1. Today’s Concept: Ampere’s Law
Physics 2112 Unit 15
Today’s Concept:
Ampere’s Law

2. Ampere’s Law We know for an infinite current carrying wire
But what is 2pR? Circumference of circle!

3. Current enclosed by that closed loop
Ampere’s Law
Any closed loop
Current enclosed by that closed loop

4. Checkpoint 1A
Two loops are placed near identical current carrying wires as shown in Case 1 and Case 2 below.
For which loop is ∫B·dl greater?
Case 1
Case 2
The integral is the same for both

5. Checkpoint 1B
Two loops are placed near identical current carrying wires as shown in Case 1 and Case 2 below.
For which loop is ∫B·dl greater?
Case 1
Case 2
The integral is the same for both

6. Checkpoint 1C
Two loops are placed near current carrying wires as shown in Case 1 and Case 2 below. In both cases the direction of the current in the two wires are opposite to each other.
For which loop is ∫B·dl greater?
Case 1
Case 2
The integral is the same for both

7. Example 15.1 (B field from a thick wire)
A wire with a radius of r=1cm has a uniform current of 1A flowing through it.
What is the B field 1 meter from the center of the wire?
What is the B field 0.5cm from the center of the wire?

8. Example 15.1 (graph) X
X X X
X X X X X
A wire with a radius of r=1cm has a uniform current of 1A flowing through it. B r

9. CheckPoint 2A
An infinitely long hollow conducting tube carries current I in the direction shown. X
What is the direction of the magnetic field inside the tube?
clockwise
counterclockwise
radially inward to the center
radially outward from the center
the magnetic field is zero

10. Why is that? X X

11. Example 15.3 (Pipe of current)y
An infinitely long cylindrical shell carries a uniformly distributed current of 5A out of the screen. The inner radius is a=4cm and outer radius=8cm
What is B at r = 2cm?
What is B at r = 6cm?
What is B at r = 16cm? I a x b
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.

12. Example 15.3 (Pipe of current)
Conceptual Analysis
Complete cylindrical symmetry (can only depend on r)  can use Ampere’s law to calculate B
Strategic Analysis
Calculate B for the three regions separately:
1) r < a
2) a < r < b
3) r > b
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.
For circular path concentric with shell.

13. Example 15.2 (Two thick wires)
Two thick cables both of radius R and length L carry a current, I, side-by-side as shown to the left. The left cable has the current into the screen and the right cable has the current out of the screen.
A B X C D
What is the magnetic field at points A, B, C and D?
- A is at the center of the left cable
- B is a distance R/2 from the center of the left cable
- C is at the point where the cables touch.
- D is the bottom of the left cable

14. The Plan What is the magnetic field at points A, B, C and D?X C D
Conceptual Analysis
use Ampere’s law to calculate B from each cable separately
Strategic Analysis
Note direction of B from each cable at each point.
Add B like vectors

15. Sign of the dot product
I into screen

16. Ampere’s Law dl B dl B dl B

17. Sign of the dot product dl B dl B dl B

18. Sign of the dot product dl B dl B dl B

19. B Field in Solenoid
~cancel out X X X X . . . .
add up

20. . . . . . . . . B Field in Solenoid X X L n = turns per unit length
(Ideal Solenoid L>>>r)

21. Solenoid   Bar Magnet

22. CheckPoint 2B
A current carrying wire is wrapped around cardboard tube as shown below.
In which direction does the magnetic field point inside the tube?
left
right up
down
out of the screen
into the screen

23. Example 15.3 (B from Solenoid)
A long thin solenoid consists of 500 turns of wire carrying 1.5A. It has a length of 250cm and a radius of 1cm.
What is the magnetic field in the exact center of the coil?
What is the contribution to this field from the 250th coil (the center coil)?

24. . . . . . . . . Make Sense? Note: B250/Btot = 0.024 (1/500 = 0.002)X X . . . . . . . .
Note:
B250/Btot = (1/500 = 0.002)
So closest coil contributes over 10 tens more than average coil. Make sense?

25. When does “Loop”  “Solenoid”?

26. A hint…..