Week8_1 - Ampere's Law Ampere's Law r r states that the...

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Ampere’s Law ± Ampere’s Law states that the line integral of around any closed path equals μ o I where I is the total steady current passing through any surface bounded by the closed path o dI μ ⋅= Bs r r ± d r r d s r d r r
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Ampere’s Law, cont ± Ampere’s Law describes the creation of magnetic fields by all continuous current configurations ± Most useful for this course if the current configuration has a high degree of symmetry ± Put the thumb of your right hand in the direction of the current through the amperian loop and your figures curl in the direction you should integrate around the loop
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Amperian Loops ± Each portion of the path satisfies one or more of the following conditions: ± The value of the magnetic field can be argued by symmetry to be constant over the portion of the path ± The dot product can be expressed as a simple algebraic product B ds ± The vectors are parallel
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Amperian Loops, cont ± Conditions: ± The dot product is zero ± The vectors are perpendicular ± The magnetic field can be argued to be zero at all points on the portion of the path
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Field Due to a Long Straight Wire – From Ampere’s Law ± Want to calculate the magnetic field at a distance r from the center of a wire carrying a steady current I ± The current is uniformly distributed through the cross section of the wire
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Field Due to a Long Straight Wire – Results From Ampere’s Law ± Outside of the wire, r > R ± Inside the wire, we need I’, the current inside the amperian circle (2 ) 2 o o dBr I I B r π μ ⋅= = = Bs r r ± 2 2 2 ) ' ' 2 o o r I I I R I Br R πμ = = ⎛⎞ = ⎜⎟ ⎝⎠ r r ±
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Field Due to a Long Straight Wire – Results Summary ± The field is proportional to r inside the wire ± The field varies as 1/ r outside the wire ± Both equations are equal at r = R
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Magnetic Field of a Toroid ± Find the field at a point at distance r from the center of the toroid ± The toroid has N turns of wire (2 ) 2 o o dB r N I NI B r πμ μ π ⋅= = = Bs r r ±
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Magnetic Field of a Solenoid ± A solenoid is a long wire wound in the form of a helix ± A reasonably uniform magnetic field can be produced in the space surrounded by the turns of the wire ± Each of the turns can be modeled as a circular loop ± The net magnetic field is the vector sum of all the fields due to all the turns
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Magnetic Field of a Solenoid, Description ± The field lines in the interior are ± Approximately parallel to each other ± Uniformly distributed ± Close together ± This indicates the field is strong and almost uniform
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Magnetic Field of a Tightly Wound Solenoid ± The field distribution is similar to that of a bar magnet ± As the length of the solenoid increases ± The interior field becomes more uniform ± The exterior field becomes weaker
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Ideal Solenoid – Characteristics ± An ideal solenoid is approached when ± The turns are closely spaced ± The length is much greater than the radius of the turns ± For an ideal solenoid, the field outside of solenoid is negligible ± The field inside is uniform
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This note was uploaded on 06/02/2008 for the course PHYS 102 taught by Professor N/a during the Spring '08 term at Drexel.

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Week8_1 - Ampere's Law Ampere's Law r r states that the...

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