Movement of Charged Particles in Electric Fields

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Presentation transcript:

Movement of Charged Particles in Electric Fields 2.1.13 Consider a uniform field between two parallel plates, distance d apart. The p.d. between the plates is V. Fe - V d A negatively charged particle of mass, m and charge, Q is placed near the negative plate as shown. There is a constant electrical force, Fe in the direction shown. + (Note: gravitational forces can be assumed negligible by comparison to electric forces.) The work done by the field is converted into kinetic energy.

Work done = Ek Fd = ½ mv2 – 0 QEd = ½ mv2 (F = QE) QV = ½ mv2 (V = Ed) The final speed of the particle can be found using: Page 13 student materials

Example In a cathode ray oscilloscope electrons are accelerated over a p.d. of 10kV. Calculate the speed at which they pass through the hole in the anode.

mc2 = m0c2 + Ek => mc2 = m0c2 + QV Page 14 student material So electrons can be accelerated to very high speeds with relatively small voltages. If V, above, is increased to 1MV we find the speed would exceed the speed of light. We must include relativistic effects for speeds greater than about 10% of c. mc2 = m0c2 + Ek => mc2 = m0c2 + QV Where m is the relativistic energy. Remember: Page 14 student material

Fast moving protons strike a screen with a speed of 2. 0 x 10 6 ms-1 Fast moving protons strike a screen with a speed of 2.0 x 10 6 ms-1. Glass is largely composed of silicon which has an atomic number 14. Calculate the closest distance of approach that a proton could make in a head-on collision with a silicon nucleus. Answer =9.7 x 10-13 m

Rutherford scattering – 1912 Geiger and Marsden – fired a beam of alpha particles through a gold foil – some deflected at angles but a few were deflected backwards - head on collision http://www.bing.com/videos/search?q=rutherford+scattering+experiment&FORM=HDRSC3#view=detail&mid=530FFEFE785CFF3B92A2530FFEFE785CFF3B92A2

Head-on Collision of Charged Particle with Nucleus A charged particle moving at speed, v towards a nuclei will be brought to rest before it reaches it, if it has a positive charge. Initially the particle is far from the nucleus. + q v ++ +++ Q infinity At closest approach the charge is brought to rest at a distance, r from the nucleus. r + q ++ +++ Q v = 0

Change in Ek = change in electrostatic Ep The particle may be brought to rest before it actually reaches the nucleus Change in Ek = ½ mv2 – 0 = ½ mv2 Change in electrostatic Ep = qQ 1 - 0 = qQ 1 r r 4π 4π Change in Ek = change in electrostatic Ep

http://www. bing. com/videos/search http://www.bing.com/videos/search?q=rutherford+scattering+experiment&FORM=HDRSC3#view=detail&mid=530FFEFE785CFF3B92A2530FFEFE785CFF3B92A2

Millikan’s oil drop experiment page 16 pupil materials Electric force = EQ or VQ d Gravitational force = mg The term quantum is used to describe a quantity which exists in integral multiples, so we can say that charge is quantised in units of 1.6 x 10 -19 C. Q = ne (n = +-1, +-2, etc)