Currents and Magnetism

• Textbook Sections 22-4 – 22-7

Physics 1161: PreLecture 13

Force of B-field on Current

+ v

• Force on 1 moving charge:– F = q v B sin()– Out of the page (RHR)

• Force on many moving charges:– F = (q/t)(vt)B sin()

= I L B sin()

– Out of the page!

v

L = vt

B

I = q/t+ + ++

Net force on loop is zero.

Look from here

But the net torque is not!

Torque on Current Loop in B field

A B

CD

B

I

XF

•F

A B

CD

F

F

The loop will spin in place!

Torque on loop is = 2 x (L/2) F sin() = ILWB sin()

Force on sections B-C and A-D: F = IBW

(length x width = area) LW = A !

Torque is = I A B sin()

W

L

A B

CD

B

I

XF

•F

Torque on Current Loop in B field

A B

CD

F

F

L/2 L/2

Torque tries to line up the normal with B!

(when normal lines up with B, =0, so =0! )

Even if the loop is not rectangular, as long as it is flat:

= I A B sin

(area of loop)

Magnitude:

= I A B sin

Direction:

N

# of loops

A

B

C

DB

normal

F

F

Torque on Current Loop

between normal and B

Currents Create B Fields

Lines of B

Here’s a current-carrying wire.

Current I OUT of page.

•

Right-Hand Rule, 2

Thumb: along IFingers: curl along B-field lines

r = distance from wire

0 410 7Tm/A

B

0I2r

r

Magnitude of B a distance r from (straight) wire:

B

Right Hand Rule 2

wire

I Fingers give B!

Force between current-carrying wires

•I towards us

B•

Another I towards usF

Conclusion: Currents in same direction attract!

•

I towards us B

Another I away from us

F

Conclusion: Currents in opposite direction repel!

Note: this is different from the Coulomb force between like or unlike charges.

Comparison:Electric Field vs. Magnetic Field

Electric MagneticSource Charges Moving ChargesActs on Charges Moving ChargesForce F = Eq F = q v B sin()Direction Parallel E Perpendicular to v,B

Field Lines

Opposites Charges Attract Currents Repel

Magnetic Fields of Currents

• http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfie.html#c1

B Field Inside SolenoidsMagnitude of Field anywhere inside of solenoid : B=0 n I

Right-Hand Rule 3 gives Direction:

Fingers – curl around solenoid in direction of I

Thumb - points in direction B ==

n is the number of turns of wire/meter on solenoid.

= 4 x10-7 T m /A

(Note: N is the total number of turns, n = N / L)

Magnetic field lines look like bar magnet!

Solenoid has N and S poles!

B Field Inside SolenoidsMagnitude of Field anywhere inside of solenoid : B=0 n I

Right-Hand Rule for loop/solenoid

Fingers – curl around coil in direction of conventional (+) current

Thumb - points in direction of B along axis

n is the number of turns of wire/meter on solenoid.

= 4 x10-7 T m /A

(Note: N is the total number of turns, n = N / L)

Magnetic field lines look like bar magnet!

Solenoid has N and S poles!