Ampere’s Law applied to long straight wiresAmpere’s Law applied to long straight wires

The value of the The value of the magnetic fieldmagnetic field near a near a long straight wire is long straight wire is directly proportionaldirectly proportional to to the the currentcurrent in the wire. in the wire.

In order to make this an In order to make this an equation multiply in a equation multiply in a

proportionality constant.proportionality constant.

μμ00 = 4 = 4ππ x 10 x 10-7-7 T . m/A T . m/A

2oIBr

µπ

=

The The magnetic fieldmagnetic field is is inversely proportionalinversely proportional to the to the distancedistance from the from the wire.wire.

Note that it really isn’t the distance Note that it really isn’t the distance from the wire, but the circumference from the wire, but the circumference of the circle that the magnetic field of the circle that the magnetic field circumvents.circumvents.

B B αα I I B B αα 1/r 1/r

k = k = μμoo/2/2ππkI

Br

=

IBr

α

oIBl

µ=Most general Most general

form.form.

Ampere’s Law and Solenoids.Ampere’s Law and Solenoids.

A solenoid can be A solenoid can be considered to be a set of considered to be a set of circular loops placed side circular loops placed side by side that carry the by side that carry the same current. It same current. It produces a uniform produces a uniform magnetic field inside it.magnetic field inside it.

Can beCan be placed into placed into Ampere’s Law equation Ampere’s Law equation as as number of loopsnumber of loops per per unit length.unit length.

3 D of a magnetic field in a solenoid.

oN IB

l

µ=

SummarySummaryLong straight wire vs. solenoidLong straight wire vs. solenoid

Long straight wire: Long straight wire:

2oIBr

µπ

=

Solenoid:Solenoid:

What is similar? What is different? Why?What is similar? What is different? Why?

oN IB

l

µ=

Review: 2Review: 2ndnd Right Hand Rule Right Hand RuleImagine grabbing onto a wire with your right hand. Imagine grabbing onto a wire with your right hand.

Put your thumb in the direction of the current. Put your thumb in the direction of the current. Your fingers then curl in the direction of the B Field.Your fingers then curl in the direction of the B Field.

Sample ProblemSample Problem

A vertical electric wire in the wall of a A vertical electric wire in the wall of a building carries a current of 22 A upward. building carries a current of 22 A upward. What is the magnetic field at a point 5 cm What is the magnetic field at a point 5 cm out from this wire?out from this wire?

Givens:

I = 22 A

r = 5 cm 0.05 m

7

5

4 10 (22)

2 (0.05)

8.8 10

B

B x T

ππ

−

−

×=

=

Tie in to Previous KnowledgeTie in to Previous Knowledge

A second wire in the wall is parallel to the first A second wire in the wall is parallel to the first wire and is also 5 cm away. If there is a current wire and is also 5 cm away. If there is a current in this second wire, then what direction will the in this second wire, then what direction will the electrons (and consequently the wire) be electrons (and consequently the wire) be pushed?pushed?

What will the magnitude of the force be?What will the magnitude of the force be?

Tie in to Previous KnowledgeTie in to Previous Knowledge

A second wire in the wall is parallel to the first A second wire in the wall is parallel to the first wire and is also 5 cm away. If there is a current wire and is also 5 cm away. If there is a current in this second wire, then what direction will the in this second wire, then what direction will the electrons (and consequently the wire) be electrons (and consequently the wire) be pushed?pushed?

What will the magnitude of the force be?What will the magnitude of the force be?