College Physics B

Electric Circuits Resistors in Series Resistors in Parallel Superconductivity College Physics B - PHY2054C Magnetic Fields Bar Horseshoe Magnets Magnetic Fields Electro- Magnetic Fields from Currents Current Loop

09/22/2014

My Office Hours: Tuesday 10:00 AM - Noon 206 Keen Building College Physics B Outline

Electric Circuits Resistors in Series Resistors in Parallel 1 Electric Circuits Superconductivity

Magnetic Resistors in Series Fields Bar Magnets Resistors in Parallel Horseshoe Magnets Superconductivity Electro- magnetism Magnetic Fields from Currents 2 Magnetic Fields Current Loop Bar Magnets Horseshoe Magnets

3 Magnetic Fields from Currents Current Loop College Physics B Resistors in Series

Electric Circuits Resistors in Series Resistors in Parallel Superconductivity

Magnetic Fields Bar Magnets Horseshoe Magnets

Electro- magnetism Magnetic Fields from Currents Current Loop When current passes through one resistor and then another, the resistors are said to be in series:

′ E − I R 1 − I R 2 = 0 Kirchhoff s Loop Rule Any number of resistors can be connected in series. The resistors will be equivalent to a single resistor with:

R equiv = R 1 + R 2 + R 3 + ... College Physics B Review Question 1

Electric Circuits Resistors in Series Resistors in Parallel Two light bulbs, A and B, are connected in series to Superconductivity

Magnetic a constant source. When a wire is connected Fields B A Bar Magnets across as shown, bulb Horseshoe Magnets Electro- A burns more brightly. magnetism Magnetic Fields from Currents Current Loop B burns as brightly. C burns more dimly. D goes out. College Physics B Review Question 1

Electric Circuits Resistors in Series Resistors in Parallel Two light bulbs, A and B, are connected in series to Superconductivity

Magnetic a constant voltage source. When a wire is connected Fields B A Bar Magnets across as shown, bulb Horseshoe Magnets Electro- A burns more brightly. magnetism Magnetic Fields from Currents Current Loop B burns as brightly. C burns more dimly. D goes out. College Physics B Resistors in Parallel

Electric Circuits Resistors in Series Resistors in Parallel Superconductivity

Magnetic Fields Bar Magnets Horseshoe Magnets

Electro- magnetism Magnetic Fields from Currents Current Loop

Applying the Junction Rule (Kirchhoff ’s Junction Rule)

For path 1, +E − I 1 R 1 = 0

For path 2, +E − I 2 R 2 = 0 The total current is: I = I + I = E + E = E ( 1 + 1 ) 3 1 2 R 1 R 2 R 1 R 2 College Physics B Equivalent Resistance - Parallel

Electric Circuits Resistors in Series Resistors in Parallel Superconductivity

Magnetic Fields Bar Magnets Horseshoe Magnets

Electro- magnetism Magnetic Fields from Currents Current Loop College Physics B Circuit Analysis

Electric Circuits Resistors in Series Resistors in Parallel Superconductivity 1 Some complex circuits can be solved by combinations of

Magnetic series and parallel rules. Fields Bar Magnets Horseshoe Magnets 2 Other circuits must be analyzed directly by Kirchhoff’s Rules. Electro- • Loop Rule: The total change in the around magnetism Magnetic Fields from any closed circuit path must be zero. Currents Current Loop • Junction Rule: The current entering a circuit junction must equal the current leaving the junction.

3 Connecting resistors in series always gives a total resistance larger than the resistance of any of the component resistors.

4 Connecting resistors in parallel always gives a total resistance smaller than the resistance of any of the component resistors. College Physics B Ammeters

Electric Circuits Resistors in Series Resistors in Parallel Superconductivity

Magnetic Fields Bar Magnets Horseshoe Magnets

Electro- magnetism Magnetic Fields from Currents Current Loop An Ammeter is a device that measures current. • An ammeter must be connected in series with the desired circuit branch. • An ideal ammeter will measure current without changing its value. ➜ Must have a very low resistance. College Physics B Voltmeters

