CH 20: MAGNETISM

EXAMPLE: HOW MANY TURNS IN A SOLENOID How many turns should a 2 m solenoid have in order to produce a 0.4 T magnetic field when a 3 A current is ran through it? PRACTICE: FIND CURRENT IN LOOP PERPENDICULAR TO PAGE The single loop below has a radius of 10 cm and is perpendicular to the page (shown at a slight angle so you can better visualize it). If the magnetic field at the center is 10-6 T directed left, what is the magnitude of the current? What is the direction of the current at the top of the wire: into the page (towards left) or out of the page (towards right)?


CH 20: MAGNETISM

EXAMPLE: DESIGNING A SOLENOID You are tasked with designing a solenoid that produces a magnetic field of 0.03 T at its center with a radius of 4 cm and length of 50 cm. What is the minimum total length of 12 A wire you should buy to construct this solenoid? PRACTICE: FIND CURRENT THROUGH SOLENOID A long wire having total resistance of 10 Ω is made into a solenoid with 20 turns of wire per centimeter. The wire is connected to a battery, which provides a current in order to produce a 0.04 T magnetic field through the center of the solenoid. What voltage must this battery have?


CH 20: MAGNETISM

EXAMPLE: MAGNETIC FIELD BY TWO CONCENTRIC LOOPS Two wire loops are arranged concentrically, as shown below. The inner wire has diameter 4 m and clock-wise current 5 A. The outer wire has diameter 6 m and counter-clockwise current 7 A. What is the magnitude and direction of the net magnetic field that is produced at the center of the two loops?

PRACTICE: MAGNETIC FIELD BY TWO CONCENTRIC SOLENOIDS The two tightly wound solenoids below both have length 40 cm and current 5 A in the directions shown. The left solenoid has radius 20 cm and 50 m of total wire. The right solenoid has radius 0.5 cm and 314 m of total wire. The thinner solenoid is placed entirely inside the wider one so their central axes perfectly overlap. Assume wires don’t touch. What is the magnitude and direction of the magnetic field that is produced by a combination of the two solenoids at their central axis?


CH 20: MAGNETISM

CONCEPT: MAGNETIC FIELD BY TOROIDAL SOLENOIDS Remember: Magnetic Field at the center of a LOOP B = - Magnetic Field at the center of a SOLENOID B = Solenoids can be arranged in a doughnut shape to form Toroidal Solenoids aka Toroids

B = _________________ - NOTE _____ is back, AND _____ NOT _____! - B exists between _____ and _____, zero outside. - R is “mean radius” = ___________________ EXAMPLE: A 300-turn toroidal solenoid has inner and outer radii 12 and 16 cm, respectively. If 5 A of current runs through the wire, what is the magnitude of the magnetic field produced:

(a) at the center of the solenoid

(b) at 14 cm away from the center

(c) at 20 cm away from the center


CH 20: MAGNETISM

CONCEPT: BIOT-SAVART LAW WITH CALCULUS

Biot-Savart Law reduces to familiar equations:

- Point charge: 𝐵 =𝜇0

4𝜋

𝑞𝑣𝑠𝑖𝑛𝜃

𝑟2

- Current-carrying wire: 𝐵 =𝜇0𝐼

2𝜋𝑟

EXAMPLE: Show that the Biot-Savart law for a current is the same as the equation above for a point charge.

For ANY current, magnetic field 𝑟 away is

= __________________

- Known as Biot-Savart Law

i

𝑟


CH 20: MAGNETISM

EXAMPLE: MAGNETIC FIELD DUE TO FINITE, CURRENT-CARRYING WIRE What is the magnetic field at the position shown in the following figure due to the finite, current-carrying wire?

i

z

x -a +a

z


CH 20: MAGNETISM

PRACTICE: MAGNETIC FIELD AT CENTER OF RING OF CURRENT What is the magnetic field at the center of the following ring of current?

i

r


CH 20: MAGNETISM

CONCEPT: AMPERE’S LAW WITH CALCULUS

- Like for Gauss’ law, the magnetic field depends ONLY on the current enclosed by an “Amperian loop”. EXAMPLE: Using Ampere’s law, find the magnetic field due to an infinitely long, current-carrying wire.

ANY magnetic field, , must satisfy the following equation:

∮ ⋅ 𝒅𝒍

𝑆= __________________

- Known as Ampere’s Law

S i

𝑑𝑙


CH 20: MAGNETISM

EXAMPLE: MAGNETIC FIELD DUE TO A SOLENOID What is the magnetic field along the axis of a solenoid?


CH 20: MAGNETISM

PRACTICE: MAGNETIC FIELD DUE TO SOLID, CYLINDRICAL CURRENT-CARRYING CONDUCTOR A solid, cylindrical conductor carries a uniform current density, 𝑱. If the radius of the cylindrical conductor is 𝑹, what is the

magnetic field at a distance 𝒓 from the center of the conductor when 𝒓 < 𝑹? What about when 𝒓 > 𝑹?

J


CH 20: MAGNETISM

physics - giancoli 7e ch 20:...

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