1 / 11

Physics 2102 Lecture 16

Physics 2102 Jonathan Dowling. Physics 2102 Lecture 16. Ampere’s law . André Marie Ampère (1775 – 1836). q. q. Flux=0!. Ampere’s law: Remember Gauss’ law?. Given an arbitrary closed surface, the electric flux through it is proportional to the charge enclosed by the surface.

forest
Download Presentation

Physics 2102 Lecture 16

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Physics 2102 Jonathan Dowling Physics 2102 Lecture 16 Ampere’s law André Marie Ampère (1775 – 1836)

  2. q q Flux=0! Ampere’s law: Remember Gauss’ law? Given an arbitrary closed surface, the electric flux through it is proportional to the charge enclosed by the surface.

  3. Gauss’ law for Magnetism: No isolated magnetic poles! The magnetic flux through any closed “Gaussian surface” will be ZERO. This is one of the four “Maxwell’s equations”.

  4. i4 i3 i2 i1 ds Ampere’s law: a Second Gauss’ law. The circulation of B (the integral of B scalar ds) along an imaginary closed loop is proportional to the net amount of current traversing the loop. Thumb rule for sign; ignore i4 As was the case for Gauss’ law, if you have a lot of symmetry, knowing the circulation of B allows you to know B.

  5. Sample Problem • Two square conducting loops carry currents of 5.0 and 3.0 A as shown in Fig. 30-60. What’s the value of ∫B∙dsthrough each of the paths shown?

  6. R Ampere’s Law: Example 1 • Infinitely long straight wire with current i. • Symmetry: magnetic field consists of circular loops centered around wire. • So: choose a circular loop C -- B is tangential to the loop everywhere! • Angle between B and ds = 0. (Go around loop in same direction as B field lines!)

  7. i r R Ampere’s Law: Example 2 • Infinitely long cylindrical wire of finite radius R carries a total current i with uniform current density • Compute the magnetic field at a distance rfrom cylinder axisfor: • r < a (inside the wire) • r > a (outside the wire) Current into page, circular field lines

  8. Current into page, field tangent to the closed amperian loop r Ampere’s Law: Example 2 (cont) For r>R, ienc=i, so B=m0i/2pR For r < R

  9. Solenoids

  10. All loops in the figure have radius r or 2r. Which of these arrangements produce the largest magnetic field at the point indicated? Magnetic Field of a Magnetic Dipole A circular loop or a coil currying electrical current is a magnetic dipole, with magnetic dipole moment of magnitude m=NiA. Since the coil curries a current, it produces a magnetic field, that can be calculated using Biot-Savart’s law:

  11. Sample Problem Calculate the magnitude and direction of the resultant force acting on the loop.

More Related