1. Currents and Magnetism
Physics 102: Lecture 09
Currents and Magnetism 1

2. Summary of Today Last time: Today: Magnetic forces on moving charge
magnitude F=qvBsin()
direction: right-hand-rule
Today:
Magnetic forces on currents and current loops
Magnetic fields due to currents
long straight wire
solenoid

3. Force of B-field on Current
Force on 1 moving charge:
F = q v B sin(q)
Out of the page (RHR) q v +
Force on many moving charges:
F = q v B sin(q)
= (q/t) (vt) B sin(q)
= I L B sin(q)
Out of the page! v
L = vt B
I = q/t +
Use large right hand. Then do demo 184.

5. Preflight 9.1
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. a b c d B I
Demo 253 Prop for forces on loop
What is the direction of the force on section A-B of the wire?

6. Preflight 9.2
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. a b c d B I X F
What is the direction of the force on section B-C of the wire?

7. Force on Loop
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. B I L 
F=IBLsin a b c d B I
Here  = 180º I B
Force on C-D is Zero!
same as for A-B!

9. ACT/Force on Loop (cont’d)
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. a b c d B I • F
(a) force is zero
(b) out of the page
(c) into the page

10. Torque on Current Loop in B fielda b c d B I X F • a b c d F
Look from here
The loop will spin in place!
82% got that the net force was zero, but then some thought it wouldn’t move. Could be confusion about move vs spin.
Demo 68: Big orange magnet and flip coil
Preflights 9.3, 9.4
Net force on loop is zero.
But the net torque is not!
“As long as the net force on the loop is zero, there is no reason for the loop to move.”

11. Torque on Current Loop in B fieldW L a b c d B I X F • a b c d F f
Force on sections B-C and A-D: F = IBW
Torque on loop is t = L F sin(f) = ILWB sin(f)
(length x width = area) LW = A !
 Torque is t = I A B sin(f)

13. ACT: Torque on Current Loop
What is the torque on the loop below?
t < IAB
t = IAB
t > IAB
x x x x x x x x x x x x x x x x 16

14. Torque on Current Loop N t = I A B sinf Direction: normal Magnitude: f
between normal and B
Direction:
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. N
(area of loop)
# of loops

15. ACT: Torque B B I
(2) I
(1)
Compare the torque on loop 1 and 2 which have identical area, and current.
1) t1 > t ) t1 = t2 3) t1 < t2

17. Currents Create B Fields
Magnitude:
Lines of B B
Current I OUT • r
r = distance from wire
Right-Hand Rule, part deux!
Thumb: on I
Fingers: position you want to know B at
Palm: gives B

18. Fingers give B! Right Hand Rule Part 2! I wire

19. ACT/Preflight 9.6
A long straight wire is carrying current from left to right. Near the wire is a charge q with velocity v v I
(a) r •
(b) F
Compare magnetic force on q in (a) vs. (b)
a) has the larger force b) has the larger force c) force is the same for (a) and (b)
Hint: think about magnitude and direction of magnetic field in each case.

21. ACT: Adding Magnetic Fields
Two long wires carry opposite current B x x
What is the direction of the magnetic field above, and midway between the two wires carrying current – at the point marked “X”?
1) Left 2) Right 3) Up 4) Down 5) Zero

22. Force between current-carrying wires
I towards us B • •
Another I towards us F
Conclusion: Currents in same direction attract! •
I towards us B F 
Another I away from us
Demo 740: force between two wires
Conclusion: Currents in opposite direction repel!

23. Comparison: Electric Field vs. Magnetic Field
Electric Magnetic
Source Charges Moving Charges
Acts on Charges Moving Charges
Force F = Eq F = q v B sin(q)
Direction Parallel E Perpendicular to v,B
Field Lines
Opposites Charges Attract Currents Repel

25. ACT: Force between Wires
What is the direction of the force on the top wire, due to the two below?
1) Left 2) Right 3) Up 4) Down 5) Zero

26. B Field Inside Solenoids
Magnitude of Field anywhere inside of solenoid : B=m0 n I
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)
Another Right-Hand Rule gives Direction:
Curl fingers in direction of current
Thumb point in direction of B
Demo 183: overhead and iron filings w/solenoid
Magnetic field lines look like bar magnet!
Solenoid has N and S poles!

27. ACT: The force between the two solenoids is …
(1) Attractive
(2) Zero
(3) Repulsive