As You Come In…

• What hand do you use to determine the magnetic force on a current-carrying wire in a magnetic field?

Illustrating Magnetism

Image obtained from: http://www.met.reading.ac.uk/pplato2/h-flap/phys4_2f_5.png

• Magnetic field lines• Lines: the more lines per unit

area, the stronger the B field• Direction: drawn from N end

to S end• “Test magnet”– compass• Red: magnetic north• Blue: magnetic south

Illustrating Magnetism

• Magnetic field lines• Lines: the more lines per unit

area, the stronger the B field• Direction: drawn from N end

to S end• “Test magnet”– compass• Red: magnetic north• Blue: magnetic south

Image obtained from: http://cdn2.miniphysics.com/wp-content/uploads/2012/03/magnetic-field-lines.jpg

Illustrating Magnetism

• Magnetic field lines• Lines: the more lines per unit

area, the stronger the B field• Direction: drawn from N end

to S end• “Test magnet”– compass• Red: magnetic north• Blue: magnetic south

Image obtained from: http://upload.wikimedia.org/wikipedia/commons/5/57/Magnet0873.png

Illustrating Magnetism

• Magnetic field lines• Lines: the more lines per unit

area, the stronger the B field• Direction: drawn from N end

to S end• “Test magnet”– compass• Red: magnetic north• Blue: magnetic south

Image obtained from: http://www.school-for-champions.com/science/images/magnetic_detection__iron_filings.jpg

Illustrating Magnetism

Image obtained from: http://lpscience.fatcow.com/mgagnon/images/magphotos/Bfieldhorseshoe.jpg

• Magnetic field lines• Lines: the more lines per unit

area, the stronger the B field• Direction: drawn from N end

to S end• “Test magnet”– compass• Red: magnetic north• Blue: magnetic south

Parallel B lines between ends of horseshoe magnet

Illustrating Magnetism

Image obtained from: http://cdn.c.photoshelter.com/img-get/I0000NsAZUNtMmCM/s/860/860/Fphoto-02036612-0FPb.jpg

• Magnetic field lines• Lines: the more lines per unit

area, the stronger the B field• Direction: drawn from N end

to S end• “Test magnet”– compass• Red: magnetic north• Blue: magnetic south

Magnetic Field Lines—Solenoid

• Consider case of solenoid• Solenoid—series of loops in a

current-carrying wire• Circuit open—nothing happens• Circuit closed– magnetic field!

Image obtained from: http://onlinephys.com/magneticfield4.gif

Magnetic Field Lines—Solenoid

• Consider case of solenoid• Solenoid—series of loops in a

current-carrying wire• Circuit open—nothing happens• Circuit closed– magnetic field!

Image obtained from: http://onlinephys.com/magneticfield4.gif

N S

Magnetic Field Lines—Solenoid

• Consider case of solenoid• Solenoid—series of loops in a

current-carrying wire• Circuit open—nothing happens• Circuit closed– magnetic field!• Induced by current—moving

charge results in B field

Image obtained from: http://onlinephys.com/magneticfield4.gif

N S

Magnetic Field Lines—Solenoid

• Current through hoop/solenoid• Induced B field normal to plane

of current• Direction: right-hand rule• CCW current: outward B field• CW current: inward B field

I

I

⨡

⨡ B

⨡

As You Come In…

• What direction is the magnetic field in the hoop?I

⨡

Magnetic Field Lines—Solenoid

• Magnetic field inside solenoid/hoopB = μ0nI• B: magnetic field intensity (T)• μ0: permeability of free space–

1.26 × 10-6 Tm/A• n: number of loops per unit of

length (units: m-1 or 1/m)• I: current (A)

I

I

⨡

⨡ B

⨡

⨡ ⨡

• Current through length of wire• Induced B field normal to

current• Direction: right-hand rule• Outward (+z) current: CCW B

field• Inward (-z) current: CW B

field

Magnetic Field Lines—Wire

I

⨡

B

⨡

x

y

z

• Current through length of wire• Induced B field normal to

current• Direction: right-hand rule• Outward (+z) current: CCW B

field• Inward (-z) current: CW B

field

Magnetic Field Lines—Wire

I

⨡

B

⨡

x

y

z

Magnetic Field Lines—Wire

• Magnetic field decreases with increasing distance from wire• Magnetic field around wire:

B = • B: magnetic field intensity (T)• μ0: permeability of free space–

1.26 × 10-6 Tm/A• I: current (A)• r: distance from center of wire (m)

⨡

⨡

I

⨡

B

⨡

x

y

z

• Where does come from?• Magnetic field strength is equal

along entire surface of cylinder• Surface area of cylinder:

SA = l• In 2-D, this shape is the

circumference of a circleC =

Magnetic Field Lines—Wire

I

⨡

B

⨡

x

y

z

dl

Magnetic Force Between Wires

• Consider case of extremely long wires with current running through each• Each wire induces a magnetic

field• Magnetic fields apply force to

current-carrying wires• Recall: FB = lI × B for current-

carrying wires

⨡ ⨡ ⨡

I1

⨡I2

⨡

B1⨡

B2

⨡

Magnetic Force Between Wires

• Magnetic force on wire 2 by wire 1:FB2 = lI2 × B1

• Magnetic field induced by I1:B1 =

• Magnetic force becomes:FB2 = lI2 ×

⨡ ⨡ ⨡

I1

⨡I2

⨡

B1⨡

B2

⨡

⨡

⨡

⨡ ⨡

⨡

Magnetic Force Between Wires

• What is direction of B1 when it touches I2?

I1

⨡I2

⨡

B1⨡

B2

⨡

Magnetic Force Between Wires

• What is direction of B1 when it touches I2?• Inward (-z-direction)• Perpendicular to I2

• This means δ = 90°• Magnitude of FB2:

FB2 = l• For every 1 m of wire,

FB2 =

I1

⨡I2

⨡

B1

⨡

Magnetic Force Between Wires

• Direction of FB2:• pointing up (+y)• B pointing in (-z)• FB points left (-x) according to

right-hand rule• Thus, for every 1 m of wire,

FB2 = towards I1

⨡I2

⨡

B1

⨡

×

⨡

Homework Assignment

• Determine FB1 for the example we have been using

I1

⨡I2

⨡

⨡

B1 B2