Chapter 27 – Magnetic Field and Magnetic Forces- Magnetism- Magnetic Field- Magnetic Field Lines and Magnetic Flux- Motion of Charged Particles in a Magnetic Field- Applications of Motion of Charged Particles- Magnetic Force on a Current-Carrying Conductor- Force and Torque on a Current Loop1) A moving charge or collection of moving charges (e.g. electric current) produces a magnetic field. (Chap. 28).2) A second current or charge responds to the magnetic field andexperiences a magnetic force. (Chap. 27).1. MagnetismPermanent magnets: exert forces on each other as well as on unmagnetizedFe pieces. - The needle of a compass is a piece of magnetized Fe. - If a bar-shaped permanent magnet is free to rotate, one end points north (north pole of magnet).- An object that contains Fe is not by itself magnetized, it can be attracted by either the north or south pole of permanent magnet.- A bar magnet sets up a magnetic field in the space around it and a second body responds to that field. A compass needle tends to align with the magnetic field at the needle’s position.1. Magnetism- Magnets exert forces on each other just like charges. You can draw magnetic field lines just like you drew electric field lines.- Magnetic north and south pole’s behavior is not unlike electric charges.For magnets, like poles repel and opposite poles attract.- A permanent magnet will attract a metal like iron with either the north or south pole.Magnetic poles about our planet- We observed monopoles in electricity. A (+) or (-) alone was stable, and field lines could be drawn around it.- Magnets cannot exist as monopoles. If you break a bar magnet between N and S poles, you get two smaller magnets, each with its own N and S pole.Magnetic declination / magnetic variation: the Earth’s magnetic axis is not parallel to its geographic axis (axis of rotation)  a compass reading deviates from geographic north.Magnetic inclination: the magnetic field is not horizontal at most of earth’s surface, its angle up or down. The magnetic field is vertical at magnetic poles.Magnetic Poles versus Electric Charge-In 1820, Oersted ran experiments with conducting wires run near a sensitive compass. The orientation of the wire and the direction of the flow both moved the compass needle.- Ampere / Faraday / Henry  moving a magnet near a conducting loop can induce a current.- The magnetic forces between two bodies are due to the interaction between moving electrons in the atoms.- Inside a magnetized body (permanent magnet) there is a coordinated motion of certain atomic electrons. Not true for unmagnetized objects.2. Magnetic FieldElectric field:1) A distribution of electric charge at rest creates an electric field E in the surrounding space.2) The electric field exerts a force FE= q E on any other charges in presence of that field.Magnetic field:1) A moving charge or current creates a magnetic field in the surrounding space (in addition to E).2) The magnetic field exerts a force Fmon any other moving charge or current present in that field. - The magnetic field is a vector field  vector quantity associated with each point in space.ϕsinBvqBvqFm==⊥BvqFm×=- Fmis always perpendicular to B and v.2. Magnetic FieldInteraction of magnetic force and charge- The moving charge interacts with the fixed magnet. The force between them is at a maximum when the velocity of the charge is perpendicular to the magnetic field.Right Hand RulePositive charge moving in magnetic field direction of force follows right hand ruleNegative charge  F directioncontrary to right hand rule.⊥= vBqFUnits: 1 Tesla = 1 N s / C m = 1 N/A m1 Gauss = 10-4 TRight Hand RuleIf charged particle moves in region where both, E and B are present:)( BvEqF×+=Measuring Magnetic Fields with Test Charges- In general, if a magnetic field (B) is present, the electron beam is deflected. However this is not true if the beam is // to B (φ = 0, π  F=0  no deflection).Ex: electron beam in a cathode X-ray tube.No deflection  F = 0  v // BDeflection  F ≠ 0  F ┴ v, BElectron q< 0 F has contrary direction to righthand rule- Magnetic field lines may be traced from N toward S (analogous to the electric field lines).- At each point they are tangent to magnetic field vector.- The more densely packed the field lines, the stronger the field at a point.- Field lines never intersect.3. Magnetic Field Lines and Magnetic Flux- The field lines point in the same direction as a compass (from N toward S).- Magnetic field lines are not “lines of force”.- Magnetic field lines have no ends  they continue through the interior of the magnet.Magnetic Flux and Gauss’s Law for Magnetism∫∫∫⋅=⋅==Φ⊥AdBdABdABBϕcos- Magnetic flux is a scalar quantity.- If B is uniform:ϕcosBAABB==Φ⊥0=⋅=Φ∫AdBBUnits: 1 Weber (1 Wb = 1 T m2 = 1 N m / A)- Difference with respect to electric flux  the total magnetic flux througha closed surface is always zero. This is because there is no isolatedmagnetic charge (“monopole”) that can be enclosed by the Gaussian surface. - The magnetic field is equal to the flux per unit area across an area at right angles to the magnetic field = magnetic flux density.⊥Φ=dAdBB4. Motion of Charged Particles in a Magnetic FieldBqmvR =BvqFm×=- Magnetic force perpendicular to v  it cannot change themagnitude of the velocity, only its direction. - F does not have a component parallel to particle’s motion  cannot do work.- Motion of a charged particle under the action of a magnetic field alone is always motion with constant speed. - Magnitudes of F and v are constant (v perp. B)  uniformcircular motion.RvmBvqF2=⋅⋅=Radius of circular orbit in magnetic field: + particle  counter-clockwise rotation.- particle  clockwise rotation.A charged particle will move in a plane perpendicular to the magnetic field.- If v is not perpendicular to B  v//(parallel to B) constant because F//= 0 particle moves in a helix. (R same as before, with v = v┴).Cyclotron frequency: f = ω/2πAngular speed: ω = v/R mBqmvBqv ==ω5. Applications of Motion of Charged ParticlesVelocity selectorSource of charged particles- Particles of a specific speed can be selected from the beam using an arrangement of E and B fields.- Fm(magnetic) for + charge