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Lecture

# March 6.doc

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School
Department
Physics
Course
PHYS 102
Professor
Zaven Altounian
Semester
Winter

Description
Phys 102 Alanna Houston March 6, 2008 Simple Right Hand Rule: - Imagine holding the wire carrying the current with your right hand, the thumb in the direction of the current. Your fingers will then give the sense of direction of the magnetic field B - A circle with a dot coming out of it is a vector pointing out of the plane - A circle with an x is a vector pointing into the plane - The simple right hand rule applies to many geometries including current in a loop: - Determination of Magnetic Field Strengths Produced by Electric Currents: - General Case: o What is the magnetic field at point P due to the current I? o o Let us take a small segment of the wire, delta L and calculate the field, delta B it produces at P. It has been found, experimentally, that delta B ~ I delta L o o The inverse square law applies as well: o o In addition, the component of the displacement r perpendicular to the current contributes to the field at point P o DeltaB ~ sin ϕ (The current does not produce a field on itself Phys 102 Alanna Houston o Putting it all together, o (Biot-Savart Law) o The proportionality constant o o o For a medium other than vacuum, we replace mu not by mu, the permeability of the medium. For permanent materials, such as Fe, mu can be very large (mu ~ 5000 mu not) o To find the total magnetic field at point P, we must ad vectorially all contributions delta B from each current segment Delta L. Integration may be necessary. The direction of the B-field is determined directly by the right hand rule - To summarize: - Important Geometries: - The B-field at the centre of a circular current loop of radius r: - Phys 102 Alanna Houston - Every segment delta L is the same distance from the centre (r is a constant) - Delta L is tangent to the radius r (i.e. ϕ = 90 degrees) - - The direction of the B-field at the centre is determined from the simple RHR. In this case, it will point into the plane containing the
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