Magnetic fields & electromagnetic induction

Learning outcomes describe magnetic fields in terms of magnetic flux & flux density use Fleming’s left and right hand rules to describe interactions between magnetic field & current quantitatively describe B fields around a straight current-carrying wire and a solenoid quantitatively describe the force on a charged particle moving at right angles to a uniform B field explain electromagnetic induction using Faraday’s & Lenz’s law use the concept of flux linkage to explain how transformers work describe how B fields are used in circular particle accelerators recall the postulates and key consequences of special relativity solve related quantitative problems

Teaching challenges fields are abstract involves 3-D thinking but generally illustrated in 2-D involves rates of change different concepts have similar names some physical quantities have a variety of equivalent units students may need simple trigonometry to find the magnetic flux, or magnetic force, correctly identifying angle .

Permanent magnets Magnetic field lines start and finish at poles. Physicists picture this as a ‘flow’ in magnetic circuit. magnetic flux (phi), unit Weber magnetic flux density B, unit Weber m-2 or Tesla Carl Gauss & Wilhelm Weber investigated geomagnetism in 1830s, made accurate measurements of magnetic declination and inclination, built the first electromagnetic telegraph. Magnetic flux density sometimes referred to as magnetic field strength.

Defining magnetic flux density Fleming’s left-hand rule: Force on the wire is perpendicular to both l and B. Demo current balance: weight on one side balanced by magnetic force on other side. This is a method for measuring B. 1 Tesla = 1 N A-1m-1 Typical magnetic field strengths: Earth’s field bar magnet MRI magnet B ~50 mT 0.1 T 0.2 – 3.0 T

Electromagnetism Electric currents have loops of B flux around them. Current-turns produce flux.

Magnetic fields near currents long straight wire long solenoid, N turns and length l  is the permeability of free space

Forces on parallel currents parallel - attract anti-parallel - repel

Forces on parallel currents At the top wire in the diagram, Defining the ampere (straight wires of infinite length) If the current in each wire is exactly 1 A, and the distance between the wires is 1 m, then the force on each metre length of the wires will be 2 x 10-7 N. Practice questions: TAP Forces on currents Demo forces on parallel and anti-parallel currents.

Force on a moving charge Demonstration: fine beam tube uniform B-field at right angles to an electron beam with v F is perpendicular to v, so the beam travels in a circular path. Cyclotron invented by E Lawrence, 1928. Now replaced by synchrotron, in which B-field magnetic field E-field are both carefully synchronized with the travelling particle beam.

Fluxes and forces Michael Faraday (experimenting in 1830s at the Royal Institution) pictured magnetic field lines as flexible and elastic magnetic attraction: field lines try to get shorter & straighter magnetic repulsion: field lines cannot cross

Faraday’s law of induction Induced emf is proportional to rate of ‘cutting’ field lines. N is number of turns on the secondary coil. N is its flux linkage. Induced emf is proportional to rate of change in coil’s flux linkage. NOTE: Eddy currents are induced in iron core linking primary and secondary coils. These can be reduced by laminations in core.

No relative motion means no induced emf. can be: 1 the flux cut by a moving wire 2 the change in flux due to a magnet moving 3 the change in flux due to a stationary electromagnet which is changing in strength No relative motion means no induced emf. Under what conditions is there an induced current?

Experiments Force on a current-carrying wire Current balance Investigating fields near currents (using a Hall probe) Investigating electromagnetic induction Faraday’s law Jumping ring

Practice questions (Adv Physics) Changes in flux linkage (Adv Physics) Flux or flux linkage? TAP Rates of change (Adv Physics) Graphs of changing flux and emf

Endpoints rotating coil (AC) generator: motors produce a ‘back emf’