Currents and Magnetism

• Textbook Sections 22-4 – 22-7

Physics 1161: Lecture 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+ + ++

force is zero out of the page into the page

B

IL

F=ILBsin

Here = 0.A B

CD

B

I

Preflight 13.1A rectangular loop of wire is carrying current as shown. There is a uniform magnetic field parallel to the sides A-B and C-D.

What is the direction of the force on section A-B of the wire? 45%

36%

18%

What is the direction of the force on section B-C of the wire?force is zero

out of the page into the page

A B

CD

B

I

XF

Preflight 13.2A rectangular loop of wire is carrying current as shown. There is a uniform magnetic field parallel to the sides A-B and C-D.

Palm into page.

v

F

B

9%

45%

45%

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!

Preflights 13.3, 13.4

91%

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

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

(length x width = area) LW = A !

Torque is =

W

LA B

CD

B

I

XF

• F

Torque on Current Loop in B field

A B

CD

F

F

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

LA 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

BC

D B

normal

F

F

Torque on Current Loop

between normal and B

Compare the torque on loop 1 and 2 which have identical area, and current.

1 2 3

0% 0%0%

1 1 > 2

2 1 = 2 3 1 < 2

Compare the torque on loop 1 and 2 which have identical area, and current.

1 2 3

0% 0%0%

Area points out of page for both! = 90 degrees

= I A B sin1 1 > 2

2 1 = 2 3 1 < 2

Currents Create B Fields

Lines of B

Current I OUT

•

Right-Hand Rule-2 Thumb: along IFingers: curl along B field lines

r = distance from wire

0 410 7Tm/A B

0I2r r

Magnitude:B

Right Hand Rule 2!

wire

I Fingers give

B!

θ is angle between v and B (θ = 90° in both cases)

A long straight wire is carrying current from left to right. Near the wire is a charge q with velocity v

Compare magnetic force on q in (a) vs. (b)(a) has the larger force (b) has the larger force force is the same for (a) and (b)

B 0I2rsame

F qvBsinsame

•Bv

I

v(a)

r• •

r(b)

FF

Preflight 13.6

27%

59%14%

Two long wires carry opposite current. What is the direction of the magnetic field above, and midway between the two wires carrying current – at the point marked “X”?

1 2 3 4 5

0% 0% 0%0%0%

1. Left 2. Right 3. Up 4. Down 5. Zero

x

x

Two long wires carry opposite current. What is the direction of the magnetic field above, and midway between the two wires carrying current – at the point marked “X”?

1 2 3 4 5

0% 0% 0%0%0%

1. Left 2. Right 3. Up 4. Down 5. Zero

x

x

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

Right Hand Rule 3Magnetic Field of Solenoid

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 (+) currentThumb - 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!

What is the direction of the magnetic field produced by these solenoids?

Right Hand Rule!

Preflight 13.8

(1)to the Right(2)to the Left

76%

24%

What is the net force between the two solenoids?

1 2 3

0% 0%0%

1. Attractive2. Zero 3. Repulsive

What is the net force between the two solenoids?

1 2 3

0% 0%0%

1. Attractive2. Zero 3. RepulsiveLook at field lines, opposites attract.Look at currents, same direction attract.