Anr-4:lPhysics 48 (Fall20l1)--_:_==:__,\v. Chapter 29: Magnetic Fields Due to Carrents"Nothing can bring you peace but yourself. " - Ralph lValdo Emerson"The foolish man seeks happiness in the distance, the wise man grows it under his feet. "James Oppenheim"Happiness is not a stcrtion ),ou arrive at, but a manner of traveling." - Margaret B. RunbeckReading: sections 764 - 781Outline:= Biot-Savart Lawmagnetic fie1d from a long straight wiremagnetic field from a infinite straight wiremagnetic field at the center ofa circular arc+ force between two parallel cunents= Ampere's Lawusing Aqtp"t"'. tu*= solenoids and toroids+ current carrying coil as a magnetic dipole (read on your own)Problem Solving TechniquesA few of the eariy problems deal with the fieid of a long shaight wire. You should be able to find themagnitude and direction of the field at any point in space, given the current in the wire. UseB : /hi/21v to find the magnitude and the right-hand rule to find the direction. You may be asked forthe total fie1d of two or more long straight wires. You will then need to carry out vector addition.Once you have found the magnetic field you may be asked for the force it exerts on a movingcharge. Use qi x E . Don't forget to include the sine of the angle between i and .D when youcalculate the magnitude. Know how to use the right-hand rule to find the direction ofthe force. Besure to take into account the sign ofthe charge.Some problems ask you to use the Biot-savart law to compute the magnetic field of a current. Dividethe current into infinitesimal eiements, write the expression for the field ofan element, then integrateeach component over the current. You will need to write the integrand in terms of a single variable.If the wire is straight place it along the x-axis, say, and use the coordinate x ofpoints along the wireas the variable ofintegration. If the wire is a circular loop use the angle made by a radial line with acoordinate axis as fhe variable ofintepration.
ln many cases you may think of an electrical circuit as composed of finite straight-1ine and circular-arc segments, each of which produces a magnetic field. You can then calculate the field produced byeach s"egment and vectorially sum the individual fields to find the total field. Use the result given inProbleri 11 if you need to frnd the field on the perpendicular bisector of a finite straight wire. Tofrnd the field at some other point you sill need to integlate the BiofSavart 1aw. Use the proceduregiven in Section 1 for an infinite wire but replace the limits of integration with finite values. lJse
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Magnetic Field, Ampere, James Oppenheim, Carrents, Ralph lValdo Emerson, Margaret B. Runbeck