Physics 201- Introduction to Electricity & Magnetism
November 15- Applying Ampere's Law

How to use Ampere's Law to calculate B
• Determine if there is any symmetry for the current distribution.  If there is any symmetry, determine if it is one of the special cases that allows us to use Ampere's Law without having to integrate- plane, cylinder or solenoid (or torus).  If there isn't one of these three types of symmetry, then using Ampere's Law will be difficult and you might be better off using a Biot- Savart.
• Draw an Amperian loop with the same symmetry as the magnetic field.  Choose the size of the loop such that the loop lies at the location where you want to determine the magnetic field.  With the proper choice of an Ameprian loop, the magnetic field will be either be parallel or perpendicular to the dl vector, making the integral doable.
• Evaluate the line integral,  ,which gives us the total magnetic field along our loop.  Look for ways to simplify the integral by examining each portion of our Amperian loop separately.  That way (with the correct symmetry) the magnetic field should be constant over each portion of the loop.  At this stage the magnetic field is still unknown, so leave it as simply B
• Determine the amount of current enclosed by the Amperian loop.  If the current distribution is continuous you may have to integrate over the volume or area to find the total current.
• Now with Ampere's Law use your line integral and enclosed current to solve for the magnetic field.

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 Jeff Phillips phillips@lmu.edu Loyola Marymount University Fall 2002