Magnetism Chapters 20-22

MagnetismChapters 20-22

Chapter 20magnetism • Magnets and Magnetic Fields • Electric Currents Produce Magnetic Fields • The Force on an Electric Current in a Magnetic Field • The Force on Electric Charges Moving in Magnetic Fields • Magnetic Field Due to a Long, Straight Wire • Force Between Two Parallel Wires • Electromagnets

Magnetism • Magnets are dipoles, meaning they have two ends, or poles, called north and south. • Like poles repel; unlike poles attract.

Magnetism • If you cut a magnet in half, you don’t get a magnet with only north pole or only a south pole – you get two smaller magnets with both poles.

Magnetic fields • Magnetic fields can be visualized using magnetic field lines, which are always closed loops. • Notice that the magnetic field goes from NORTH to SOUTH.

Uniform Magnetic Field • A uniform magnetic field is constant in magnitude and direction. • The field between these two wide poles is nearly uniform.

Magnetic field • Symbol: B • Unit of B: • the tesla, T. • 1 T = 1 N/A·m. • Another unit sometimes used: the gauss (G). • 1 G = 10-4 T • Notation for vectors going into or coming out of a page:

Magnetic Fields • Use Right Hand Rule #1 to determine the direction of the magnetic field lines. • Point thumb in the direction of current. • Curl your fingers, they show the direction of the magnetic field. • This experiment shows that an electric current produces a magnetic field.

Practice Right-Hand Rule #1 • Example: Remember: How do you show a vector going into or coming out of the page? • Try this one: • What is the direction of the magnetic field produced by the current-carrying wire below? • Draw it. I

Force on an Electric Current in a magnetic field • A magnet exerts a force on a current-carrying wire. (First observed by Oersted.) • The direction of the force is not in the direction of either pole – it is perpendicular to the direction of the current and perpendicular to the direction of the magnetic field. • The direction can easily be found by using another right-hand rule.

Right-Hand Rule #2 • Using your right-hand: point your index finger in the direction of the conventional current. • Point your middle finger in the direction of the magnetic field, B. • Your thumb now points in the direction of the magnetic force, Fmagnetic. B N I S

Practice - Right-Hand Rule #2 • Find the direction of the magnetic force on a current-carrying wire due to the magnetic field B. B I B N S N S I

Force on an Electric Current in a magnetic field • If the direction of I is perpendicular to B, then θ= 90˚ and sin θ = 1. • If I is parallel to B, then θ = 0˚ and sinθ= 0. • So, this means the force is zero when I is parallel to B. • The magnitude of the force on a wire in a magnetic field depends on: • the current (I) • the length of the wire (l) • the magnetic field (B) • its orientation (θ)

What if the velocity of the charged particle isn't perpendicular to B? • Because the magnetic force is the cross-product of velocity and magnetic field, only the component of velocity perpendicular to the field matters for the magnetic force. B I

Assignment Concept Questions Practice Problems See Examples 20-1 and 20-2 on p.559. p.577 # 1-3 • p. 576 • #2-4, 6 “If you’re considered a chick magnet, you should be careful about which way you face because you could easily become a chick repellent.” ~Demitri Martin

Magnetic Fields vs. Electric Fields • Magnetic fields are similar to electric fields, • produced only by moving charges (a single moving charge or a current) • Magnetic fields create a force only on moving charges • The direction for the electric force is along the line drawn from one charge to another, the direction of the magnetic force is perpendicular to both B and I or v.

Force on An Electric Charge moving in a magnetic field • Once again, the direction is given by a right-hand rule. • The rule is for positive particles. • Notice the difference between positive and negative particles. • Use the opposite of the RHR for negative particles (or left hand). • The magnitude of the force on a moving charge is related to the force on a current: • The force is greatest when the particle moves perpendicular to B (θ = 90°)

Force on An Electric Charge moving in a magnetic field • If a charged particle, in this case an electron, is moving perpendicular to a uniform magnetic field, its path will be circular.

Which way Will the particle move? Example 1: x xxxx x xxxx x xxxx x xxxx x xxxx Example 2: B +q B F X F -q

Magnetic field due to a long straight wire • The strength of the magnetic field at a point around the wire is directly proportional to the current in the wire and inversely proportional to its distance from the wire: • Where: • B = magnetic field (T) • I = current (A) • r = distance of point in field from wire (m) • The constant μ0 is called the permeability of free space (or vacuum permeability). • It has the value:

Force between two parallel wires • The magnetic field produced at the position of wire 2 due to the current in wire 1 is: • So, the force this field exerts on a length l2 of wire 2 is: Remember F=IlB?

Forces between two parallel wires • What about the direction? • Parallel currents exert an attractive force on each other • Antiparallel currents exert a repulsive force on each other

What else is Magnetic? • The Magnetic Field of the Earth is also a magnetic dipole! • By the way, technically the north magnetic pole is located in southern hemisphere and the south magnetic pole is located in the northern hemisphere.

Assignment • Practice Problems • p.578 • #10 - 14 • Concept Questions • p.576 • #8 - 10

Summary of Chapter 20 • A magnet has 2 poles: north and south • We can imagine that a magnetic field surrounds every magnet • The SI unit for magnetic field B is the tesla, T • Electric currents produce magnetic fields • A magnetic field exerts a force on an electric current • F = IlBsinθ • A magnetic field exerts a force on a charge q moving with velocity v • F = qvBsinθ • The magnitude of the magnetic field produced by a current I in a long straight wire, at distance r from the wire is • B = μ0I / 2πr • Two currents exert a force on each other via the magnetic field each produces • Parallel currents in the same direction attract each other • Parallel currents in opposite directions repel

Chapter 21Electromagnetic induction • Induced EMF • Faraday’s Law of Induction • Lenz’s Law • EMF induced in a Moving Conductor • Changing Magnetic Flux Produces an Electric Field

Solenoids • The magnetic field of a solenoid can be fairly large because it is the sum of the fields due to the current in each loop. • A long coil of wire consisting of many loops of wire is called a solenoid.

electromagnets • If a piece of iron is inserted in the solenoid, the magnetic field greatly increases because the iron becomes a magnet. • Such electromagnets have many practical applications.

Applications of electromagnets • An electric motor takes advantage of the torque on a current loop, to change electrical energy to mechanical energy.

Applications of electromagnets • Loudspeakers use the principle that a magnet exerts a force on a current-carrying wire to convert electrical signals into mechanical vibrations, producing sound.

Reminders From Chapter 20 • Scientists began to wonder… If an electric current can produce a magnetic field, can a magnetic field induce an electric current? • Two scientists independently determined that it can. • Michael Faraday (English) • Joseph Henry (American) • In chapter 20 we learned two ways in which electricity and magnetism are related. • An electric current produces a magnetic field. • A magnetic field exerts a force on an electric current or a moving electric charge.

Induced EMF • So, a changing magnetic field induces an emf– this is called electromagnetic induction. • Faraday concluded that although a constant magnetic field produces no current in a conductor, a changing magnetic field does. • This is called induced current.

Induced EMF • This figure shows that: • if a magnet is moved quickly into a coil of wire, a current is induced in a wire • if the magnet is quickly removed, a current is induced in the opposite direction. • If the magnet and coil are held steady, no current is induced.

Faraday’s Law of Induction • Magnetic flux (ΦB): • B, magnetic field (T) • A, the loop’s area (m2) • θ, the loop’s angle (°) • Unit of magnetic flux: • Weber (Symbol: Wb) • 1 Wb = 1 T·m2 • For a loop to “feel” the changing magnetic field, some of the field lines need to pass through it. • The amount of magnetic field lines that pass through the loop is called the magnetic flux.

Faraday’s Law of Induction • FYI: The magnetic flux is proportional to the total number of lines passing through the loop. • θ is the angle between B and a line drawn perpendicular to the face of the loop. • See how the angle effects the flux.

Faraday’s Law of Induction • Magnetic flux will change if the area of the loop changes:

Faraday’s Law of Induction • Magnetic flux will change if the angle between the loop and the field changes:

Assignment Concept Questions Practice Problems p. 610 #7 90’s Flowchart • p.609 • #2+3

Faraday's Law of Induction Faraday’s Law of Induction is one of the basic laws of electromagnetism. It states that the size of the induced emf is proportional to the rate of change of flux through the coil’s face. Faraday’s law of induction for N loops: • Faraday’s law of induction for 1 loop:

Lenz’s Law • So, we now have 2 magnetic fields: • The original changing magnetic field (or flux) that induced the current • The magnetic field that the current then produces • The second field opposes the change in the first. • Lenz’s law states that an electric current induced by a changing magnetic field will flow such that it will create its own magnetic field that opposes the magnetic field that created it.

Lenz’s Law Example • When the magnet is moved in a metal that conducts electricity, like copper, the magnet create currents in the metal. • The electric currents in the metal create a magnetic force in the opposite direction of the moving magnet.

Lenz’s Law • So the minus sign in the previous equation (from Faraday’s Law of Induction) is from Lenz’s Law. It gives the direction of the induced emf. • A current produced by an induced emf moves in a direction so that the magnetic field it produces tends to restore the changed field (systems don’t like change).

Assignment Concept Question: • p.609 • #1 Practice Problems: • p.610 • #1, 4, 5, 11a

Lenz’s Law • Lenz’s Law is used to determine the direction of the conventional current induced in a loop due to a change in magnetic flux inside the loop. • The steps on the next slide will make it really easy for you to determine the direction of an induced current – just be sure to remember there are twodifferent magnetic fields.

Problem Solving using Lenz’s Law • Determine whether the magnetic flux is increasing, decreasing, or unchanged. • The magnetic field due to the induced current: • points in the opposite direction to the original field if the flux is increasing • points in in the same direction if it is decreasing • is zeroif the flux is not changing. • Once you know the direction of the magnetic field, use the right-hand rule to determine the direction of the current. • Remember that the original field and the field due to the induced current are different.

Example #1Direction of Induced Current? • If you pull the loop from a B-field to no B-field, the B-flux decreases. • If the B-flux decreases, the new magnetic field inside of the loop will be in the same direction as the original B-field. • Use the right hand rule for loops to determine the current. • If the field inside the loop is pointing out. The current must be counter-clockwise. • Pulling the loop to the right out of a magnetic field which points out of a page.

Example #2Direction of Induced Current? • Use RHR to determine the direction of the B-field from straight wire. • It’s going into the page where the loop is located • Is B-flux increasing or decreasing? • Increasing if current in wire is increasing. • So the new magnetic field inside the loop will be in the opposite direction. (out of the page) • Use the RHR again to determine the induced current in the loop. • It must be counter-clockwise. I increasing 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

EMF induced in a moving conductor • If the rod is made to move at a speed v, in a time t it travels a distance ∆x (=v∆t). • Therefore the area of the loop increases by an amount ∆A (=l∆x) • So, the induced emf has a mgnitude: • E = Blv • Assume that a uniform magnetic field is perpendicular to the area bounded by the U-shaped conductor and the movable rod resting on it.

Assignment • Practice Problems • p.610 • #9-10, 11b, 17 • Concept Questions • p.609 • #4-6

Magnetism Chapters 20-22