1. Chapter 19 Magnetic Force on Wires Solenoids Mass Spectrometers

3. The magnetic field around a very long, current carrying wire is given by: The magnetic field is a vector quantity, so it has a direction!!!! Where the constant of proportionality is known as the permeability of free space and is found to be

4. I Wrap your hand around the wire with your thumb pointed in the direction of the current. Your fingers curl around the wire in the direction the magnetic field points.

5.  = 90 o If the wires are parallel, the magnetic field from one wire will be perpendicular to the direction of the current in the other wire. I1I1 I2I2 d If we have two very long, current carrying wires parallel to one another, what force do they feel?

6. I1I1 I2I2 d 1 2

7. In what direction does the force act??? Using the right hand rule, we determine that the magnetic field from wire 1 at the location of wire 2…. Is into the page! Now, using the OTHER right hand rule (the one for magnetic force on a current carrying wire in a magnetic field), we find that the direction of the force on wire 2... Is UP toward wire 1! I1I1 I2I2 r 1 2

8. I1I1 I2I2 r 1 2 Parallel wires carrying current in the OPPOSITE direction are repelled from one another. Parallel wires carrying current in the SAME direction are attracted to one another. You might be able to guess…

10. But what if the wire isn’t a very long, straight wire? What if it’s a loop of wire instead? We won’t go into the details of the magnetic field created by a single loop, but this is what it looks like --- a lot like the field of a bar magnet!

11. However, we will look at the magnetic field created by a whole bunch of such loops combined…AKA

12. Solenoids produce fairly uniform magnetic fields inside their boundaries, and generate negligible fields outside their boundaries. Where n is the number of turns per unit length of the solenoid. The magnetic field is directed parallel to the axis of the solenoid. The right hand rule for currents will help you determine toward which end the field points.

13. A solenoid has length of 25 cm, radius of 1 cm, 400 turns, and carries a current of 3 A. What is the value of the magnetic field inside the solenoid?

14. We saw that charged particles in a uniform magnetic field will move in a circle. We can take advantage of our understanding of the magnetic force to create a device which can tell us the elemental composition of unknown particles. x x x x x r

15. r We saw that the radius of the circle is determined by the mass, speed, and charge of the particles, and the strength of the magnetic field. If we know the velocity at which a particle enters a magnetic field, the strength of that field, and the particle’s charge, we can measure the radius of curvature of the particle.

16. x x x x x d We can measure d using a photographic plate (for example) to record the location of the end of the particle’s path. d = 2 r

17. If two particles with the same charge enter the magnetic field with the same velocity, then the difference in the radii of their paths must be due to a difference in their masses. x x x x x x x x x d1d1 d2d2

18. d1d1 d2d2 Mass Spectrometer