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

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Example 1: Magnetic Field of a Wire

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Find the magnetic field outside a current-carrying wire

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Find the magnetic field inside a current-carrying wire

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Graph the magnetic field of a current-carrying wire as a function of the distance from the center of the wire

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Example 2: Magnetic Field in a Solenoid

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?

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2011 Free Response Question 3

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

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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3.6 Ampere's Law