Magnetic Fields

Magnetic Fields and Forces

• a single magnetic pole has never been isolated

• magnetic poles are always found in pairs

• Earth itself is a large permanent magnet

Magnetic Fields and Forces

Magnetic Fields and Forces

• We can represent the magnetic field ( ) by means of drawings with magnetic field lines

• We can define a magnetic field at some point in space in terms of the magnetic force that the field exerts on a charged particle moving with a velocity

• Magnetic poles exert attractive or repulsive forces on each other and that these forces vary as the inverse square of the distance between interacting poles

B

B

BF

v

Magnetic Fields and Forces

• The magnitude FB of the magnetic force exerted on the particle is proportional to the charge q and to the speed v of the particle

• The magnitude and direction of depend on the velocity of the particle and on the magnitude and direction of the magnetic field (Tesla, T=N.s/(C.m), in SI unit)

• When a charged particle moves parallel to the magnetic field vector, the magnetic force acting on the particle is zero

BF

B

Magnetic Fields and Forces

BF qv B

sinBF qv B qvB

Magnetic Fields and Forces

Example #13Example #13

• An electron in a television picture tube moves toward the front of the tube with a speed of 8.0 x106 m/s along the x axis (see the figure). Surrounding the neck of the tube are coils of wire that create a magnetic field of magnitude 0.025 T, directed at an angle of 600 to the x axis and lying in the xy plane. Calculate the magnetic force on the electron.

Magnetic Force Acting on a Current-Carrying

Conductor

• The resultant force exerted by the field on the wire is the vector sum of the individual forces exerted on all the charged particles making up the current

Magnetic Force Acting on a Current-Carrying

Conductor

Magnetic Force Acting on a Current-Carrying

Conductor

Magnetic Force Acting on a Current-Carrying

Conductor

B dF q v B nAL

BF IL B

n : the number of charges per unit volume

Magnetic Force Acting on a Current-Carrying

Conductor

BdF Ids B

b

B

a

F I ds B

Magnetic Force Acting on a Current-Carrying

Conductor

• The magnetic force on a curved current-carrying wire in a uniform magnetic field is equal to that on a straight wire connecting the end points and carrying the same current

Magnetic Force Acting on a Current-Carrying

Conductor

• The net magnetic force acting on any closed current loop in a uniform magnetic field is zero

Quiz#3Quiz#3

• Rank the wires according to the magnitude of the magnetic force exerted on them, from greatest to least

Sources of the Magnetic Field

• The Biot–Savart Law

02

ˆ

4

I ds rdB

r

02

ˆ

4

I ds rB

r

0 : 4 x 10-7 T.m/A

Magnetic Field Surrounding a Thin, Straight Conductor

0

2

IB

a

Magnetic Field on the Axis of a Circular Current Loop

20

32 2 22

x

IRB

x R

0

2

IB

R

At x=0

If x>>R

20

32

IRB

x

Magnetic Field on the Axis of a Circular Current Loop

The Magnetic Force Between

Two Parallel Conductors

• Parallel conductors carrying currents in the same direction attract each other

• Parallel conductors carrying currents in opposite directions repel each other0 2 0 1 2

1 1 2 1 2 2

I I IF I lB I l l

a a

Ampère’s Law

Ampère’s Law• The line integral of around any closed

path equals 0I, where I is the total steady current passing through any surface bounded by the closed path

sdB

002

2

IB ds B ds r I

r

Quiz#4Quiz#4

• Rank the magnitudes of for the closed paths in the figure from least to greatest

B ds

The Magnetic Field of a Solenoid

• A solenoid is a long wire wound in the form of a helix

The Magnetic Field of a Solenoid

The Magnetic Field of a Solenoid

1 1Path Path

B ds B ds B ds Bl

0B ds NI Bl

From Ampère’s Law

N: the number of turns

n: the number of turns per unit length

0B nI

Magnetic Flux

B B dA

Magnetic Flux

cosB BA

Gauss’s Law in Magnetism

• The net magnetic flux through any closed surface is always zero

The Magnetic Field of the Earth

Faraday’s Law of Faraday’s Law of InductionInduction

• An electric current can be induced in a secondary circuit by a changing magnetic field

• An induced emf is produced in the secondary circuit by the changing magnetic field

• The emf induced in a circuit is directly proportional to the time rate of change of the magnetic flux through the circuit

Faraday’s Law of Faraday’s Law of InductionInduction

Bd

dt

BdNdt

a coil consisting of N loops all of the same area

Faraday’s Law of Faraday’s Law of InductionInduction

Lenz’s Law• The induced current in a loop is in

the direction that creates a magnetic field that opposes the change in magnetic flux through the area enclosed by the loop

Lenz’s Law