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
I
L
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? 49%
36%
15%
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
13%
38%
50%
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
78%
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
L
A 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
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
Compare the torques on loops 1 and 2 which have identical areas and currents.
1 2 3
0% 0%0%
1 1 > 2
2 1 = 2
3 1 < 2
Compare the torques on loops 1 and 2 which have identical areas and currents.
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
0I2r
same
F qvBsinsame
•B
v
I
v(a)
r• •
r
(b)
FF
Preflight 13.6
28%
55%18%
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 (+) 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!
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
65%
35%
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.
Top Related