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# Physics 2102 Lecture 16 - PowerPoint PPT Presentation

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.

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Jonathan Dowling

### Physics 2102 Lecture 16

Ampere’s law

André Marie Ampère

(1775 – 1836)

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.

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

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.

• 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?

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!)

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

r

Ampere’s Law: Example 2 (cont)

For r>R, ienc=i, so

B=m0i/2pR

For r < R

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:

Sample Problem arrangements produce the largest magnetic field at the point indicated?

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