Lecture Notes (Forces Caused By Magnetic Fields)

Intro: - as you saw in studying Coulomb’s law, electrically charged bodies exert forces on each other; when the charged bodies are at rest, the forces are “electric” forces, or Coulomb forces - “electric fields” act as the sources of these forces; but when the charged bodies are moving (as when two parallel wires carry currents), new forces in addition to the electric forces are present - these new forces are called “magnetic” and are caused by “magnetic fields” set up by the moving charges Forces on Currents in Magnetic Fields: - experiments show that a stationary charged particle does not interact with a static magnetic field, however, when moving through a magnetic field, a charged particle experiences a magnetic force - this force has a maximum value when the charged particle is traveling in a direction perpendicular to the magnetic field - the magnetic force has a minimum value when the charged particle is traveling along the magnetic field lines - there is a helpful rule that relates the velocity (v) of the charged particle, the direction of the magnetic field (B), and the magnetic force (F) experienced by the charged particle; it is called the third right hand rule

- the third right hand rule states that with your thumb in the direction of v and your four fingers in the direction of B, the force is directed out of the palm of your hand

- the mathematical relationship of magnetic force can be summarized as follows:

sinθqF vB

- magnetic force, F, is in newtons (N) - electric charge, q, is in coulombs (C) - velocity of the charged particle, v, is in meters per second (m/s) - magnetic field strength, B, is in teslas (T) - angle theta, θ, is the angle between the direction of v and the direction of B is in degrees (°) - many times another unit is substituted for magnetic field strength B; instead of teslas another unit called the gauss (G) is used - the conversion for these units is: 1 T =104 G - as stated earlier the magnetic force is maximal when the charge is traveling perpendicular to the field (θ = 90°)

- the force is minimal (zero) when the charge is traveling along the field lines (θ = 0°) - the force on a wire in a magnetic field can be demonstrated using the experiment below:

- arrows are used to describe the direction of a magnetic field; when the direction of the field is into the page X's are used, when the field is coming out of the page dots are used

X X X X X X X X X

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Magnetic field directed out of the page

Magnetic field directed into the page

- Michael Faraday discovered that the magnetic force on a current carrying wire is at right angles to both the direction of the velocity of the charge and the direction of the magnetic field (the experiment diagrammed in the pictures above) - up to this point we have been dealing with the magnetic force applied to a current carrying wire; let's take a look at the forces between wires carrying current

- as we can see in the diagram above, two current carrying wires will attract each other when the currents are in the same direction - conversely, two current carrying wires will repel each other when their currents move in opposite directions - it is possible to mathematically calculate the force of magnetism that is exerted on a current carrying wire passing through a magnetic field at right angles to the wire

- the equation is:

ILF B

- magnetic force, F, in newtons (N) - magnetic field strength, B, in teslas (T) - current in wire, I, in amperes (A) - length of wire, L, in meters (m) Loudspeakers: - a loudspeaker is one application of the force generated on a current carrying wire in a magnetic field - a loudspeaker converts electrical energy to sound energy using a coil of fine wire mounted on a paper cone and placed in a magnetic field

- the current in the speaker will change direction rapidly, causing the paper cone to vibrate; this is what generates the sound waves Galvanometers: - galvanometers are devices used to measure small amounts of electrical current

- galvanometers work by using the magnetic forces generated on a small piece of wire which is carrying a current - the magnetic forces create a rotational force (torque) on the wire; the greater the torque, the greater the current measured by the galvanometer

- these devices can read currents as little as 50 μA Electric Motors: - if you modify the design of a galvanometer slightly, you end up with an electric motor; the main difference between the two is that the current is made to change direction every time the coil makes a half rotation (180 º) - electric motors are designed this way so they can rotate a full turn of 360 º - an electric motors convert electrical energy to kinetic energy; they consist of a rigid current carrying loop that rotates when placed in the field of a magnet

- at this point (when the wire is in the same direction as the magnetic field lines) the force on the wire is zero - in an electric motor the loop has to be able to rotate a full 360º; therefore, the current must reverse direction just as the loop reaches 180º; this will allow the motor to provide continuous rotation in one direction

- split-ring commutators are used to reverse current direction - pieces of graphite that make contact with the commutators called brushes allow current to flow into the loop; graphite is used because it is a good conductor as well as a good lubricant - as the loop changes brushes, the current the loop experiences reverses and the loop continues to rotate - this process repeats every half-turn, causing the loop to spin in the magnetic field Electric Motor Animation - the loops of wire in an electric motor is called the armature; it is mounted on a shaft or axle - the total force acting on the armature is: n ILF B where n is the total number of turns in the armature

- the magnetic field is generated by permanent magnets or an electromagnet called a field coil; the speed of the motor is controlled by varying the amount of current through the motor Force on a Single Charged Particle: - charged particles do not have to be in a wire, but can also move freely through space - there are many applications for controlling the direction of a charged particle, but air must not be present, however, in order to remove any collisions with air molecules - televisions and computer monitors are examples of modern day cathode-ray tubes - a cathode-ray tube is a glass tube with a sealed wire at each end, each wire ended in a metal plate called an electrode; outside the tube, each wire runs to a source of high voltage (battery) - the negative plate is called the cathode and the positive plate is called the anode

Cathode ray tube

electrodes

anode cathode

ammeter

voltage source

- British physicist, J.J. Thomson (1856 - 1940) created the cathode-ray tube

- scientists discovered that if you pass an electric current through the low-pressure gas in the tube, the tube itself glowed with a pale green color

- it was shown that the green glow was produced by something that comes out of the cathode and travels down the tube until it hits the glass; hence the name cathode rays - in 1897, Thomson hypothesized that cathode rays were negatively charged particles; these were later called electrons - the electrons in a television or computer monitor are focused by magnets to form a narrow beam that move up and down the screen of the tube; the tube is coated with phosphor that glows when hit by an electron, thereby producing the picture

- the magnetic force on a single electron moving perpendicular to a magnetic field of strength B can be determined by the following mathematical equation:

qF B v - the charge is measured in coulombs, the velocity in meters per second (m/s) and the magnetic field strength in teslas (T) - note that when using the third right hand rule on finding the direction of the magnetic force on the electron, since it is negative you will have to use your left hand Auroras (Northern & Southern Lights): - when cosmic radiation, charged particles from the sun and other celestial phenomena outside our solar system, collides and interacts with molecules in our atmosphere, bright lights result

- these auroras occur only at locations near the north and south poles; they form here because of the structure of the Earth's magnetic field

- another interesting result of the structure of the Earth's magnetic field is the formation of two radiation belts around the planet - these belts are called the Van Allen belts named for their discoverer, James Van Allen - the Van Allen belts are composed of high- energy electrons and protons temporarily trapped in the Earth's magnetic fields

- any spacecrafts and/or persons traveling through these belts must have protective shielding to withstand the intense radiation

James Van Allen (1914-present)