Magnetic Field Sources

Magnetic Fields

• A force field that denotes the area in which the non-contact force of permanent magnets or current carrying conductors can exert their influence

• Fields are concentrated at the poles

• Same properties with Electric field lines except that there is no magnetic monopole

Magnetic field lines

Magnetic Force

• Like poles repel, opposite attract

• An object that contains iron but is not itself magnetized is attracted by either pole of a permanent magnet.

Magnetic Force

Magnetic interactions can be described as:

• A moving charge or a current creates a magnetic field in the surrounding space (in addition to its electric field)

• The magnetic field exerts a force Fm on any other moving charge or current that is present in the field.

• The magnetic force Fm acting on a positive charge q moving with velocity v is perpendicular to both Fm and the magnetic field B.

Units of Magnetic Fields

• SI units: tesla, T1 tesla = 1 T = 1 N/A·m

• Or: gauss, G1 G = 10-4 T

Magnetic Force on Moving Charge• Moving charged particles are deflected in magnetic

fields

• Right-Hand Rule

F q v B

Grip and Hand Rules

Out of the Page

In to the Page

The magnetic force is always perpendicular to v; a particle moving under the action of a magnetic field alone moves with a constant speed.

Magnetic Force on Moving Charge

Motion of charged particles in a magnetic field

Motion of charged particles in a magnetic field

Fig. 27.18

Motion of charged particles in a magnetic field

Fig. 27.17

Applications of motion of charged particles

Velocity Selector• Particles of a specific

speed can be selected from the beam using an arrangement of electric and magnetic fields called a velocity selector.

Magnetic Force on Current Carrying Wire

sinIlBF

BIlF

M

M

Magnetic Force on Current Carrying Wire

Ampere’s Law

enclosedIlB 0

• Used to determine the magnetic field yielded by current-carrying wire

• Ampere’s law states that the product B and length of line segment around any closed path equals µ0 times the net current through the area enclosed by the path.

• Direction of Magnetic field is determined by corkscrew method

Ampere’s LawB=0I/2L

Magnetic field profile of 2 parallel current carrying wires

Solution

)P (point

)P (point

)P (point

3

2

1

dI

dI

dI

BBB

dI

dI

dI

BBB

dI

dI

dI

BBB

total

total

total

362

22

884

00012

00021

00021

Magnetic Field in Solenoid

Magnetic Field in SolenoidB=0nI

Ampere’s Experiment

B1=0I1/2L F= 0I1I2l/2L

Exercise

B1=0I1/2L F/l= 0I1I2/2L

ExampleSuspending a current with a current

A horizontal wire carries a current I1=80 A dc. A second parallel wire 20 cm below it must carry how much current I2 so that it doesn’t fall due to gravity? The lower wire is a homogenous wire with a mass of 0.12 g per meter of length.

F/L = mg/L=1.18 x 10-3 N/m

0I1I2/2 L = 1.18 x 10-3 N/m

I2= 15 A

Definitions

• Ampere current flowing in each of the two long parallel conductors 1 m apart, which results in a force of exactly 2 x 10-7 N/m of length of each conductor.

• Coulomb one ampere-second

Solution Set

F/l= 0I1I2/2L

FA/l= 5.83 x 10-5N/m; 90

FB/l=3.37 x 10-5N/m; -60

FC/l=3.37 x 10-5N/m; 240