Magnetic Fields Objective I can describe the structure

Magnetic Fields Objective: I can describe the structure of magnetic fields and draw magnetic field lines.

magnetism The earliest magnets were found naturally in the mineral magnetite Magnets produce magnetic forces and have magnetic field lines

Magnets have two ends or poles, called north and south. Magnetic Fields are strongest near the poles of the magnet and the magnetic field lines are closer together. Unlike poles of magnets attract each other and like poles of magnets repel.

The earth is like a giant magnet! The nickel iron core of the earth gives the earth a magnetic field much like a bar magnet.

Magnetic Field and Moving Charges All moving charges create magnetic fields. Spinning electrons in atomic orbits create magnetic fields. When the electrons are not spin paired then the atom is a small magnet. 5

magnetic domains Magnetic substances like iron, cobalt, and nickel are composed of small areas where the magnetic fields of groups of atoms are aligned. These regions are called domains.

When domains of a magnetic substance align in the same direction a permanent magnet is formed. These domains are typically composed of billions of atoms. 7

Electricity &Magnetism Objective: I can use the right hand rule to determine the direction of the magnetic filed near current carrying wire. I can use right hand rules to determine forces on moving charges in magnetic fields.

Objective: I can use F=BILsinΘ, F = BqvsinΘ, and B = (μo /2π) (I/r) to determine the forces on current carrying wires and magnetic field strength near current carrying wires. 9

• The force on electric current in a magnetic field is given by F = BIL sinθ If the direction of the current is perpendicular to the field (θ = 900), then the force is Fmax = BIL The magnitude of B is defined as B = Fmax IL

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The SI Unit for magnetic field B is the tesla (T). It is clear that 1 T = 1 N/Am

Charges in a Magnetic Field • Moving charges experience a force due to a magnetic field. • FB = B × qv • Magnitude of FB is: • FB = Bqv sin Θ • where is the angle between v and B. • Direction is from the right hand rule.

Magnetic Force on Moving Charge: Right Hand Rule • Magnetic Force vector F on charge q moving with velocity v • |F| = q|v| |B| sinθ • Point the thumb of your right hand along the velocity vector v. • Your fingers point in the direction of the magnetic field lines. • The force on the charged particle is out of your palm. All three vectors F, v, B are perpendicular to each other.

Charges in a Magnetic Field • If a charge moves perpendicular to a uniform magnetic field, it will travel in a circular path. FB or magnetic = Fcentripetal

Application • Earth’s magnetic field shields us from incoming charged particles. However, since Earth’s magnetic field goes from the south pole to the north, particles can travel parallel to the field and enter the atmosphere near the poles. The “aurora” is the result.

Aurora

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Electricity and Magnetism All flowing charges including current create magnetic fields.

Calculation of Magnetic Field Near a Long Straight Wire • Magnetic Field Lines form loops around the current, Direction given by right hand rule. • The magnetic field strength B is proportional to the current, I, and inversely proportionate to the distance from the wire, r.

Force Between Two Current Carrying Wires • F = BIL • B = F • IL I 1 I 2

Electromagnet When an electric current is passed through a coil of wire wrapped around a metal core, a very strong magnetic field is produced. This is called an electromagnet.

Amperes Law, Magnetic Field inside a long solenoid • Inside a solenoid of length L with total of N windings. • B = μ 0 (N/L) I • B = μ 0 n l • n = N/L = windings per unit length • Outside the solenoid, the magnetic field is much weaker (but not exactly zero).

Sign of Magnetic Flux • We are free to choose either direction around a loop to label as the positive current. • However, for Lenz law to make sense, we force our sign convention for magnetic flux such that positive current creates positive self flux (negative current produces negative self flux). • A loop with current produces a magnetic field pattern similar to a permanent magnetic dipole.

Magnetic Flux • The Magnetic flux through a loop is defined as the product of the area of the surface bounded by the loop times the component of magnetic field perpendicular to the surface. • ΦM = A B⊥= A B cosθ • B⊥= B cosθ : – θ measured relative to perpendicular to surface A • If the loop has N windings, the total flux is N ΦM = N A B cosθ

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External and Self Flux • Magnetic Flux can come from an external B-field, or from the B-field generated by the current in the coil. • Solenoid of length L with a total of N carrying current I (only case we know how to calculate exactly) • Total flux = NΦM = N A B • NΦM = N (πr 2) μ 0 (N/L) I = μ 0 N 2 I (πr 2 /L)

Electromagnetic Induction • Mechanical Universe: Electromagnetic Induction Video

Induction • Electric field or EMF creates current in a circuit. • Electric current creates magnetic field • A CHANGING magnetic FLUX in a circuit induces an EMF in the circuit. The induced current produces a magnetic flux that opposes the change (Lenz’ law). • EMF = −(ΔΦM/Δt) • T · m 2/s= (Tesla·Coulomb m/s) (m/Coulomb) = Newton (m/Coulomb) = Joule/Coulomb=Volt

AC Circuits and Inductors • • • I(t) = I 0 sin(ωt) Frequency f = ω/2π Period = 1/f = 2π/ω ΔI/Δt = ω I 0 cos(ωt), AC Voltage required to drive current in inductor (overcome self EMF) V = - EMF = L ΔI/Δt = ωL I 0 cos(ωt), VAC = IAC XL AC EMF leads current by ¼ oscillation XL = ωL

AC Circuits and capacitors • • I(t) = I 0 sin(ωt) Q(t) = (I 0/ω) sin(ωt) VAC = IAC XC AC Voltage lags current by ¼ oscillation • XC = 1/(ωC)

What is a galvanometer? A galvanometer is an electromagnet that interacts with a permanent magnet. The stronger the electric current passing through the electromagnet, the more is interacts with the permanent magnet. Galvanometers are used as gauges in cars and many other applications. The greater the current passing through the wires, the stronger the galvanometer interacts with the permanent magnet.

What are electric motors? An electric motor is a device which changes electrical energy into mechanical energy.

How does an electric motor work? Go to the next slide

Simple as that!!

We have seen how electricity can produce a magnetic field, but a magnetic field can also produce electricity! How? What is electromagnetic induction? Moving a loop of wire through a magnetic field produces an electric current. This is electromagnetic induction. A generator is used to convert mechanical energy into electrical energy by electromagnetic induction. Carefully study the next diagrams:

Direct current versus alternating current – AC vs DC : What’s the difference? Direct current is electrical current which comes from a battery which supplies a constant flow of electricity in one direction. Alternating current is electrical current which comes from a generator. As the electromagnet is rotated in the permanent magnet the direction of the current alternates once for every revolution. Go to this website and click the button for DC then for AC to visually see the difference between the two. You can see that the DC source is a battery – current flows in one direction. The AC source is the generator and the current alternates once for each revolution.

Flux in Transformer Φ = flux through a single winding or either coil. (produced by currents in either or both circuits) EMF(primary) = − NP ΔΦ/Δt EMF(secondary) = − NS ΔΦ/Δt ε P / ε S = NP / NS Energy conservation requires ε P IP = ε S IS Ι P / Ι S = NS / NP