# 1 Electricity and magnetism Electricity Electric charge, electric field and potential, current, resistance and capacitance Magnetism Moving electric charge,

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<ul><li><p>Electricity and magnetism</p></li><li><p>Electric currents and magnetic fieldsMagnets were discovered in ancient times. The Chinese discovered the Earth magnet and invented the compass 220 BC.</p><p>2000+ yearsEarth's magnetic field (and the surface magnetic field) is approximately a magnetic dipole, with one pole near the north pole (see Magnetic North Pole) and the other near the geographic south pole (see Magnetic South Pole). An imaginary line joining the magnetic poles would be inclined by approximately 11.3 from the planet's axis of rotation. The cause of the field is explained by dynamo theory. SouthNorth</p></li><li><p>Electric currents and magnetic fieldsIn 1820, Hans Christian Oersted discovered that currents generate magnetic fields:</p><p> Direction: Right-hand ruleR Magnitude:</p></li><li><p>Moving charges and magnetic field and magnetic forceCurrent comes from moving charges. Magnetic field actually relates to moving charge as electric field relates to charge, through the force F on the charge:Electric field E and charge q: F = qE, here the force F is the electric charge q.Magnetic field B and moving charge qv: F = qvB, here the force F is the electric charge q which is moving with velocity v.</p><p>(comes from the cross product of two vectors)Combine the two formulas, one has the famous Lorentz force law:</p><p>F = qE + qvB</p></li><li><p>The force between two wires with currentsThe B field generated by I1 in wire 1 at the location of wire 2 is</p><p>For small charge dq in wire 2, the force it experiences follows Lorentz law: dF = dq vB</p><p>Check the vectors directions, the magnitude dF is </p><p>dF = dq vB</p><p>dq v = dqdl/dt = dq/dt dl = I2dl</p><p>So F over L isThe direction of the force F depends on the direction of the two currents: same direction, attract; difference direction: repel.</p></li><li><p>The definition of the current unit Ampere and examplesWhen I1 = I2 = I, and the same direction, then the current I is defined to be 1 Ampere if the two wires are 1 meter apart, and the force between them is 210-7 N per 1 meter wire length.</p><p>In the diagram, one current flows through the straight wire and another current flows around the wire loop, with the magnitudes shown. What are the magnitude and direction of the force exerted on the wire loop by the current in the straight wire? </p></li><li><p>example</p></li><li><p>Biot-Savart lawWhen the current follows a wire that is not straight, we use Biot-Savart law to calculate the B field this current generates at a point P in space:</p><p>This is similar to Coulombs Law that relates electric field to electric charges:The B field generated by the full section of wire is then: The formular relates magnet field to currents.and</p></li><li><p>ExampleUsing Biot-Savart Law to derive the formula for magnetic field of a long straight wire:</p></li><li><p>magnetic field of a long straight wire</p></li><li><p>Examplemagnetic field at the center of a half circle:</p></li><li><p>Amperes LawAmperes Law: </p></li><li><p>Examples of using Amperes LawCurrent genersted magnetic field</p><p>Outside a long straight wireInside the wireOf a sheet conductorOf a solenoidOf a toroid</p></li><li><p>Examples of using Amperes LawCurrent genersted magnetic field</p><p>Inside the wire</p></li><li><p>Examples of using Amperes LawCurrent genersted magnetic field</p><p>of a sheet conductor</p></li><li><p>Examples of using Amperes LawCurrent genersted magnetic field</p><p>Of a solenoid</p></li><li><p>Examples of using Amperes LawCurrent genersted magnetic field</p><p>Of a toroid</p></li></ul>

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