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College Physics B Electric Circuits Resistors in Series Resistors in Parallel Superconductivity College Physics B - PHY2054C Magnetic Fields Bar Magnets Horseshoe Magnets Magnetic Fields Electromagnetism 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 Superconductivity Magnetic Fields Bar Magnets Horseshoe Magnets 1 Electric Circuits Resistors in Series Resistors in Parallel Superconductivity Electromagnetism Magnetic Fields from Currents Current Loop 2 Magnetic Fields Bar Magnets Horseshoe Magnets 3 Electromagnetism 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 Electromagnetism 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 R1 − I R2 = 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 Superconductivity Magnetic Fields Bar Magnets Two light bulbs, A and B, are connected in series to a constant voltage source. When a wire is connected across B as shown, bulb A Horseshoe Magnets Electromagnetism Magnetic Fields from Currents Current Loop A burns more brightly. 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 Superconductivity Magnetic Fields Bar Magnets Two light bulbs, A and B, are connected in series to a constant voltage source. When a wire is connected across B as shown, bulb A Horseshoe Magnets Electromagnetism Magnetic Fields from Currents Current Loop A burns more brightly. 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 Electromagnetism 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 3 = I 1 + I 2 = E R1 + E R2 = E ( R11 + 1 R2 ) College Physics B Electric Circuits Resistors in Series Resistors in Parallel Superconductivity Magnetic Fields Bar Magnets Horseshoe Magnets Electromagnetism Magnetic Fields from Currents Current Loop Equivalent Resistance - Parallel College Physics B Circuit Analysis Electric Circuits Resistors in Series Resistors in Parallel Superconductivity 1 Some complex circuits can be solved by combinations of series and parallel rules. 2 Other circuits must be analyzed directly by Kirchhoff’s Rules. Magnetic Fields Bar Magnets Horseshoe Magnets • Loop Rule: The total change in the electric potential around Electromagnetism any closed circuit path must be zero. Magnetic Fields from Currents • Junction Rule: The current entering a circuit junction must Current Loop 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 Electromagnetism 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 Electromagnetism 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 Electric Circuits Resistors in Series Resistors in Parallel Superconductivity Magnetic Fields Bar Magnets Horseshoe Magnets Electromagnetism Magnetic Fields from Currents Current Loop Superconductivity At very low temperatures, the linearity of resistance breaks down. • The resistivities of metals approach a nonzero value at very low temperatures. • 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 Electromagnetism Magnetic Fields from Currents John Robert Schrieffer Nobel Laureate Emeritus Professor at Florida State 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 Superconductivity Magnetic Fields Bar Magnets Horseshoe Magnets 1 Electric Circuits Resistors in Series Resistors in Parallel Superconductivity Electromagnetism Magnetic Fields from Currents Current Loop 2 Magnetic Fields 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 Electromagnetism 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: • Compass needles • Speakers • Computer hard disks College Physics B Electric Circuits Resistors in Series Resistors in Parallel Superconductivity Magnetic Fields Bar Magnets Horseshoe Magnets Electromagnetism Magnetic Fields from Currents Current Loop Magnetic Poles College Physics B Electric Circuits Resistors in Series Resistors in Parallel Superconductivity Magnetic Fields Bar Magnets Magnetic Field Lines A bar magnet is a permanent magnet in the shape of a bar. • The symbol for the ~ magnetic field is B. Horseshoe Magnets Electromagnetism Magnetic Fields from Currents Current Loop • SI unit of the magnetic field is the Tesla (T ) • The magnetic field lines can be deduced from the pattern of the iron 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 Electric Circuits Resistors in Series Resistors in Parallel Superconductivity Magnetic Fields Bar Magnets Magnetic Field Lines A bar magnet is a permanent magnet in the shape of a bar. • The symbol for the ~ magnetic field is B. Horseshoe Magnets Electromagnetism Magnetic Fields from Currents Current Loop • SI unit of the magnetic field is the Tesla (T ) • 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 Magnetic Fields Bar Magnets Horseshoe Magnets Electromagnetism Magnetic Fields from Currents Current Loop The magnetic field lines always form closed loops. ➜ A general property of magnetic fields, not just bar magnets. The magnetic poles are analogous to positive and negative charges. College Physics B Electric Circuits Resistors in Series Resistors in Parallel Superconductivity Magnetic Fields Bar Magnets Horseshoe Magnets Electromagnetism Magnetic Fields from Currents Current Loop Question 2 Electrical charges and magnetic poles have many similarities, but one important “difference” is: A Opposite magnetic poles repel. B One magnetic pole cannot create magnetic poles in other materials. C A magnetic pole cannot be isolated. D Magnetic poles do not produce magnetic fields. College Physics B Electric Circuits Resistors in Series Resistors in Parallel Superconductivity Magnetic Fields Bar Magnets Horseshoe Magnets Electromagnetism Magnetic Fields from Currents Current Loop Question 2 Electrical charges and magnetic poles have many similarities, but one important “difference” is: A Opposite magnetic poles repel. B One magnetic pole cannot create magnetic poles in other materials. C A magnetic pole cannot be isolated. D Magnetic poles do not produce magnetic fields. College Physics B Electric Circuits Resistors in Series Resistors in Parallel Superconductivity Horseshoe Magnet Can be made by bending a bar magnet. Magnetic Fields • There are poles at the ends Bar Magnets of the horseshoe magnet. Horseshoe Magnets Electromagnetism Magnetic Fields from Currents Current Loop • The field is largest in the horseshoe gap. • The field is directed across the gap. ➜ iron yoke to strengthen field College Physics B Outline Electric Circuits Resistors in Series Resistors in Parallel Superconductivity Magnetic Fields Bar Magnets Horseshoe Magnets 1 Electric Circuits Resistors in Series Resistors in Parallel Superconductivity Electromagnetism Magnetic Fields from Currents Current Loop 2 Magnetic Fields Bar Magnets Horseshoe Magnets 3 Electromagnetism Magnetic Fields from Currents Current Loop College Physics B Electric Circuits Connection between Electricity and Magnetism Resistors in Series Resistors in Parallel Superconductivity Magnetic Fields Sources of Electric Fields Sources of Magnetic Fields Bar Magnets Horseshoe Magnets Electromagnetism Magnetic Fields from Currents Current Loop Electric Charge College Physics B Electric Fields Electric Circuits Resistors in Series Resistors in Parallel Superconductivity Capacitor Magnetic Fields Bar Magnets Horseshoe Magnets Electromagnetism Magnetic Fields from Currents Current Loop Michael Faraday (1791 - 1867) Static Point Charges College Physics B Electric Circuits Resistors in Series Resistors in Parallel Superconductivity Magnetic Fields Bar Magnets Horseshoe Magnets Electromagnetism Magnetic Fields from Currents Current Loop Faraday’s Cage College Physics B Electric Circuits Connection between Electricity and Magnetism Resistors in Series Resistors in Parallel Superconductivity Magnetic Fields Sources of Electric Fields Sources of Magnetic Fields Bar Magnets Horseshoe Magnets Electromagnetism Magnetic Fields from Currents Current Loop Electric Charge Moving Electric Charge College Physics B Electromagnetism Electric Circuits Resistors in Series Resistors in Parallel Superconductivity Christian Oersted (1777 - 1851) Magnetic Fields Bar Magnets Horseshoe Magnets Electromagnetism Magnetic Fields from Currents Current Loop Field around a currentcarrying wire is fairly weak College Physics B Magnetic Field from Current Electric Circuits Resistors in Series Resistors in Parallel Superconductivity Magnetic Fields Moving charges produce magnetic fields: Bar Magnets Horseshoe Magnets Electromagnetism Magnetic Fields from Currents • An electric current consists of moving charges, so it will produce a magnetic field. Current Loop • The iron filings show the magnetic field pattern due to the current. College Physics B Electric Circuits Resistors in Series Resistors in Parallel Superconductivity Magnetic Fields Bar Magnets Horseshoe Magnets Electromagnetism Magnetic Fields from Currents Question 3 A current in a