Magnetic Fields & Forces

Oersted discovered that an electric current will produce a magnetic field around conductor only a moving charge creates a magnetic field

the magnetic field is circular around the wire and always at right angles to the wire the direction of the field is determined by direction of current flow

the strength of the magnetic field varies directly as the current and inversely as the distance from the wire (Ampere s Law)

Direction conventions Into page Out of page towards you

Point the thumb in the direction of current flow, and curl the fingers. The fingers point in the direction of the magnetic field. 1 st Hand Rule

Current conventional current is the direction positive charges move (from + to -) Conventional current includes protons, alpha particles etc. Electron current is the direction of electron flow

for electron current use the LEFT HAND Use the RIGHT HAND for conventional current

AP Current flow is the direction of positive charges! Use the right hand rule!

Example A beam of alpha particles is fired into the plane of the page. Determine the direction of the magnetic field around the beam. Current flow

Example Two long parallel conductors carry conventional current out of the plane of the page. Will the wires be attracted or repelled? Since the fields are in opposite directions in the region between the conductors, they will attract

AP Ampere s Law B 2 0 I r Magnitude of field at a distance r from a conductor 0 = vacuum permeability = 4 x 10-7 (T m)/a

Magnetic Fields From a Coil if a currentcarrying wire is formed into a loop, the magnetic field inside the coil will be increased Electron flow in wire

Magnetic Fields From a Coil the magnetic field of a coil is like the field of a bar magnet north and south poles Electron flow in wire

Formation of the field in a coil Electron flow into the plane of screen Electron flow out of the plane of screen, use 1 st hand rule to determine direction of field around each loop

Properties of the field Uniform strength and direction inside coil Weak field outside the field strength in the coil varies directly as the number of loops and directly as the current

A solenoid is a coil that is long straight coil of wire used to generate a nearly uniform magnetic field similar to that of a bar magnet

2nd Hand rule (for coils) curl the fingers in direction of the current flow in the coil point the thumb straight out, the thumb will point in the direction of the north pole of the electromagnet See P 588 S N Electron flow

Example Which 2 arrows indicate the correct direction of the magnetic field lines? Electron flow

Example Determine the direction of the magnetic field at point P. a. Top of page b. Bottom of page c. Into page d. Out of page

Moving Charges in Magnetic Fields moving charges (electrons, protons, alpha particles, etc) can be deflected by magnetic fields the magnitude of the force on the particle depends on the magnetic field strength, the charge on the particle and the velocity (magnitude and direction) of the particle

Lunar Transit as seen by Solar Dynamic Observatory

indicates that the velocity is at right angles to the magnetic field F qv B m the magnetic force on the particle is zero if the particle is going parallel to the magnetic field if the direction of travel (v) is at right angles to the magnetic field vector, the resulting force has a max. magnitude and is perpendicular to BOTH v and B

F B = qvb sin AP equation = angle between v and B vectors Only the perpendicular components give rise to a force.

the magnetic force deflects the charged particles from a straight line but doesn't cause them to change their speed E = 0 the magnetic field does no work on the charges W = Fd cos ( = 90 o, cos = 0)

3rd hand rule (forces on charges) thumb in direction of charge motion fingers point in the field direction (toward south pole) palm indicates the direction of the magnetic force on the charged particles

Magnetic force on moving charges

The force to the velocity vector means that the particles will go in uniform circular motion

Magnetic plasma (gas of charged particles) ejected from the sun

the centripetal force is always toward the centre of the circle and is caused by the magnetic force the radius of the circle can be found by setting F m = F c

Derive an equation to find the radius of the circle: F m = F c qvb mv r 2 qvbr mv2 qbr mv r mv qb

Forces on Current-carrying conductors if a current-carrying conductor is placed in a perpendicular magnetic field, a force will be exerted on the conductor F I B m l = wire length in magnetic field at right angles to field

F B = BIl sin AP Equation

Combined fields are in opposite direction: attract Magnetic field of conductor and magnets are in same direction: fields repel

Determine the direction of the magnetic force in the following diagram. The direction of electron current is out of the page. Example

Example A wire carries an electron current of 15 A through a perpendicular magnetic field. Determine the magnitude and direction of the magnetic force acting on the wire.

F = (15 A)(0.20 m)(0.25 T) = 0.75 N to the right side of the page.

Example Identify the path followed by the following particles: proton High speed electron 3 2 4 Neutral particle 1

Example Calculate the magnitude and direction of the magnetic force acting on a proton traveling north at 3.52 x 10 5 m/s through a magnetic field of 0.280 T, if the magnetic field is directed upward.

Solution v 1.58 x 10-14 N, east

Example A proton is accelerated from rest through a potential difference of 3.34 x 10 5 V. It then enters a region perpendicular to a 0.0200 T magnetic field. How large is the radius of the path?

Example A proton moving at 1.00 km/s is 5.50 mm from a wire carrying 5.00 A to the top of the page. Determine the magnitude and direction of the magnetic force on the proton. Wire, I = 5.00 A

Solution B = 1.818 x 10-4 T into the page F m = 2.91 x 10-20 N towards the wire

Northern lights The Aurora, often called the northern or southern lights, are caused by interactions between Earth's upper atmosphere and charged particles from the Sun.

Northern Lights Charged particles spiral around the magnetic field lines and strike the upper atmosphere in the north and south

Mass Spectrometers Determines the mass of charged particles Use electric and magnetic fields to separate molecules

Ion chamber Sample is ionized by an electron beam then accelerated by an electric field

Velocity Selection Charged particles then travel through mutually electric and magnetic fields Particles with correct speed are undeflected

Derive an equation to determine the velocity of the particles leaving the velocity selector. Velocity Selector

Derive Equation:

Separation Different ions are separated by the magnetic field depending on: the mass of the ion. Lighter ions are deflected more than heavier ones. the charge on the ion. Ions with 2 (or more) positive charges are deflected more than ones with only 1 positive charge

Separation Ions having low mass (low momentum) will be deflected most by this field high momentum ions will not be deflected enough and will collide with the wall

+q - slit x x x x x x x x v + E B R Photographic plate 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 m 2 The larger the mass, The larger the radius 2 mv R qvb m 1

Detection The output of the mass spectrometer shows a plot of relative intensity vs the mass-to-charge ratio (m/q) F c mv r mv 2 F m qv qr B B m q rb v

Detection By varying the strength of the magnetic field, different mass-tocharge ratios detected