Magnetism

Objectives Motion of a charged particle in a uniform magnetic field. Force on a current carrying wire in a magnetic field. Magnetic Field around a current carrying wire.

Review We’ve studied several forces so far. …and what causes them… Thrust & Tension (push-pull) Friction …and what causes them… Gravity Electricity …and now…

Magnetism Examples To design things efficiently, we need… Equations. Refrigerator magnets. Compass. Electric Motors and generators. Toys! To design things efficiently, we need… Equations.

Equations Slow down, each one in time!

Force at a distance. Magnetism is a field force. A compass aligns to the earth’s magnetic field. Earth’s “north pole” is really a magnetic south pole. Opposites attract. The north end of the needle points to the “North pole” since it’s really south! Let’s Draw it…

Force field of a magnet Magnets attract most iron alloys. Magnets will attract/repel other magnets. A compass will plainly show the direction of a magnetic field. Magnetic fields also interact with electrically charged particles. A magnetic field has direction, so…

It’s a vector! Perhaps a good time to define some variables You try!

What are they? F - ? Force q - ? Charge v - ? Velocity B - ?

To B or not to B (That’s interdisciplinary) You got it, B must be the magnetic field vector. Units are Tesla, T (a smart dude) Fun with units ; (Newtons per coulomb per (meter per second) or (Newton seconds/coulomb meter) Earth’s field is about 55 x 10-6 T Magnets can be much stronger.

Cross Product The equation contains a cross product. We’ll need to drag out the right hand rule. The force on a charged particle MOVING though a magnetic field is perpendicular to its velocity and the magnetic field.

Right hand rule. F B v

Conventions Velocity gets an arrow Fields can be draw as dots (out of page) …or crosses (into page) q, v B (into page)

What happens? q, v B (into page) Let’s draw it. ex1

What happens? B (into page) q, v What if we increase the mass or charge?

Let’s apply this equation. Mass spectrometry is a technique to identify the mass to charge ratio of ions of a substance. It can be used to identify elements present in a gas. Turn the unknown into a gas, ionize it, shoot it into a magnetic field and observe! Piece of cake.

The algebra.

What if... What if we increase q? …m …B …v

Let’s pull it together. An alpha particle enters a magnetic field of 2.5 x 10-2 Telsa with a velocity of 1.4 x 105 m/s, perpendicular to the field. It has a charge of 2e and a mass of 6.64 x 10-27 kg. What is the radius of its path while in the magnetic field? ex2

Elmo time

Answer I got 11.6 cm… How about you?

Cross Product note The force will be perpendicular to both velocity and magnetic field. When the angle is other than 90 deg the sine come into play.

Right hand rule. F B v q=30 deg

Let’s redo the last one with a new angle of 30 deg. An alpha particle enters a magnetic field of 2.5 x 10-2 Telsa with a velocity of 1.4 x 105 m/s, at 30 deg to the field. It has a charge of 2e and a mass of 6.64 x 10-27 kg. What is the radius of its path while in the magnetic field? ex3

Answer The force will be halved since… So the radius doubles. Who can tell us something else about the path of the particle?

Elmo time

OK, lots of time on that one little jewel. It’s the basis of the other cool magnetic phenomena. Here’s a few more: Force on a wire in a magnetic field. Torque on a loop of current carrying wire due to a magnetic field.

Force on a wire. A 10 cm wire carries 2.0 amps perpendicular to a magnetic field of 0.25 Tesla. What is the magnitude of the force on the wire? I B 10 cm ex4

(What direction is it in?)

Magnetic Field created by a current carrying wire The new constant is the permeability of free space m0=4p x 10-7 Tm/A r is distance from wire to point being evaluated.

Calculate B What is the magnetic field strength and direction 0.15 m from a long wire carrying 500 milliamps? B I ex5

Direction Point thumb in direction of current. Fingers curl in direction of magnetic field. Field lines are concentric circles around the wire. Strength diminishes inversely with distance from the wire

I know what you must be thinking. So if a current in a wire creates a magnetic field and a magnetic field creates a force on another current carrying wire then… Of course, two wires carrying current near each other will… Attract or repel.

Mutual force between two parallel wires. Force on a wire in a magnetic field. Field caused by current in a wire.

Mutual attraction What is the force per unit length between two wires carrying 0.35 amps in the same direction 1.2 cm apart? ex6

Combine the two! Angle between the field created by one wire with the current in the other is 90 deg, so… Distance between the wires is “d”

Railgun So let’s review with an example of current physics application in our own backyard. Navy Railgun Project, NSWC Dahlgren, VA

Magnetic Field around a wire. What is the magnetic field strength between the rails 7.0 cm apart carrying 1.5 million amps up one rail and back down the other? What direction is it in? ex7

Force on a wire What is the force on the projectile between the rails? Hint: It carries the whole current across the magnetic field. F I ex8

Force between two wires What is the mutual repulsive force per length between the rails? ex9

How fast? If the mass of the projectile is 2 kg, and the rails are 5 meters long, how fast will the projectile leave the rails. Ignore friction. ex10

Questions? http://en.wikipedia.org/wiki/Nikola_Tesla