Magnetic fields & electromagnetic induction

1. Magnetic fields & electromagnetic induction

2. 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

3. 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 .

4. 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.

5. Defining magnetic flux density Fleming’s left-hand rule: Force on the wire is perpendicular to both l and B. Typical magnetic field strengths:

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

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

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

9. 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

10. 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.

11. 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

12. 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.

13. 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?

14. 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

15. 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

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