Ampere's Law

  • Ampere's Law provides an elegant method of finding the magnetic field due to current flowing in a wire in situations of planar and cylindrical symmetry



Example 1: Magnetic Field of a Wire


  1. Find the magnetic field outside a current-carrying wire
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  1. Find the magnetic field inside a current-carrying wire
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  1. Graph the magnetic field of a current-carrying wire as a function of the distance from the center of the wire


Example 2: Magnetic Field in a Solenoid

Side View Cross-Section ээээээ ээээээ в

  • Calculate the magnetic field in the middle of a solenoid (i.e. Slinky) using Ampere's Law

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Example 3: Net Force on a Wire Loop

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  • What is the direction of the net force on the loop?


2011 Free Response Question 3

b a Cross-sectional View (current into page) E\&M. 3. A section of a
 long conducting cylinder with inner radius a and outer radius b
 carries a current 10 that has a uniform current density, as shown in
 the figure above. (a) Using law, derive an expression for the
 magnitude of the magnetic field in the following regions as a function
 of the distance r from the central axis. i. ii. iii. r = 2b (b) On the
 cross-sectional view in the diagram above, indicate the direction of
 the field at point P, which is at a distance r = 2b from the axis of
 the cylinder. (c) An electron is at rest at point P. Describe any
 electromagnetic forces acting on the electron. Justify your answer.


c) Feo


2005 Free Response Question 3

Hall Probe and Meter 0 10 20 30 40 50 60 70 80 90 100 A student
 performs an experiment to measure the magnetic field along the axis of
 the long, 100-turn solenoid PQ shown above. She connects ends P and Q
 of the solenoid to a variable power supply and an ammeter as shown.
 End P of the solenoid is taped at the 0 cm mark of a meterstick The
 solenoid can be stretched so that the position of end Q can be varied.
 The student then positions a Hall probe\* in the center of the
 solenoid to measure the magnetic field along its axis. She measures
 the field for a fixed current of 3.0 A and various positions of the
 end Q. The data she obtains are shown below. Trial Position of End Q
 Measured Magnetic Field (T) n (turns/m) 1 2 3 4 5 (cm) 40 50 60 80 100
 (directed from P to Q) \_4 9.70 x 10 —4 7.70 x 10 \_4 6.80 x 10 \_4
 4.90 x 10 -4 4.00 x 10 (a) Complete the last column of the table above
 by calculating the number of turns per meter. \*A Hall Probe is a
 device used to measure the magnetic field at a point.

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