1. Today’s Concept: What Causes Magnetic Fields
Physics 2112 Unit 14
Today’s Concept:
What Causes Magnetic Fields

2. Compare to Electric Fields
v out of the screen
In the same direction as r12
Perpendicular to r12

3. B field from one moving charge
Biot-Savart Law
B field from one moving charge
But remember from previous slides
B field from tiny of current carrying wire.

4. Example 14.1 (Infinite wire of current)
What is the magnetic field a distance yo away from a infinitely long wire of current I?
Conceptual Plan
Use Biot-Savart Law
Strategic Analysis
Done in prelecture in detail
Integrate
(Similar to E field for infinite line of charge)
Direction:
Thumb: on I
Fingers: curl in direction of B

5. Main Idea Q f

6. Example 14.1 (answer)
Magnitude: B
Current I OUT r •
Remember:

7. Example 14.2 (B field from hexagon)
A current, I, flows clockwise through a hexagonal loop of wire. The perpendicular distance between each side and the center of the loop is b.
What is the magnetic field in the center of the loop? b Q f

8. Example 14.3 (From Loop)
A current, I, flows clockwise through a circular loop of wire. The loop has a radius a.
What is the magnetic field at a point P a distance yo above the plane of the loop in the center? P yo a x Q
BcosQ Q

9. Force Between Current-Carrying Wires I1
X X X X X X X X X X X X X X X X X X X
X X X X X X X X X X X X X
X X X X X X X X X X X X
X X X X X X X X X X F I2
Maybe circle muI1/2pid as B?

10. Force Between Current-Carrying Wires
I towards us d B • •
Another I towards us F
Conclusion: Currents in same direction attract! •
I towards us B d F 
Another I away from us
Maybe circle muI1/2pid as B?
Conclusion: Currents in opposite direction repel!

11. Example 14.4 (Two Current Carrying Wires)
50cm
I2 = 10A
10cm
I1 = 5A
Two current carrying wires a 10cm apart for a length for 50cm. Wire 1 carries 5A and Wire 2 carries 10A with both current to the left.
What is the magnitude and direction of the force on wire 2 due to wire 1?
Draw B and F arrows

12. CheckPoint 1A X B F
What is the direction of the force on wire 2 due to wire 1?
A) Up B) Down C) Into Screen D) Out of screen E) Zero
Draw B and F arrows

13. CheckPoint 1B
What is the direction of the torque on wire 2 due to wire 1?
A) Up B) Down C) Into Screen D) Out of screen E) Zero
Draw B and F arrows
Uniform force at every segment of wire
No torque about any axis

14. What is the direction of the force on wire 2 due to wire 1?
CheckPoint 3A
What is the direction of the force on wire 2 due to wire 1?
Up B) Down C) Into Screen
D) Out of screen E) Zero

15. What is the direction of the torque on wire 2 due to wire 1?
CheckPoint 3B
What is the direction of the torque on wire 2 due to wire 1?
Up B) Down C) Into Screen
D) Out of screen E) Zero
LET’S DRAW A PICTURE!

16. Checkpoint 2: Force on a loop
A current carrying loop of width a and length b is placed near a current carrying wire.
How does the net force on the loop compare to the net force on a single wire segment of length a carrying the same amount of current placed at the same distance from the wire?
the forces are in opposite directions
the net forces are the same.
the net force on the loop is greater than the net force on the wire segment
the net force on the loop is smaller than the net force on the wire segment
there is no net force on the loop

17. Checkpoint question
Current flows in a loop as shown in the diagram at the right. The direction is such that someone standing at point a and looking toward point b would see the current flow clockwise.
What is the orientation of the magnetic field produced by the loop at points a and b on the axis?
(A)
(B)
(C)
(D)

18. B on axis from Current Loop.. I
Resulting B Field
Current in Wire

19. Biot-Savart Works, but need to do numerically
What about Off-Axis ?
Biot-Savart Works, but need to do numerically
See Simulation!

20. Two Current Loops
Two identical loops are hung next to each other. Current flows in the same direction in both.
The loops will:
Attract each other B) Repel each other
C) There is no force between them N S
2) Look like bar magnets
Two ways to see this:
1) Like currents attract

21. Right Hand Rule Review 1. ANY CROSS PRODUCT
2. Direction of Magnetic Moment
Thumb: Magnetic Moment
Fingers: Current in Loop
3. Direction of Magnetic Field from Wire
Thumb: Current
Fingers: Magnetic Field

22. Example 14.2 y y
Two parallel horizontal wires are located in the vertical (x,y) plane as shown. Each wire carries a current of I = 1A flowing in the directions shown.
What is the B field at point P?
I1 = 1A .
4cm
3cm x z
4cm P
I2 = 1A
Front view
Side view
Conceptual Analysis
Each wire creates a magnetic field at P
B from infinite wire: B = m0I / 2pr
Total magnetic field at P obtained from superposition
The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class.
Strategic Analysis
Calculate B at P from each wire separately
Total B = vector sum of individual B fields

23. If I = 6A, what is the magnitude of the magnetic field at point P?
Example 14.5 (Curved Loop of Wire)
If I = 6A, what is the magnitude of the magnetic field at point P?
20cm
12cm P
Conceptual Plan
Use Biot-Savart Law
Strategic Analysis
Integrate both loops
Note straight sections cancel out.
0 of 250 39

24. Remember how we used Gauss’ Law to avoid doing integral in E field?
Good News!!!!!
Remember how we used Gauss’ Law to avoid doing integral in E field?
We got similar law for B fields!