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

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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 d Bs r r
Background image of page 2
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 d Bs r r
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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 d Bs r r
Background image of page 4
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
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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 ±
Background image of page 6
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
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 26

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

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online