long, straight wire produces a magnetic field. The magnetic field lines A go out from the wire to infinity. B come in from infinity to the wire. C form circles that pass through the wire. Current Loop D form circles that go around the wire. College Physics B Electric Circuits Resistors in Series Resistors in Parallel Superconductivity Magnetic Fields Bar Magnets Horseshoe Magnets Electromagnetism Magnetic Fields from Currents Question 3 A current in a long, straight wire produces a magnetic field. The magnetic field lines A go out from the wire to infinity. B come in from infinity to the wire. C form circles that pass through the wire. Current Loop D form circles that go around the wire. College Physics B Electric Circuits Resistors in Series Resistors in Parallel Superconductivity Magnetic Fields Bar Magnets Question 3 A current in a long, straight wire produces a magnetic field. The magnetic field lines D form circles that go around the wire. Horseshoe Magnets Electromagnetism Magnetic Fields from Currents Current Loop Ampère’s Law: X B k ∆L = µ0 I enclosed closed path B = µ0 I 2π r for a straight wire The constant µ0 is called the permeability of free space: µ0 = 4π × 10−7 T · m/A College Physics B Right-Hand Rule Electric Circuits Resistors in Series Resistors in Parallel Superconductivity Magnetic Fields Bar Magnets Horseshoe Magnets Electromagnetism Magnetic Fields from Currents Current Loop For a straight wire, the magnetic field lines form circles: • The direction of the field is 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 Electromagnetism Magnetic Fields from Currents Current Loop Point the thumb of your ight hand in the direction of the current: • Your thumb will be parallel to the wire. • Curling the fingers of your right hand around the wire gives the direction of the magnetic field. College Physics B Electric Circuits Resistors in Series Resistors in Parallel Superconductivity Magnetic Fields Bar Magnets Question 4 Two current-carrying wires are parallel as shown below; the current is the same in both wires. The current in both wires is flowing to the right. At a point midway between the wires, the direction of the net magnetic field is Horseshoe Magnets Electromagnetism Magnetic Fields from Currents Current Loop A to the right → B to the left ← C into the screen D out of the screen E The field is zero. •P College Physics B Electric Circuits Resistors in Series Resistors in Parallel Superconductivity Magnetic Fields Bar Magnets Question 4 Two current-carrying wires are parallel as shown below; the current is the same in both wires. The current in both wires is flowing to the right. At a point midway between the wires, the direction of the net magnetic field is Horseshoe Magnets Electromagnetism Magnetic Fields from Currents Current Loop A to the right → 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 Electromagnetism Magnetic Fields from Currents Field lines are three-dimensional. 1 A large dot (•) indicates the tip 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. Current Loop College Physics B Electric Circuits Resistors in Series Resistors in Parallel Superconductivity Magnetic Fields Bar Magnets Horseshoe Magnets Electromagnetism Magnetic Fields from Currents Current Loop Charges and Magnetic Fields • The electric current can be modeled as a collection of positive electric charges. • The charges would be moving with a velocity parallel to the current direction. • The direction of the magnetic field is given by the right-hand rule. • 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 Electric Circuits Resistors in Series Resistors in Parallel Superconductivity Magnetic Fields Bar Magnets Horseshoe Magnets Electromagnetism Magnetic Fields from Currents Current Loop Current Loop Treat the loop as many small pieces of wire: • Apply the right-hand rule to find the field from each piece of wire. • Applying superposition gives the overall pattern shown on the right. At the center of the loop: B = µ0 I 2R College Physics B Electric Circuits Resistors in Series Resistors in Parallel Superconductivity Magnetic Fields Solenoids By stacking many loops close together, the field along the axis is much larger than for a sinle loop. A helical winding of wire is called a solenoid. Bar Magnets Horseshoe Magnets Electromagnetism Magnetic Fields from Currents Current Loop ➜ More practical than stacking single loops.