Electric Circuits Resistors in Series Resistors in Parallel Superconductivity

Magnetic Fields Bar Magnets Horseshoe Magnets

Electro- magnetism Magnetic Fields from Currents Current Loop A Voltmeter is a device that measures the voltage across a circuit element. • It must be connected in parallel with the element. • An ideal voltmeter should measure the voltage without changing its value. ➜ Should have a very high resistance. College Physics B Superconductivity

Electric Circuits Resistors in Series At very low temperatures, the Resistors in Parallel Superconductivity linearity of resistance breaks

Magnetic down. Fields Bar Magnets • The resistivities of metals Horseshoe Magnets approach a nonzero value Electro- magnetism at very low temperatures. Magnetic Fields from Currents • Current Loop In some metals, resistivity drops abruptly and is zero below a critical temperature. • These metals for which the resistivity goes to zero are the called superconductors. College Physics B Superconductivity

Electric Circuits Resistors in Series Resistors in Parallel Superconductivity

Magnetic Fields Bar Magnets Horseshoe Magnets John Robert Schrieffer Electro- Nobel Laureate magnetism Magnetic Fields from Emeritus Professor at Florida State Currents Current Loop Bardeen, Cooper, and Schrieffer received the Nobel Prize in 1972 for the development of the theory of superconductivity. The BCS Theory is one of the greatest discoveries of the 20th century. College Physics B Outline

Electric Circuits Resistors in Series Resistors in Parallel 1 Electric Circuits Superconductivity

Magnetic Resistors in Series Fields Bar Magnets Resistors in Parallel Horseshoe Magnets Superconductivity Electro- magnetism Magnetic Fields from Currents 2 Magnetic Fields Current Loop Bar Magnets Horseshoe Magnets

3 Electromagnetism Magnetic Fields from Currents Current Loop College Physics B Magnetism

Electric Circuits Resistors in Series Resistors in Parallel Superconductivity

Magnetic Fields Bar Magnets Horseshoe Magnets

Electro- magnetism Magnetic Fields from Currents Current Loop The first observations of magnetic fields involved permanent magnets. Many ancient cultures discovered natural magnetic properties of materials. Permanent magnetic applications include: • needles • Speakers • Computer hard disks College Physics B Magnetic Poles

Electric Circuits Resistors in Series Resistors in Parallel Superconductivity

Magnetic Fields Bar Magnets Horseshoe Magnets

Electro- magnetism Magnetic Fields from Currents Current Loop College Physics B Lines

Electric Circuits A bar is a permanent Resistors in Series Resistors in Parallel magnet in the shape of a bar. Superconductivity Magnetic • The symbol for the Fields ~ Bar Magnets magnetic field is B. Horseshoe Magnets • Electro- SI unit of the magnetic magnetism Tesla T Magnetic Fields from field is the ( ) Currents Current Loop • The magnetic field lines can be deduced from the pattern of the filings.

Some properties of the magnetic field: • The iron filings align parallel to the magnetic field line. • The magnetic field lines go from the north pole toward the south pole. College Physics B Magnetic Field Lines

Electric Circuits A bar magnet is a permanent Resistors in Series Resistors in Parallel magnet in the shape of a bar. Superconductivity Magnetic • The symbol for the Fields ~ Bar Magnets magnetic field is B. Horseshoe Magnets • Electro- SI unit of the magnetic magnetism Tesla T Magnetic Fields from field is the ( ) Currents Current Loop • The magnetic field lines can be deduced from the pattern of the iron filings.

Some properties of the magnetic field: • The magnitude of the field decreases as you move farther from a pole. • The magnetic field lines form closed loops! College Physics B Magnetic Field Lines

Electric Circuits Resistors in Series Resistors in Parallel Superconductivity The magnetic field lines always form

Magnetic closed loops. Fields Bar Magnets ➜ A general property of magnetic Horseshoe Magnets fields, not just bar magnets. Electro- magnetism Magnetic Fields from Currents The magnetic poles are analogous Current Loop to positive and negative charges. College Physics B Question 2

Electric Circuits Resistors in Series Electrical charges and magnetic poles have many similarities, Resistors in Parallel Superconductivity but one important “difference” is:

