L11 - Chapter 29 continued Ampere's Law Andre Marie...

Info icon This preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: Chapter 29 continued .... Ampere's Law Andre Marie Ampere (1775-1836) Ampere's Law r v B ds = oiencl Enclosing a current carrying wire with a loop and taking the dot product of B and ds along that loop determines the amount of current enclosed by the loop. For geometries with a high degree of symmetry one can determine the magnetic field from Ampere's LAW Ampere's Law How do you use this equation to determine B? r v B ds = oiencl Examples of Current sources with a high degree of symmetry Long Straight Wire Toroid Solenoid 1) Long Straight Wire with a constant current For r>R, radius of wire the magnetic field must have cylindrical symmetry r v B ds = oienc B ds = oienc B 2r = oi r oi ^ t B= 2r ^ unit vecto r tangent to t Amperian loop ^ to be compared to n Example Long Straight Wire r v B ds = oienc 2 B ds = o Jr o i B ds = r R 2 2 i 2 B 2r = o 2 r R For r < R the magnetic field must have r o i r ^ cylindrical symmetry and the current B = t enclosed is only part of I 2 R 2 Example Long Straight Wire Result of considering paths 1 and 2 Sample Problem What is the magnetic field at a=0cm, b=2.0cm a) r=0 cm b) r=1.3 cm J=cr2 Solenoid - A long cylinder with wire closely wrapped around it. The length is much larger than the diameter. Ideal Solenoid r v B ds = oienc r r r r B ds + B ds a r r r r + B ds + B ds = o ienc c d b Bh + 0 + 0 + 0 = oienc Bh = o N turns i where N = nh B = o ni Constant field in x-direction r B = o ni ^ x Magnetic Field inside a donut (toroid) mmm ...... r v B ds = oienc B ds = o Ni B 2r = o Ni r o Ni ^ B= t 2r There is "circular symmetry" here, the field will be constant along the circular path concentric with the center axis of Example Problem 5 What current must flow through the wires of a toroid to generate a 1.0 T magnetic field at its center (10 cm radius) if it has 500 turns of wire? etc ..... o Ni B= 2r...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern