1. Announcements Quiz III: Thursday Quiz IV: April 21st
Final Exam: May 2cd 9am
Office Hrs 2-3pm today

2. Announcements TITLE: Fusion: Protein Machines and Lipid Materials
SPEAKER: Professor Barry R. Lentz,
Director, Program in Molecular and Cellular Biophysics University of North Carolina at Chapel Hill
TIME: Thursday Mar. 31, 2005 at 4 PM
PLACE: George P. Williams, Jr. Lecture Hall, (Olin 101)

3. Torque on a Loop: Simple
Force on left side is out of the plane
Force on right side is into the plane
Magnetic Field B a I b
Force on top and bottom is zero
There is a net torque on the loop

4. Quiz

5. Torque on a Loop: Rules
Define the area vector of a loop as a vector of length A perpendicular to the loop {we’ve done this before}
The direction of the vector is determined by right-hand-rule based on current direction
Direction of torque can be worked out using cross-product I
Magnitude of torque as well
Torque causes the loop to rotate so that the normal vector is parallel to the field I

6. Potential Energy of a Loop
When you rotate a loop in a magnetic field, the loop is doing work
Since it is doing work, the energy is changing
Integrate to get potential energy
Loop likes to align itself with magnetic field

7. Multiloops If there are N loops basically all identical, multiply by N
All the properties of the wire are summarized in the magnetic dipole moment of the wire
Units of Am2 = J/T

8. Summary of Loops
All the properties of the wire (current loops) are summarized in the magnetic dipole moment of the wire
Units of Am2 = J/T
Loop likes to align itself with magnetic field
B = 1 T
I = 1A

9. Currents make Magnetic Fields
Magnetic Field B
Current I
Magnetic Fields are created by electric currents
They are perpendicular to both the direction of the current and the separation between the wire and the point
Falls off with distance from wire
Current I P
Magnetic Field B
Direction of magnetic field is given by right-hand rule

10. The Biot-Savart Law
Must add up, i.e. integrate, the contribution from the entire current distribution. Remember: the magnetic field is a vector field, and it has a sign.
Magnetic Field B ds
Current I

11. Biot-Savart Law: Applied
In what direction is the magnetic field produced?
Right hand rule!
Remember: Electrons flow in the opposite direction of current.

12. Magnetic Field from a straight wire segment P a
x = x2
x = x1
Current I

13. Magnetic Field from a straight wire segmentP a 2 1
Current I
Infinite straight wire

14. Magnetic force between wires
At least one wire is long (L)
compared to the separation (a) .
Attractive if currents are parallel
Repulsive if the currents are anti-parallel

15. Magnetic force between wires
If I1 = 2A and I2=6A, then which is true of the forces?
F1=3F2
F1=F2/3
F1=F2

16. Quiz Remains the same Reverses Changes in magnitude but not direction
Changes to some other direction

17. Quiz
P, Q, R
Q, R, P
P, R, Q
Q, P, R

18. Magnetic field between wires
In between one must add the fields from each wire, with the correct
direction vector .

19. Application I2 I1 At least one wire is long (L)
compared to the separation (a) .
Attractive if currents are parallel
Repulsive if the currents are anti-parallel

20. Magnetic Field Integrated around a wire
Current I out of the plane
What is the integral of the magnetic field around wire on the path drawn?