Currents and Magnetism

• Textbook Sections 22-4 – 22-7

Physics 1161: Lecture 11

Force of B-field on Current

+ vq

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

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

= I L B sin(q) – Out of the page!

v

L = vt

B

I = q/t+ + ++

force is zero

out of the page

into the page

B

I

L

F=ILBsin

Here = 0.

A 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?

CheckpointCurrent Loop in Magnetic Field 1

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 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

XF

CheckpointCurrent Loop in Magnetic Field 2

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!

CheckpointCurrent Loop in Magnetic Field 3 & 4

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

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

(length x width = area) LW = A !

Torque is t =

W

L

A B

CD

B

I

XF

• F

Torque on Current Loop in B field

A B

CD

F

F

f

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

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

(length x width = area) LW = A !

Torque is t = I A B sin(f)

W

L

A B

CD

B

I

XF

•F

Torque on Current Loop in B field

A B

CD

F

F

f

L/2 L/2

Torque tries to line up the normal with B!(when normal lines up with B, f=0, so t=0! )

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

t = I A B sinf.

(area of loop)

Magnitude:

t = I A B sinf

Direction:

N# of loops

A

B

C

DB

normal

f

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

33% 33%33%

1. t1 > t2

2. t1 = t2

3. t1 < t2

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

1 2 3

33% 33%33%

Area points out of page for both!

f = 90 degrees

t = I A B sinf1. t1 > t2

2. t1 = t2

3. t1 < t2

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

0I2 r

same

F qvBsinsame

•B

v

I

v(a)

r• •

r

(b)

FF

CheckpointCharge Moving Near Current

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(q)Direction Parallel E Perpendicular to v,B

Field Lines

Opposites Charges Attract Currents Repel

CheckpointSolenoid

A solenoid is wrapped with wire carrying a current, as shown in the figure. 

What is the direction of the magnetic field produced by the solenoid? a. into the right end of the solenoid and out of the left endb. out of the right end of the solenoid and into the left end

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=m0 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.

m0 = 4p 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 force between the two solenoids?

1 2 3

0% 0%0%

1. Attractive2. Zero 3. Repulsive

What is the 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.