MAGNETIC FIELD ANDMAGNETIC FORCES

MAGNETISM: Properties of Magnets

1. If a permanent bar magnet is free to rotate, one end would point north – this is the north pole or N-pole.

2. Like poles of two magnets repel and unlike poles attract.

to northpole

3. If a permanent bar magnet is cut, it forms two smaller magnets each with its own N and S poles.*

*A magnetic monopole has not been observed in nature.

THE EARTH AS A MAGNET

The Earth's magnetic field is caused by electric currents in the liquid outer core.

magnetic inclination – angle of the magnetic field line with the surface of the earth.

Earth's magnetic field is tilted with respect to the planet's spin axis by about 11°.

The magnetic field is near horizontal at the equator and vertical at the poles.

The magnetic field of the earth ranges from 30T to 60 T.

magnetic declination – the deviation of the magnetic axis from the geographic axis.

THE EARTH AS A MAGNET

MAGNETISM AND ELECTRICITY

Hans Christian Oersted (1777-1851) Danish physicist and chemist who “accidentally” discovered the relationship between electricity and magnetism.

In 1820, Oersted discovered that the needle of a magnetic compass is deflected by a current-carrying conductor.

In 1824, Michael Faraday discovered that a moving magnet near a conducting loop produces current in the loop.

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

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

Magnetic field is a vector field, the direction of which is the direction which the N-pole of a compass needle tends to point.

For a permanent magnet, the magnetic field points out of its N-pole and into its S-pole.

MAGNETIC FIELD ( B )

EXPERIMENTAL OBSERVATIONS ON MAGNETIC FORCE ON MOVING ELECTRIC CHARGES.

A charged particle at rest experiences no magnetic force.

4. The magnetic force F is always perpendicular to both B and v.

1. The magnitude of the magnetic force F is directly proportional to the charge q.

F |q |2. The magnitude of the magnetic force F is directly

proportional to the magnitude of the magnetic field B.

F B3. The magnitude of the magnetic force F is directly proportional to the particle’s velocity v.

F v

MAGNETIC FORCES ON MOVING CHARGES

THE RIGHT-HAND RULE

V

B

F

The thumb points to the direction of the charged particle’s velocity v.

The index finger points to the direction of the magnetic field B.

The middle finger points to the direction of the magnetic force acting on the charge F.

directions of vectors:

xaway from observer:

toward the observer:

MAGNETIC FORCES ON MOVING CHARGES

BvqF ||

sin|| BvqF

BvqF

units of B:

)(111 TteslaAm

N

C

N

sm

teslaGgauss 410)(1

Example 1. A beam of protons ( q = 1.6 x 10-19 C ) moves at 3.0 x 10 5 m/s through a uniform magnetic field with a magnitude 2.0 T that is directed along the +z-axis. The velocity of each proton lies in the xz-plane at an angle of 30o to the +z-axis. Find the magnitude and direction of the force on a proton.

Example 1. A beam of protons ( q = 1.6 x 10-19 C ) moves at 3.0 x 10 5 m/s through a uniform magnetic field with a magnitude 2.0 T that is directed along the +z-axis. The velocity of each proton lies in the xz-plane at an angle of 30o to the +z-axis. Find the magnitude and direction of the force on a proton.

Example 1. A beam of protons ( q = 1.6 x 10-19 C ) moves at 3.0 x 10 5 m/s through a uniform magnetic field with a magnitude 2.0 T that is directed along the +z-axis. The velocity of each proton lies in the xz-plane at an angle of 30o to the +z-axis. Find the magnitude and direction of the force on a proton.

MAGNETIC FIELD LINES

Magnetic field lines show the direction of the magnetic field at any point in the field.

• the line through any point is tangent to the magnetic field vector.• where field lines are close together, the magnetic field magnitude is greater.

• magnetic field lines never intersect.

• the direction of the magnetic field points away from N- pole and toward S-pole.

• magnetic field lines have no ends.

MAGNETIC FIELD LINES

(a) C-shaped magnet

MAGNETIC FIELD LINES

(b) Straight Wire

MAGNETIC FIELD LINES

(c) Coil (d) Solenoid

MAGNETIC FLUX (B)magnetic flux – is a measure of the amount of magnetic field passing through a given surface.

Consider a surface area A divided into area elements dA. Determine the component of the magnetic field perpendicular to the area element.

AdBd B

dABd B cos

The magnetic flux on the area element is

where is the angle between B and the area vector A.

MAGNETIC FLUX (B)

AdBB cosBdAB

The magnetic flux for the whole area is

For a regularly-shaped area: cosBAB

Maximum magnetic flux: BAB unit: )(2 WbweberTm

AB B

Magnetic Flux Density – another term for magnetic field.

GAUSS’S LAW FOR MAGNETISM

0dAB

The total magnetic flux through a closed surface is zero.

(for any closed surface )

MOTION OF CHARGED PARTICLES IN A MAGNETIC FIELD

LCENTRIPETAMAGNETIC FF

R

mvqvB

2

qB

mvR

Radius of circular orbit in magnetic field:

MAGNETIC FORCE ON A CURRENT-CARRYING CONDUCTOR

sinBvqF

sinBt

lqF

sinBlt

qF

I

I

sinBlIF

MAGNETIC FORCE ON A STRAIGHT CONDUCTOR

I

I

sinBlIF

BlIF

Example 2. A straight horizontal copper rod carries a current of 50.0 A from west to east in a region between the poles of a large electromagnet. In this region, there is a horizontal magnetic field in the direction 45o NE with a magnitude of 1.20 T. Find the magnitude and direction of the force on a 1.00-m section of the rod.

sinBlIF 45sin)20.1)(00.1)(50( TmAF

upwardNF ,4.42

sinBdlIdF

MAGNETIC FORCE ON A CONDUCTOR

BldIFd

For any conductor (straight or not), divide it into infinitesimal segments dl.

sinBdlIF

Example 3. Find the total magnetic force on a composite conductor carrying a current I (see figure below).

0 BlIF A

jILBBLIF B

semicircle portion (FC ):

BdlIdF

BRdIdF

cosBRdIdFx

sinBRdIdFy

0cos0

dRBIFx

0sin dRBIFy

IRBRBIFy 2)]0cos()cos[(

jIRBF C 2

jIRBjILBFFFF CBA 20

jRLIBF )2(

B is eastward.

(a)

x

(b)

MAGNETIC TORQUE Consider a wire loop carrying a current I inside a

uniform magnetic field of magnitude B.

BIL

W

axis

Fx

F

B

F

Ix

F

W/2 W/2

axis

Fr 22 WF

2)(2 WILB

MAGNETIC TORQUE

B

F

Ix

F

W/2 W/2

axis 2)(2 WILB

LWIB)(

BIA

If the current loop has N number of turns

NBIA

MAGNETIC TORQUE

BIAmax

When the magnetic field and the area vector are perpendicular, the magnetic torque is maximum.

B

F

Ix

F

W/2 W/2

A

B

F

I

x

F

A

sin2

W sinBIA

If the angle between the magnetic field and the area vector is , the magnetic torque is

MAGNETIC MOMENT

AI

The product IA is called the magnetic moment (which is a vector whose direction is that of the area vector).

sinB

B

B

F

I

x

F

sin2

W

Magnetic torque tends to rotate the loop in the direction of decreasing .

ELECTRIC MOTOR

ANSWER: 0.024 T, +y direction

ANSWERS: (a) 0.030 T, +j(b) 0.017 T, -j