Magnetic Fields A Opposite magnetic poles repel. Bar Magnets Horseshoe Magnets

Electro- B One magnetic pole cannot create magnetic poles in magnetism other materials. Magnetic Fields from Currents Current Loop C A magnetic pole cannot be isolated. D Magnetic poles do not produce magnetic fields. College Physics B Question 2

Electric Circuits Resistors in Series Electrical charges and magnetic poles have many similarities, Resistors in Parallel Superconductivity but one important “difference” is:

Magnetic Fields A Opposite magnetic poles repel. Bar Magnets Horseshoe Magnets

Electro- B One magnetic pole cannot create magnetic poles in magnetism other materials. Magnetic Fields from Currents Current Loop C A magnetic pole cannot be isolated. D Magnetic poles do not produce magnetic fields. College Physics B Horseshoe Magnet

Electric Circuits Resistors in Series Can be made by bending a bar Resistors in Parallel Superconductivity magnet. Magnetic • Fields There are poles at the ends Bar Magnets Horseshoe Magnets of the horseshoe magnet. Electro- • The field is largest in the magnetism Magnetic Fields from Currents horseshoe gap. Current Loop • The field is directed across the gap.

➜ iron yoke to strengthen field College Physics B Outline

Electric Circuits Resistors in Series Resistors in Parallel 1 Electric Circuits Superconductivity

Magnetic Resistors in Series Fields Bar Magnets Resistors in Parallel Horseshoe Magnets Superconductivity Electro- magnetism Magnetic Fields from Currents 2 Magnetic Fields Current Loop Bar Magnets Horseshoe Magnets

3 Electromagnetism Magnetic Fields from Currents Current Loop College Physics B Connection between

Electric and Magnetism Circuits Resistors in Series Resistors in Parallel Superconductivity

Magnetic Fields Sources of Electric Fields Sources of Magnetic Fields Bar Magnets Horseshoe Magnets

Electro- magnetism Magnetic Fields from Currents Current Loop College Physics B Electric Fields

Electric Circuits Resistors in Series Resistors in Parallel Superconductivity

Magnetic Capacitor Fields Bar Magnets Horseshoe Magnets

Electro- magnetism Magnetic Fields from Currents Current Loop (1791 - 1867)

Static Point Charges College Physics B Faraday’s Cage

Electric Circuits Resistors in Series Resistors in Parallel Superconductivity

Magnetic Fields Bar Magnets Horseshoe Magnets

Electro- magnetism Magnetic Fields from Currents Current Loop College Physics B Connection between Electricity

Electric and Magnetism Circuits Resistors in Series Resistors in Parallel Superconductivity

Magnetic Fields Sources of Electric Fields Sources of Magnetic Fields Bar Magnets Horseshoe Magnets

Electro- magnetism Electric Charge Moving Electric Charge Magnetic Fields from Currents Current Loop College Physics B Electromagnetism

Electric Circuits Resistors in Series Resistors in Parallel Christian Oersted Superconductivity (1777 - 1851) Magnetic Fields Bar Magnets Horseshoe Magnets

Electro- magnetism Magnetic Fields from Currents Current Loop Field around a current- carrying wire is fairly weak College Physics B Magnetic Field from Current

Electric Circuits Resistors in Series Resistors in Parallel Superconductivity Moving charges produce magnetic Magnetic Fields fields: Bar Magnets Horseshoe Magnets • An consists Electro- magnetism of moving charges, so it will Magnetic Fields from Currents produce a magnetic field. Current Loop • The iron filings show the magnetic field pattern due to the current. College Physics B Question 3

Electric Circuits Resistors in Series A current in a long, straight wire produces a magnetic field. Resistors in Parallel Superconductivity The magnetic field lines

Magnetic Fields A go out from the wire to infinity. Bar Magnets Horseshoe Magnets

Electro- B come in from infinity to the wire. magnetism Magnetic Fields from Currents C form circles that pass through the wire. Current Loop D form circles that go around the wire. College Physics B Question 3

Electric Circuits Resistors in Series A current in a long, straight wire produces a magnetic field. Resistors in Parallel Superconductivity The magnetic field lines

Magnetic Fields A go out from the wire to infinity. Bar Magnets Horseshoe Magnets

Electro- B come in from infinity to the wire. magnetism Magnetic Fields from Currents C form circles that pass through the wire. Current Loop D form circles that go around the wire. College Physics B Question 3

