Magnetism

1. Magnetism AP Physics B Chapter 20 Notes

2. Magnets and Magnetic Fields--Basics Magnets are dipoles, meaning they have a north and south and can never be isolated Opposite poles attract Like poles repel Magnets create magnetic fields

3. Magnets and Magnetic Fields--Basics Magnetic fields are three dimensional and can be depicted by field lines Field lines are continuous and leave the north and travel to south Similar to E field lines—need magnitude and direction (vector with symbol B)

4. Earth’s Magnetic Field and Compasses The Earth’s magnetic field is similar to a bar magnet Geographic north is magnetic south—but not exactly (angle of declination) Not all field lines are parallel to the Earth’s surface (angle of dip) A compass is a magnet free to rotate—aligns with Earth’s magnetic field

5. Uniform Magnetic Fields Most magnetic fields are not uniform (constant in magnitude and direction) A uniform field can be made between two wide faces placed close together relative to the width

6. Electric Currents and Magnetic Fields Oersted first discovered that an electric current produces a magnetic field (use a compass like a test charge in mapping an E field) The direction of the field is found using the first Right Hand Rule: You point your thumb in direction of conventional current flow and your fingers point in the direction of magnetic field (B) RHR—1

7. Electric Currents and Magnetic Fields Wires do not have to be straight…magnetic fields in a coiled wire will always go in the same direction on the inside of the coil (into the page here) and the outside of the coil (out of the page here) B I

8. Force on a Current in Magnetic Field When a current carrying wire is put into a fixed magnetic field it experiences a force (two magnetic fields interact) The direction of the force is found by the second right hand rule: Fingers in direction of I, palm B and thumb F.

9. Force on a Current in Magnetic Field An alternative RHR-2 is to point fingers in direction of B, use thumb for I (as in RHR-1) and then palm faces direction of F Here the wire if pushed to the right. This is for conventional current flow (+ charge). Reverse for negative charge!

10. Force on a Current in Magnetic Field Experimentally the force acting on a current carrying wire in a magnetic field was found to directly vary with the length of wire (L ), size of magnetic field (B ), current (I ) and the angle the wire makes with B: F=ILBsinθ Note: Maximum force occurs when the wire and magnetic field are at right angles

11. Force on a Current in Magnetic Field Rearrange to get B defined (for maximum F) B=F/(IL) Units for B: Tesla 1 T = 1 N/Am Sometimes see Gauss: 1 G = 10-4 T

12. Notes on Drawing Convention Notes on convention: For vectors coming out of the paper, a dot is used (represents the tip of an arrow coming at you) For vectors going into paper, a X is used (represents the tail of an arrow going away from you)

13. Sample Problem A 36-m length wire carries a current of 22A running from right to left. Calculate the magnitude and direction of the magnetic force acting on the wire if it is placed in a magnetic field with a magnitude of 0.50 x10-4 T and directed up the page.

14. More Complicated Sample Problem The voice coil of a speaker has a diameter of 0.025 m, contains 55 turns of wire, and is placed in a 0.10-T magnetic field. The current in the voice coil is 2.0 A. Determine the magnetic force that acts on the coil and the cone.

15. Force on a Moving Charge in B Current represents charge flow, so it follows that a charge moving in a magnetic field will also experience a force—as long as a component of its velocity acts perpendicular to B. F = 0 F = Fmax 0<F<Fmax

16. Force on a Moving Charge in B You use the same RHR to determine direction of the force—with your thumb pointing in the direction of positive charge flow

17. Force on a Moving Charge in B To quantify the F, if N charges of q pass a point in a given time, I=Nq/t. If t is the time it takes a charge q to travel distance L, then L=vt, using F=ILBsinΘ, F=qvBsinΘ Note: Again Fmax=qvB

18. Example Problem A proton in a particle accelerator has a speed of 5.0x106 m/s. The proton encounters a magnetic field whose magnitude is 0.40 T and whose direction makes and angle of 30.0 degrees with respect to the proton’s velocity. Find (a) the magnitude and direction of the force on the proton and (b) the acceleration of the proton. (c) What would be the force and acceleration if the particle were an electron?

19. Force on a Moving Charge in B Suppose an electron moving at v enters a magnetic field acting out of the page, find the direction of the force acting on it at point 1: Down Now it changes direction, at point 2 find F: Left e-v 1 2 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 Again it changes direction, at point 3 find F: Up So a charge moving in a uniform B travels in a circular motion 3

20. Force on a Moving Charge in B If two charges start at the origin of the defined axis system, they will move in circles: FB=FC=m(v2/r)

21. Force on a Moving Charge in B Handy tricks to remember: • Charges entering a magnetic field will tend to move in a circular path of FB=FC or qvB = m(v2/r) or r = (mv)/qB • FB may need to equal other forces, e.g., FG or any other ma. • Draw a picture to help you visualize what is happening.

22. Force on a Moving Charge in B A singly charged positive ion has a mass of 2.5 x 10-26 kg. After being accelerated through a potential difference of 250 V, the ion enters a magnetic field of 0.5 T, in a direction perpendicular to the field. Calculate the radius of the path of the ion in the field.

23. Magnetic Field Around I-Carrying Wire B I B 1/2πr Permeability of free space

24. Magnetic Field Around I-Carrying Wire The long straight wire carries a current of 3.0 A. A particle has a charge of+6.5x10-6 C and is moving parallel to the wire at a distance of 0.050 m. The speed of the particle is 280 m/s. Determine the magnitude and direction of the magnetic force on the particle.

25. Magnetic Field Around I-Carrying Wire Consider the interaction of two current carrying wires. F21= I2LB21sin θ where B21 = μ0I1/(2πr) is the B-field at 2 from 1 F21= I2L{μ0I1/(2πr)}sin θ= I1L{μ0I2/(2πr)}sin θ= F12,the force on 1 by 2 Currents Opposite Currents Same

26. Domains and Magnetism Magnets are made up of tiny regions called domains (collection of atoms whose electron spins are organized so that there is a magnetic effect) In non-magnetic materials, domains are arranged randomly so the magnetic effect is canceled. When arranged in the same direction, a material is magnetic. It can be made so by putting it in the presence of a strong magnet.

27. Applications—Electric Motor Consider a loop of wire carrying a current in a fixed magnetic field. The two sides of the loop will experience equal magnitude forces by acting in opposite directions—creating torque.

28. Applications—Electric Motor Torque will cause the loop to rotate until it is normal to the magnetic field.

29. Applications—Electric Motor Basic components of a DC motor Split Ring Commutator

30. Applications—Electric Motor When current is flowing, When current is cut, inertia torque rotates the coil. keeps the coil rotating.

31. Applications—Mass Spectrometer A mass spectrometer measures the mass to charge ratio of atoms and is used to identify unknown atoms and their concentrations. Use knowledge of F caused by E and B and can determine m and therefore identity of sample. Accelerate with E field to v Count the number of ions hitting. Ionize sample to +1e