Chapter 27 Sources of Magnetic Field

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Chapter 27 Sources of Magnetic Field. Topics. The Biot-Savart Law Gauss’s Law for Magnetism Ampere’s Law. The Biot-Savart Law. A point charge produces an electric field. When the charge moves it produces a magnetic field, B :. m 0 is the magnetic constant:. As drawn, the field

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Chapter 27Sources of Magnetic Field

Topics
• The Biot-Savart Law
• Gauss’s Law for Magnetism
• Ampere’s Law
The Biot-Savart Law

A point charge produces an electric field.

When the charge moves it produces a

magnetic field, B:

m0 is the magnetic

constant:

As drawn, the field

is into the page

The Biot-Savart Law

Example:

Compute field at

point P, due to particle

moving along z axis

The Biot-Savart Law

When the expression for B is extended

to a current element, Idl, we get the

Biot-Savart law:

The magnetic field

at a given point P1 is

the sum of the field from each element

P

Biot-Savart Law: InfinitelyLong Straight Wire

The magnetic field due to an infinitely long

current-carrying wire can be computed

from the Biot-Savart law. The magnitude of

the magnetic field is:

Force Between Conductors

Recall that the force on a

current-carrying wire in

a magnetic field is

Therefore, two parallel wires,

with currents I1 and I2 exert

a magnetic force on each

other. The force on wire 2 is:

Magnetic Flux

Just as we did for electric fields, we

can define, for a magnetic

field, a flux in a similar

way:

But there is a profound difference

between the two kinds of flux…

Gauss’s Law for Magnetism

Isolated positive and negative electric

charges exist. However, no one has ever

found an isolated magnetic north or south

pole, that is, no one has ever found a

magnetic monopole

Consequently, for any closed surface the

magnetic flux into the surface is exactly

equal to the flux out of the surface

Gauss’s Law for Magnetism

This yields Gauss’s law for magnetism

Unfortunately, however, because this law

does not relate the magnetic field to its

source it is not useful for computing

magnetic fields. But there is a law that is…

I

Ampere’s Law

If one sums the dot product around

a closed loop that encircles a steady current

I then Ampere’s law holds:

That law can be used to compute magnetic fields, given a problem with sufficient symmetry