Electric Circuits Resistors in Series A current in a long, straight wire produces a magnetic field. Resistors in Parallel Superconductivity The magnetic field lines

Magnetic Fields D form circles that go around the wire. Bar Magnets Horseshoe Magnets Electro- Ampère’s Law: magnetism Magnetic Fields from Currents Current Loop B L I X k ∆ = µ0 enclosed closed path

µ I B = 0 for a straight wire 2π r

The constant µ0 is called the permeability of free space:

−7 µ0 = 4π × 10 T · m/A College Physics B Right-Hand Rule

Electric Circuits Resistors in Series Resistors in Parallel Superconductivity

Magnetic Fields Bar Magnets Horseshoe Magnets For a straight wire, the magnetic Electro- magnetism field lines form circles: Magnetic Fields from Currents • The direction of the field is Current Loop always tangent to the circles. • The magnitude of the field decreases as the distance from the wire increases. • The direction of the field is given by the right-hand rule. College Physics B Right-Hand Rule

Electric Circuits Resistors in Series Resistors in Parallel Superconductivity

Magnetic Fields Bar Magnets Horseshoe Magnets Point the thumb of your ight hand in Electro- magnetism the direction of the current: Magnetic Fields from Currents • Your thumb will be parallel to Current Loop the wire. • Curling the fingers of your right hand around the wire gives the direction of the magnetic field. College Physics B Question 4

Electric Circuits Resistors in Series Two current-carrying wires are parallel as shown below; the Resistors in Parallel Superconductivity current is the same in both wires. The current in both wires is Magnetic flowing to the right. At a point midway between the wires, the Fields Bar Magnets direction of the net magnetic field is Horseshoe Magnets Electro- → magnetism A to the right Magnetic Fields from Currents ← Current Loop B to the left C into the screen D out of the screen E The field is zero. • P College Physics B Question 4

Electric Circuits Resistors in Series Two current-carrying wires are parallel as shown below; the Resistors in Parallel Superconductivity current is the same in both wires. The current in both wires is Magnetic flowing to the right. At a point midway between the wires, the Fields Bar Magnets direction of the net magnetic field is Horseshoe Magnets Electro- → magnetism A to the right Magnetic Fields from Currents ← Current Loop B to the left C into the screen D out of the screen E The field is zero. College Physics B Plotting Field Lines

Electric Circuits Resistors in Series Resistors in Parallel Superconductivity

Magnetic Fields Bar Magnets Horseshoe Magnets Electro- Field lines are three-dimensional. magnetism Magnetic Fields from Currents 1 A large dot (•) indicates the tip Current Loop of the vector when it points out of the plane. 2 A cross (×) denotes the tail of the vector when it points into the plane. College Physics B Charges and Magnetic Fields

Electric Circuits Resistors in Series • The electric current can be modeled as a collection of Resistors in Parallel Superconductivity positive electric charges. Magnetic • Fields The charges would be moving with a velocity parallel to Bar Magnets Horseshoe Magnets the current direction. Electro- • The direction of the magnetic field is given by the magnetism Magnetic Fields from Currents right-hand rule. Current Loop • A positive charge moving to the left produces the same magnetic field as a negative charge moving to the right.

Principle of Superposition The Principle of Superposition states the total magnetic field produced by two or more different sources is equal to the sum of the fields produced by each source individually. College Physics B Current Loop

Electric Circuits Resistors in Series Treat the loop as many small pieces Resistors in Parallel Superconductivity of wire: Magnetic • Fields Apply the right-hand rule to Bar Magnets Horseshoe Magnets find the field from each piece Electro- of wire. magnetism Magnetic Fields from • Currents Applying superposition gives Current Loop the overall pattern shown on the right.

At the center of the loop:

µ I B = 0 2R College Physics B Solenoids

Electric Circuits Resistors in Series By stacking many loops close together, the field along the axis Resistors in Parallel Superconductivity is much larger than for a sinle loop. Magnetic Fields A helical winding of wire is called a solenoid. Bar Magnets Horseshoe Magnets ➜ More practical than stacking single loops. Electro- magnetism Magnetic Fields from Currents Current Loop