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Class 9 Physics 106 Learning Outcomes Class 9 More Circuit Analysis and Magnetic Fields Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits Physics 106 An RC Circuit Example The Magnetic Field The Lorentz Force Winter 2017 Press CTRL-L to view as a slide show. Learning Outcomes Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Last time we learned about: I Resitivity I How resistivity changes with temperature Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example I Series and parallel circuits with resistors The Magnetic Field I Kirchhoff’s Laws The Lorentz Force Learning Outcomes Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Today we will discuss: I Examples of Series-Parallel Reduction I Magnetic Fields Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example I Series RC Circuits and Time Constants The Magnetic Field I Using Kirchhoff’s Rules The Lorentz Force Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit Series-Parallel Reduction Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Problem-Solving Strategy Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example I Combine all resistors in series Virtual Circuit I Combine all resistors in parallel Kirchhoff’s Rules I Sketch the new circuit after each step RC Circuits I Continue until one resistor remains The Magnetic Field I Find the voltage and currents step by step back to the beginning The Lorentz Force An RC Circuit Example Equivalent Resistance − Complex Circuit Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Equivalent Resistance -Complex Circuit Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Equivalent Resistance -Complex Circuit Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Find all the currents, voltages, and powers Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Virtual Circuit Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit You can construct your own circuits and measure voltages and currents by going to the "Resources" Tab and then look for the Resistor Network Virtual Lab. Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Kirchhoff’s Rules Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors I Junction Rule I I The sum of the currents entering any junction must equal the sum of the currents leaving that junction Loop Rule I The sum of the potential differences across all the elements around any closed circuit loop must be zero Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Applying Kirchhoff’s Rules Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force 1.Mark each junction. Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force 2. Label all currents - between each pair of junctions. Choose a direction - it doesn’t have to be right! Here there are 6 currents. Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force 2. Label all currents - between each pair of junctions. Choose a direction - it doesn’t have to be right! Here there are 6 currents. Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force 3. Number of junction equations: If there are N junctions, there are N − 1 junction equations. Here there are 4 junctions, so there are 3 junction equations. Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Class 9 4. Write the junction equations: Current in = Current out. Physics 106 Learning Outcomes A. I3 + I6 = I1 B. I1 = I4 + I2 C. I2 = I5 + I6 Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force 5. Number of loop equations = Number of currents − Number of junction equations. Here: 6−3=3, so we need 3 loops. A. I3 + I6 = I1 B. I1 = I4 + I2 C. I2 = I5 + I6 Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force 6. At least one loop must cover every circuit element. Class 9 Physics 106 Learning Outcomes A. I3 + I6 = I1 B. I1 = I4 + I2 C. I2 = I5 + I6 Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force 7. Put a plus or minus on every resistor (side current goes in is +) and battery (+ is positive terminal). A. I3 + I6 = I1 B. I1 = I4 + I2 C. I2 = I5 + I6 Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Class 9 8. Write the loop equations. Physics 106 A. I3 + I6 = I1 B. I1 = I4 + I2 C. I2 = I5 + I6 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force 1: +6 − 2I3 − 1I1 − 4I4 = 0 2: −3I6 + 2I3 − 6 + 6I5 − 7I6 = 0 3: −6I5 + 4I4 − 5I2 = 0 8. Write the loop equations. Class 9 Physics 106 When you go around the loop, ignore the current arrows! Follow the loop in the direction of the loop arrow! A. I3 + I6 = I1 B. I1 = I4 + I2 C. I2 = I5 + I6 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force 1: +6 − 2I3 − 1I1 − 4I4 = 0 2: −3I6 + 2I3 − 6 + 6I5 − 7I6 = 0 3: −6I5 + 4I4 − 5I2 = 0 9. Solve the system of equations using your favorite method. Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors A. I3 + I6 = I1 B. I1 = I4 + I2 C. I2 = I5 + I6 Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field 1: +6 − 2I3 − 1I1 − 4I4 = 0 2: −3I6 + 2I3 − 6 + 6I5 − 7I6 = 0 3: −6I5 + 4I4 − 5I2 = 0 The Lorentz Force Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit RC Circuits Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force A Charging RC Circuit Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit I When the circuit is closed, the capacitor starts to charge. Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force A Charging RC Circuit Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example I The capacitor continues to charge until it reaches its maximum charge, Q = CV . Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force A Charging RC Circuit Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example I Once the capacitor is fully charged, the current in the circuit is zero. Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force A Charging RC Circuit Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit I The larger the resistance, the longer it takes to charge Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force A Charging RC Circuit Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit I The larger the capacitance, the longer it takes to charge Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Charging a Capacitor in an RC Circuit Class 9 Physics 106 Learning Outcomes I The charge on the capacitor is q(t) = Q(1 − e−t/τ ) where τ = RC is the time constant. I At t = 0, the charge is 0. I As t gets large, q goes to Q = C . I When t = τ , q = Q(1 − e) = 0.632Q Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force A Discharging RC Circuit Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit I A charged capacitor is discharged through a resistor. Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force A Discharging RC Circuit Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit I Initially the voltage across the capacitor is V = Q/C. Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Discharging a Capacitor in an RC Circuit Class 9 Physics 106 I I I I The charge decreases in time as q(t) = Qe−t/τ Learning Outcomes Series-Parallel Reduction with Resistors Example At t = 0, the charge is Q = CV . Virtual Circuit As t gets large, the charge goes to 0. The Magnetic Field At t = τ , the charge decreases to 0.368Q. (0.368=1-0.632) Kirchhoff’s Rules RC Circuits An RC Circuit Example The Lorentz Force Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit An RC Circuit Example Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force An RC Circuit Example Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example I I A 10 Ω resistor and a 30 µF capacitor are connected in series with a 12 V battery and a switch. What is the final charge on the capacitor? Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field I Q = CV = 360µF The Lorentz Force An RC Circuit Example Class 9 Physics 106 Learning Outcomes I A 10 Ω resistor and a 30 µF capacitor are connected in series with a 12 V battery and a switch. I How long does it take after the switch is closed for the capacitor to reach 50% of its final charge? Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force An RC Circuit Example Class 9 Physics 106 Learning Outcomes I A 10 Ω resistor and a 30 µF capacitor are connected in series with a 12 V battery and a switch. I How long does it take after the switch is closed for the capacitor to reach 50% of its final charge? Series-Parallel Reduction with Resistors Example q(t) = Q(1 − e−t/τ ) Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force An RC Circuit Example Class 9 Physics 106 Learning Outcomes I A 10 Ω resistor and a 30 µF capacitor are connected in series with a 12 V battery and a switch. I How long does it take after the switch is closed for the capacitor to reach 50% of its final charge? Series-Parallel Reduction with Resistors Example q(t) = Q(1 − e−t/τ ) q(t1/2 ) = Q /2 = Q(1 − e−t1/2 /τ ) Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force An RC Circuit Example Class 9 Physics 106 Learning Outcomes I A 10 Ω resistor and a 30 µF capacitor are connected in series with a 12 V battery and a switch. I How long does it take after the switch is closed for the capacitor to reach 50% of its final charge? Series-Parallel Reduction with Resistors Example q(t) = Q(1 − e−t/τ ) Q /2 = Q(1 − e−t1/2 /τ ) Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force An RC Circuit Example Class 9 Physics 106 Learning Outcomes I A 10 Ω resistor and a 30 µF capacitor are connected in series with a 12 V battery and a switch. I How long does it take after the switch is closed for the capacitor to reach 50% of its final charge? Series-Parallel Reduction with Resistors Example q(t) = Q(1 − e−t/τ ) 1/2 = (1 − e−t1/2 /τ ) Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force An RC Circuit Example Class 9 Physics 106 Learning Outcomes I A 10 Ω resistor and a 30 µF capacitor are connected in series with a 12 V battery and a switch. I How long does it take after the switch is closed for the capacitor to reach 50% of its final charge? Series-Parallel Reduction with Resistors Example q(t) = Q(1 − e−t/τ ) 1/2 = (1 − e−t1/2 /τ ) e−t1/2 /τ = (1/2) Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force An RC Circuit Example Class 9 Physics 106 Learning Outcomes I A 10 Ω resistor and a 30 µF capacitor are connected in series with a 12 V battery and a switch. I How long does it take after the switch is closed for the capacitor to reach 50% of its final charge? Series-Parallel Reduction with Resistors Example q(t) = Q(1 − e−t/τ ) 1/2 = (1 − e−t1/2 /τ ) 1/e−t1/2 /τ = 1/(1/2) Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force An RC Circuit Example Class 9 Physics 106 Learning Outcomes I A 10 Ω resistor and a 30 µF capacitor are connected in series with a 12 V battery and a switch. I How long does it take after the switch is closed for the capacitor to reach 50% of its final charge? Series-Parallel Reduction with Resistors Example q(t) = Q(1 − e−t/τ ) 1/2 = (1 − e−t1/2 /τ ) 1/e−t1/2 /τ = 1/(1/2) e+t1/2 /τ = 2 Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force An RC Circuit Example Class 9 Physics 106 Learning Outcomes I A 10 Ω resistor and a 30 µF capacitor are connected in series with a 12 V battery and a switch. I How long does it take after the switch is closed for the capacitor to reach 50% of its final charge? Series-Parallel Reduction with Resistors Example q(t) = Q(1 − e−t/τ ) 1/2 = (1 − e−t1/2 /τ ) 1/e−t1/2 /τ = 1/(1/2) e+t1/2 /τ = 2 ln(e+t1/2 /τ ) = ln(2) Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force An RC Circuit Example Class 9 Physics 106 Learning Outcomes I A 10 Ω resistor and a 30 µF capacitor are connected in series with a 12 V battery and a switch. I How long does it take after the switch is closed for the capacitor to reach 50% of its final charge? Series-Parallel Reduction with Resistors Example q(t) = Q(1 − e−t/τ ) 1/2 = (1 − e−t1/2 /τ ) 1/e−t1/2 /τ = 1/(1/2) e+t1/2 /τ = 2 ln(e+t1/2 /τ ) = ln(2) t1/2 = τ ln(2) Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force An RC Circuit Example Class 9 Physics 106 Learning Outcomes I A 10 Ω resistor and a 30 µF capacitor are connected in series with a 12 V battery and a switch. I How long does it take after the switch is closed for the capacitor to reach 50% of its final charge? Series-Parallel Reduction with Resistors Example q(t) = Q(1 − e−t/τ ) 1/2 = (1 − e−t1/2 /τ ) 1/e−t1/2 /τ = 1/(1/2) e+t1/2 /τ = 2 ln(e+t1/2 /τ ) = ln(2) t1/2 = τ ln(2) = R × C × ln(2) = 208µs Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit The Magnetic Field Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Magnetic Fields Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example I I I Moving charges produces magnetic fields in addition to electric fields. To feel a magnetic force, a test charge must also be moving. Magnetic fields are used to describe the Coulomb force when charges are in motion. Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Magnetic Fields and Wires Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example I I I Moving electrons in wires produce magnetic fields, whereas stationary charges do not. Wires therefore produce magnetic fields. This was first observed by Hans Christian Oersted in 1820. Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Magnets Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example I I I Magnetite or loadstone is a naturally occurring magnet. From ancient times, people used magnetite as a compass. The magnetic field in permanent magnets is caused by electrons moving in atoms. Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Magnets Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors I I I Magnets have north poles and south poles. Like poles repel each other and unlike poles attract each other Magnetic poles cannot be isolated I I If a permanent magnetic is cut in half repeatedly, you will still have a north and a south pole Some physicists believe magnetic "monopoles" should exist, but none have yet been found Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Magnetic Fields Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors I I ~ A vector field, we write it as B That means that at every point in space we can find ~ a magnitude and direction for B. I Its direction at a point is the direction the north pole of a compass needle points. I Magnetic field lines can be used much like electric field lines. Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Magnetic Field Lines Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force I A compass can be used to show the direction of the magnetic field lines. Earth’s Magnetic Field Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit I The north pole of a magnet is the "north-seeking" pole Kirchhoff’s Rules RC Circuits An RC Circuit Example I That means the magnetic pole near the Earth’s north geographic pole is actually a south magnetic pole. The Magnetic Field The Lorentz Force Earth’s Magnetic Field Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example I The Earth’s magnetic field is similar to that of a huge bar magnet deep in the Earth’s interior. Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Units of Magnetic Field Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit I The SI unit of magnetic field is the Tesla (T) I Another commonly used unit is a Gauss(G) I 1 T = 104 G Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force A Few Typical B Values Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example I I I Conventional laboratory magnets Up to 25000 G or 2.5 T Superconducting magnets Up to 300000 G or 30 T Earth’s magnetic field 0.5 G or 5 x 10−5 T Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example The Lorentz or Magnetic Force Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force The Electric Force (a Quick Review) Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors ~ E = qE ~ F Example Virtual Circuit Kirchhoff’s Rules RC Circuits I The magnitude of the electric force on a test charge depends on I I I The test charge (q) The electric field (E) The direction of the force depends on: I The direction of the electric field An RC Circuit Example The Magnetic Field The Lorentz Force The Magnetic Force Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example I The magnitude of the magnetic force on a test charge depends on: I I I I The test charge, q The magnetic field, B The velocity of the test charge, v The angle between the magnetic field and the test charge, θ Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force The Magnetic Force Class 9 Physics 106 Learning Outcomes I First consider the magnetic field vector and the velocity vector Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force The Magnetic Force Class 9 Physics 106 I Call the angle between the vectors θ I The magnitude of the force is Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit F = qvB sin θ Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force The Magnetic Force Class 9 Physics 106 Learning Outcomes I F = qvB sin θ I If the test charge moves in the direction of the field,there is no force. Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force The Magnetic Force Class 9 Physics 106 Learning Outcomes I F = qvB sin θ I If the test charge moves opposite the direction of the field,there is no force. Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force The Magnetic Force Class 9 Physics 106 Learning Outcomes I F = qvB sin θ I The force is largest when the velocity and B field are perpendicular. Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force The Magnetic Force Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit I The direction of the magnetic force on a test charge depends on: I I ~ The magnetic field vector, B The velocity vector, ~v Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force The Magnetic Force Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit I The direction of the magnetic force on a test charge depends on: I I ~ The magnetic field vector, B The velocity vector, ~v Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force The Magnetic Force Class 9 Physics 106 Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit I The direction of the magnetic force on a test charge depends on: I I ~ The magnetic field vector, B The velocity vector, ~v Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force The Magnetic Force Class 9 Physics 106 Learning Outcomes I Two vectors must always lie in a single plane. Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force The Magnetic Force Class 9 Physics 106 Learning Outcomes I The direction of the magnetic force is perpendicular to this plane. Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force The Magnetic Force Class 9 Physics 106 I But there are two directions perpendicular to a plane. Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force The Magnetic Force Class 9 Physics 106 I We select the correct choice by using the "right-hand rule." Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Right Hand Rule #1 Class 9 Physics 106 I Place your fingers in the direction of ~v . Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Right Hand Rule #1 Class 9 Physics 106 I I Place your fingers in the direction of ~v . Curl your fingers into the direction of the ~ magnetic field, B. Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Right Hand Rule #1 Class 9 Physics 106 I I I Place your fingers in the direction of ~v . Curl your fingers into the direction of the ~ magnetic field, B. Your thumb points in the direction of the ~ , on a force, F positive charge Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force Right Hand Rule #1 Class 9 Physics 106 I I I I Place your fingers in the direction of ~v . Curl your fingers into the direction of the ~ magnetic field, B. Your thumb points in the direction of the ~ , on a force, F positive charge If the charge is negative, the force is opposite that determined by the right hand rule. Learning Outcomes Series-Parallel Reduction with Resistors Example Virtual Circuit Kirchhoff’s Rules RC Circuits An RC Circuit Example The Magnetic Field The Lorentz Force
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