Physics 213 General Physics

1. 0 Physics 213General Physics Lecture 10

2. Last Meeting: Lorentz Force and Torque Today: Review Torque, Magnetic Field of Conductors and Currents, Ampere’s Law, Solenoid, and Magnetic Materials

4. q *Important: This q is not the same as in the previous slide. q is now the angle between the radius vector and the force vector. θ θ ┴

5. Torque on a Current Loop,The Standard Convention • Applies to any shape loop • N is the number of turns in the coil • Torque has a maximum value of NBIA • When q = 90° • Torque is zero when the field is perpendicular to the plane of the loop

6. Determining Magnetic Moments and Torques for a Current Loop • Directions are always determined with right-hand rule. • Magnitudes are given by I

7. μ = ┴ θ μ θ μ

8. Motors

9. Review μ

10. I (B) (C) It will not rotate. (A)

11. I (B) (C) It will not rotate. (A)

12. Reverse the current and field. I (B) (C) It will not rotate. (A)

13. Reverse the current and field. • CW • CCW • It will not rotate CCW

14. Magnetic Fields – Long Straight Wire • A current-carrying wire produces a magnetic field • The compass needle deflects in directions tangent to the circle • The compass needle points in the direction of the magnetic field produced by the current

15. Direction of the Field of a Long Straight Wire • Right Hand Rule • Grasp the wire in your right hand • Point your thumb in the direction of the current • Your fingers will curl in the direction of the field

16. Magnitude of the Field of a Long Straight Wire • The magnitude of the field at a distance r from a wire carrying a current of I is • µo = 4  x 10-7 T.m / A • µo is called the permeability of free space

17. Ampère’s Law, and Field from Currents • Choose an arbitrary closed path around the current • Sum all the products of B|| Δℓ around the closed path • B|| Δℓ = µo I

18. Ampère’s Law to Find B for a Long Straight Wire • Use a closed circular path • The circumference of the circle is 2  r • This is identical to the result previously obtained

19. Magnetic Force Between Two Parallel Conductors • The force on wire 1 is due to the current in wire 1 and the magnetic field produced by wire 2 • The force per unit length is:

20. Magnetic Force Between Two Parallel Conductors, Derived • The force on wire 1 F1 = I1 B ℓ sin θ • B produced by wire 2 • sinq=1, so

21. Force Between Two Conductors, cont • Parallel conductors carrying currents in the same direction attract each other • Parallel conductors carrying currents in the opposite directions repel each other • Demo of two current-carrying wires attracting/repelling.

23. Circular current loops act like Magnetics, with a N and S pole.

30. Magnetic Materials

31. Demo • Magnetic materials.

32. Types of Magnetic Materials • Ferromagnetic • Permanent magnetic moments. Repel or attract depending on orientation • Paramagnetic • Induced magnetism in same direction as applied field. Materials are attracted to magnets. • Diamagnetic • Induced magnetism in opposite direction as applied field. Materials are repelled. S S S S S S S S N N N N N N N N S N N S

33. Magnetic Effects of Electrons – Spins • Electrons also have spin • The classical model is to consider the electrons to spin like tops • It is actually a quantum effect

34. Ferromagnetic Domains • Random alignment (left) shows an unmagnetized material • When an external field is applied, the domains aligned with B grow (right) • Each domain acts like a little magnet with a N and S pole. Arrows below represent the magnetic moment. S N

35. A loop of wire with a weight of 1.47 N is oriented vertically and carries a current I = 1.75 A. A segment of the wire passes through a magnetic field directed into the plane of the page as shown. The net force on the wire is measured using a balance and found to be zero. What is the magnitude of the magnetic field? (a) zero tesla (d) 1.5 T (b) 0.51 T (e) 4.2 T (c) 0.84 T X The magnetic force is pointing upwards and cancels the gravitational force:

36. Two long, straight, parallel wires separated by a distance d carry currents in opposite directions as shown in the figure. The bottom wire carries a current of 6.0 A. Point C is at the midpoint between the wires and point O is a distance 0.50d below the 6-A wire as suggested in the figure. The total magnetic field at point O is zero tesla. 1. Determine the value of the current, I, in the top wire. (a) 2 A (c) 6 A (e) This cannot be determined since (b) 3 A (d) 18 Athe value of d is not specified. X 2. Determine the magnitude of the magnetic field at point C if d = 0.10 m. (a) 2.4x10–5 T (c) 9.6x10–5 T(e) 1.4x10–4 T (b) 4.8x10–5 T (d) 1.1x10–4 T X

37. Quiz θ

38. θ