Biot-Savart Law Biot-Savart law: The constant o is called the permeability of free space o = 4 x...

Biot-Savart LawBiot-Savart law:

The constant o is called the permeability of free space

o = 4 x 10-7 T. m / A

24oμ d

dπ r

s rB

ˆI

24oμ d

π r

s rB

ˆI

for a Long, Straight ConductorThe thin, straight

wire is carrying a constant current

Integrating over all

the current elements

B

2

1

1 2

4

4

θo

θ

o

μB θ dθ

πaμ

θ θπa

I

cos

Isin sin

sin d dx θ s r k ˆˆ

2

IoμBπa

for a Curved Wire SegmentFind the field at

point O due to the wire segment

I and R are constants

will be in radians

B

4

IoμB θπR

for a Circular Loop of WireConsider the previous result, with a full circle

= 2

This is the field at the center of the loop

B

24 4 2o o oμ μ μ

B θ ππa πa a

I I I

for a Circular Current LoopThe loop has a

radius of R and carries a steady current of I

Find the field at point P

B

2

32 2 22

ox

μ aB

a x

I

Magnetic Force Between Two Parallel ConductorsTwo parallel wires

each carry a steady current

The field due to the current in wire 2 exerts a force on wire 1 of F1 = I1ℓ B2

1 21 2

I IoμFπa

Ampere’s LawAmpere’s law states

that the line integral of around any closed

path equals oI where I is the total steady current passing through any surface bounded by the closed path:

s od μ B

I

dB s

Magnetic Field of a ToroidFind the field at a

point at distance r from the center of the toroid

The toroid has N turns of wire

2

2

o

o

d B πr μ N

μ NB

πr

B s

( ) I

I

Magnetic FluxThe magnetic flux

associated with a magnetic field is defined in a way similar to electric flux

The magnetic flux B is

The unit of magnetic flux is T.m2 = WbWb is a weber

B d B A

Gauss’ Law in MagnetismGauss’ law in magnetism says the

magnetic flux through any closed surface is always zero:

0d B A

Earth’s Magnetic FieldThe 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