### Document

```Physics 1161: Lecture 13
Currents and Magnetism
• Textbook Sections 22-4 – 22-7
Force of B-field on Current
• 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)
v
q
B
+ + + +v
– Out of the page!
L = vt
I = q/t
Preflight 13.1
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.
B
C
D
q
B
A
I
B
I
F=ILBsinq
Here q = 0.
What is the direction of the force on section A-B of the wire?
force is zero
49%
out of the page 36%
into the page
15%
Preflight 13.2
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.
v
C
D
F
X
I
A
B
B
B
Palm into page.
F
What is the direction of the force on section B-C of the wire?
force is zero
13%
out of the page 38%
into the page
50%
Torque on Current Loop in B field
C
D
•
F
F
X
B
I
A
F
A
B
C
D
B
F
The loop will spin in place!
Look from here
Preflights 13.3, 13.4
Net force on loop is zero. But the net torque is not!
78%
Torque on Current Loop in B field
C
D
•
F
F
F
X
B
W
A
f
A
I
B
L
Force on sections B-C and A-D: F =
Torque on loop is t = 2 x (L/2) F sin(f) =
(length x width = area)
 Torque is
t=
LW = A !
C
D
B
F
Torque on Current Loop in B field
C
D
•
F
F
X
B
W
A
F
f
A
I
B
B
L
C
D
L/2
L/2
Force on sections B-C and A-D: F = IBW
Torque on loop is t = 2 x (L/2) F sin(f) = ILWB sin(f)
(length x width = area)
 Torque is
t = I A B sin(f)
LW = A !
F
Torque on Current Loop
Magnitude:
F
t = I A B sinf
between normal and B
Direction:
f
B
F
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 = N I A B sinf.
# of loops
(area of loop)
Compare the torques on loops 1 and 2 which
have identical areas and currents.
1. t1 > t2
2. t1 = t2
3. t1 < t2
0%
1
0%
2
0%
3
Compare the torques on loops 1 and 2 which
have identical areas and currents.
1. t1 > t2
2. t1 = t2
3. t1 < t2
t = I A B sinf
Area points out
of page for both!
f = 90 degrees
0%
1
0%
2
0%
3
Currents Create B Fields
Magnitude:
0I
B
2r
B
0  4   10 7 Tm / A
Current I OUT
r
•
r = distance from wire
Right-Hand Rule-2
Thumb: along I
Fingers: curl along B field lines
Lines of B
Right Hand Rule 2!
I
wire
Fingers
give
B!
Preflight 13.6
A long straight wire is carrying current from left to
right. Near the wire is a charge q with velocity v
v
v
•
(a)
F
r
B
•
(b)
•
F
I
r
Compare magnetic force on q in (a) vs. (b)
(a) has the larger force 28%
(b) has the larger force 55%
force is the same for (a) and (b)
0I
same B 
2r
same F  qvB sin q
18%
θ is angle between v and B
(θ = 90° in both cases)
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”?
x
1.
2.
3.
4.
5.
Left
Right
Up
Down
Zero
x
0%
1
0%
0%
2
3
0%
0%
4
5
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
B
marked “X”?
x
1.
2.
3.
4.
5.
Left
Right
Up
Down
Zero
x
0%
1
0%
0%
2
3
0%
0%
4
5
Force between current-carrying wires
I towards
us
•
F
B
•
Another I towards us
Conclusion: Currents in same direction attract!
I towards
us
•
B
 F
Another I away from us
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
Source
Acts on
Force
Direction
Electric
Magnetic
Charges
Charges
F = Eq
Parallel E
Moving Charges
Moving Charges
F = q v B sin(q)
Perpendicular to v,B
Charges Attract
Currents Repel
Field Lines
Opposites
Magnetic Fields of Currents
• http://hyperphysics.phyastr.gsu.edu/hbase/magnetic/magfie.html#c1
Right Hand Rule 3
Magnetic Field of Solenoid
B Field Inside Solenoids
Magnitude of Field anywhere inside of solenoid :
n is the number of turns of
wire/meter on solenoid.
0 = 4 x10-7 T m /A
(Note: N is the total number of turns, n = N / L)
Right-Hand Rule for loop/solenoid
Fingers – curl around coil in direction of
conventional (+) current
Thumb - points in direction of B along
axis
Magnetic field lines look like bar magnet!
Solenoid has N and S poles!
B=0 n I
Preflight 13.8
What is the direction of the magnetic field produced
by these solenoids?
(1) to the Right
(2) to the Left
65%
35%
Right Hand Rule!
What is the net force between the two
solenoids?
1. Attractive
2. Zero
3. Repulsive
0%
1
0%
2
0%
3
What is the net force between the two
solenoids?
0%
1
1. Attractive
2. Zero
3. Repulsive
Look at field lines, opposites attract.
Look at currents, same direction attract.
0%
2
0%
3
```