Magnetic Flux Gausss Law for Magnetism AmpereMaxwell Law

-Magnetic Flux -Gauss’s Law for Magnetism -“Ampere-Maxwell” Law AP Physics C Mrs. Coyle

Magnetic Flux θ

Magnetic Flux, F: The number of magnetic (flux) field lines which pass through a given cross-sectional area A Units: F webers B Tesla A area m 2 q angle formed between B and the normal to the loop (area vector A) The area vector A is perpendicular to the surface A and has a magnitude equal to the area A.

When B is perpendicular to the loop? F = BA Why?

Which has the largest magnetic flux? Answer: A

When B is along the plane of the loop? • Hint: q is the angle formed between B and the normal to the loop.

Gauss’ Law in Magnetism • Magnetic fields do not begin or end at any point – The number of lines entering a surface equals the number of lines leaving the surface • Gauss’ law in magnetism says:

Ampere’s Law – General Form • Also known as the Ampere-Maxwell law • Where is the electric flux. • The second term Id is called displacement current and is caused by electric fields that vary with time as in a capacitor.

Example: Capacitor • Consider surfaces S 1 and S 2. • The current through S 1 is I. • There is no conducting current through S 2 • The electric flux through S 2 is EA – A is the area of the capacitor plates – E is the electric field between the plates • If q is the charge on the plate at any time, FE = EA = q/eo

Example: Capacitor cont’d • The displacement current is the same as the conduction current through S 1 • The displacement current on S 2 is the source of the magnetic field on the surface boundary

• Magnetic fields are produced both by conduction currents and by time-varying electric fields

Classification of Magnetic Substances • Paramagnetic and ferromagnetic materials are made of atoms that have permanent magnetic moments • Diamagnetic materials are those made of atoms that do not have permanent magnetic moments

Classifying Materials by Permeability • Materials can be classified by how their permeability compares with the permeability of free space (mo) • Paramagnetic: mm > mo • Diamagnetic: mm < mo

Examples of Ferromagnetic Materials – – – iron cobalt nickel gadolinium dysprosium

Domains The domain is an area in a material within which all magnetic moments are aligned

Domains, Unmagnetized Material • The magnetic moments in the domains are randomly aligned • The net magnetic moment is zero

Domains, External Field Applied

Meissner Effect • Certain types of superconductors also exhibit perfect diamagnetism – This is called the Meissner effect • If a permanent magnet is brought near a superconductor, the two objects repel each other

Earth’s Magnetic Field • Like a bar magnet • The Earth’s south magnetic pole is located near the north geographic pole • The Earth’s north magnetic pole is located near the south geographic pole • Magnetic Declination

Dip Angle of Earth’s Magnetic Field • If a compass is free to rotate vertically as well as horizontally, it points to the Earth’s surface • The angle between the horizontal and the direction of the magnetic field is called the dip angle – The farther north the device is moved, the farther from horizontal the compass needle would be • The compass needle would be horizontal at the equator and the dip angle would be 0° • The compass needle would point straight down at the south magnetic pole and the dip angle would be 90°

Reversals of the Earth’s Magnetic Field • The direction of the Earth’s magnetic field reverses every few million years – Evidence of these reversals are found in basalts resulting from volcanic activity – The origin of the reversals is not understood