3/29/2016
AMPERE’S LAW
REVIEW OF GAUSS’S LAW
• The total of the electric flux out of a closed surface is equal to the charge
enclosed divided by the permittivity.
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3/29/2016
GAUSS’S LAW VS AMPERE’S LAW
• In Gauss’s Law we defined an arbitrary closed surface (Gaussian
surface) that had the correct geometry and symmetry; in
Ampere’s Law we define an arbitrary closed path (Amperian
path) that has the right geometryand symmetry.
• In Gauss’s Law we defined a differential surface area vector at
an arbitrary position on the surface; in Ampere’s Law we define a
differential length vector at an arbitrary position on the path.
• In Gauss’s Law we determined the dot product of the unknown
electric field function and the differential surface area vector; in
Ampere’s Law we determine the dot product of the unknown
magnetic field function into the differential length vector.
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3/29/2016
Magnetic Flux
The first step to understanding the complex nature of electromagnetic
induction is to understand the idea of magnetic flux.
B
A
Flux is a general term associated with a
FIELD that is bound by a certain AREA. So
MAGNETIC FLUX is any AREA that has a
MAGNETIC FIELD passing through it.
We generally define an AREA vector as one that is perpendicular to the surface of the material.
Therefore, you can see in the figure that the AREA vector and the Magnetic Field vector are
PARALLEL. This then produces a DOT PRODUCT between the 2 variables that then define flux.
Magnetic Flux – The DOT product
B  B  A
 B  BA cos 
Unit : Tm 2 or Weber(Wb)
How could we CHANGE the flux over a period of time?
 We could move the magnet away or towards (or the wire)
 We could increase or decrease the area
 We could ROTATE the wire along an axis that is PERPENDICULAR to the
field thus changing the angle between the area and magnetic field vectors.
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3/29/2016
AMPERE’S LAW
• The magnetic field in space around an electric current is proportional to the
electric current which serves as its source, just as the electric field in space is
proportional to the charge which serves as its source. Ampere's Law states
that for any closed loop path, the sum of the length elements times the
magnetic field in the direction of the length element is equal to
the permeability times the electric current enclosed in the loop.
AMPERE’S LAW
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