Electric Motor and Dynamo the Hall effect

Transcription

1 Electric Motor and Dynamo the Hall effect Frits F.M. de Mul Motor and Dynamo; Hall effect 1

2 Presentations: Electromagnetism: History Electromagnetism: Electr. topics Electromagnetism: Magn. topics Electromagnetism: Waes topics Capacitor filling (complete) Capacitor filling (partial) Diergence Theorem E-field of a thin long charged wire E-field of a charged disk E-field of a dipole E-field of a line of dipoles E-field of a charged sphere E-field of a polarized object E-field: field energy Electric motor and dynamo; Hall effect Electromagnetism: integrations Electromagnetism: integration elements Gauss Law for a cylindrical charge Gauss Law for a charged plane Laplace s and Poisson s Law -field of a thin long wire carrying a current -field of a conducting charged sphere -field of a homogeneously charged sphere Downloads: scroll to Electricity and Magnetism Motor and Dynamo; Hall effect 2

3 Electric Motor and Dynamo the Hall effect Contents 1. Magnetic (Lorentz) force 2. Hall effect 3. Electric motor 4. Dynamo 5. Conclusions 6. Hall effect reisited Motor and Dynamo; Hall effect 3

4 1. Magnetic (Lorentz) force = q. x Metal wire = ext θ positie charge, elocity q = charge = elocity = magnetic field ( induction ) To find : Rotate clockwise from to in the ( - ) plane. then follows the direction of the ± cork screw (± depending on the angle θ) = q.sin θ 0 θ : sin θ 0 : cork screw 180 θ : sin θ 0 : - cork screw Right hand rule : rotate from a to b oer smallest angle: a x b follows cork screw direction Motor and Dynamo; Hall effect 4

5 Metal wire Metal wire 1. Lorentz force = ext θ θ = q. x = electron has negatie charge. q = -1.6x10-19 C < 0! points for and charges in same direction. QUESTON: works on moing charges only ( 0)....but metal ions are at rest. Why does the wire moe? Answer: the Hall effect. Motor and Dynamo; Hall effect 5

6 2. Hall effect Lorentz force : q. = ext Electrons will deflect. Charge build-up. Field E build-up P E FL F E Q F E = until electrons feel F E = Contacts P and Q. Metal ions feel E and force F E (= ), directed to Q... and so the wire will moe. seems to act directly on the wire. Motor and Dynamo; Hall effect 6

7 3. Electric motor Lorentz force : q.! Stable = ext D A D situation C A Metal frame C = electron q = -1.6x10-19 C < 0! From Hall effect: Metal ions feel electric force, thus along the working on the electrons. can be considered as working on the current and then acting on the wire. Frame starts rotating.. until A aboe CD Frame tries to enclose as much of the fitting -field, by maximizing its area in the fitting position. Motor and Dynamo; Hall effect 7

8 3. Electric motor = ext A D int NOW it is time to reerse the contacts! Then frame will rotate further, oer etc. etc. C F E = can be considered as working on the current and then acting on the wire. Frame tries to enclose as much of the fitting -field, by maximizing its area in the fitting position, and by producing its own internal field int along the external field ext, since for the current the cork screw rule holds. Motor and Dynamo; Hall effect 8

9 4. Dynamo Lorentz force : q. = ext D V A C A C rotation Now external rotation. = electron q = -1.6x10-19 C < 0! Electrons get elocity and will feel. This produces current and int. Direction of int : counteracting ext. ( Lenz Law ) n upright situation: // ext, Thus no and there. V D int Time to interchange the contacts! Current gets sine shape in time due to sinθ, and θ aries with time. Motor and Dynamo; Hall effect 9

10 4. Dynamo Lorentz force : q. works on electrons and produces current. = ext D C rotation Secondary effect: current with ext will produce extra 2, working on the wire. This extra 2 will counteract the rotation! V A You hae to delier mechanical energy to get the dynamo rotating! 2 N. This secondary effect is also present in the electric motor and causes energy losses. Motor and Dynamo; Hall effect 10

11 5. Conclusions 1. Hall effect: - potential difference due to electric balancing force. 2. Electric motor: - tries to rotate so as to align its internal field with the external field - tries to maximize the fitting flux 3. Dynamo: - produces counteracting current and field Motor and Dynamo; Hall effect 11

12 6. Hall effect reisited h w Metal wire = electron q = -1.6x10-19 C < 0! Suppose we hae n electrons per m 3, each with elocity (m/s) All electrons that will pass the front side in the next second from now. front side h.w will now be within block (hw) with olume hw [m 3 ]. Charge passing front side in this second = n. q. hw [C]. Current = -nq.hw [C/s = A]. is proportional to n and. Motor and Dynamo; Hall effect 12

13 6.Hall effect reisited Lorentz force : q. = ext Electrons will deflect. Charge build-up. Eentually: F E = q. E = q.. Potential difference: V P V Q = E.w =..w h P w F E Q V P V Q nqh From preious slide: = -nq.h. w w nqh V P V Q ~ : Magnetometer. the end Motor and Dynamo; Hall effect 13