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Transcript
The Millikan Oil Drop Experiment & Elementary Charge Scientists wondered … Does there exist in nature a smallest unit of charge? If so, what is the magnitude of this “elementary charge”? The Millikan Oil-Drop Experiment FE = FG qe = mg q = mgr ∆Vb since e = ∆V r where DVb is the balancing value b/w the plates q DVb = mg r (-) negatively charged plate FE + e Fg Vb (+) http://www.youtube.com/watch?v=XMfYHag7Liw r positively charged plate Determining the Elementary Charge q = mgr DVb The Elementary Charge e = 1.602x10-19C (-) negatively charged plate FE + Fg q = Ne where N = # of excess/deficit of electrons e Vb (+) r positively charged plate Example 1 Two parallel plates are placed 1.5cm apart with a potential difference of 275V between them. The upper plate is negative. An oil drop of mass 4.5x10-15kg is balanced inbetween the plates similar to Millikan’s experiment. a) Is the drop charged positively or negatively? b) What is the charge magnitude on the drop? c) How many excess/deficit electrons does the drop possess? Limitations Millikan accurately calculated “e”. But his experiment did not adequately describe the motion of charged particles (due to the presence of air resistance). Instantaneous Acceleration a = FE m q2 FE + r1 q1 + r2 Acceleration of the charge will decrease because as r↑, FE↓ Conservation of Energy ET = EE + EK q2 FE + r1 ET’ = EE‘ + EK’ q1 + r2 Total Energy of the charge remains constant because as EE decreases, EK increases any change in a particle’s electric potential energy results in a corresponding change to its kinetic energy when moving in an electric field (and ignoring gravitational effects) Special Case Recall that parallel plates are a special case where e is uniform and constant … Therefore Electric Force is constant since FE = qe and so is acceleration, since a = FE m ∴ a charged particle in a uniform field moves w/ uniform acceleration Special Case Therefore, between two parallel plates : - DEE = DEK -qDV = ½ mn 2 If n 10% the speed of light (v~ 3.00x107m/s) then the answer is not valid relativistic effects increase the mass Example 2 An electron is fired horizontally at 2.5 x 106 m/s between two horizontal parallel plates 7.5 cm long. The magnitude of the electric field is 130 N/C. The plate separation is great enough to allow the electron to escape. Edge effects and gravitational forces are negligible. Find the velocity of the electron as it escapes from between the plates. Example 1 - EXTRA A particle accelerator uses two parallel plates to accelerate a helium nucleus, or a particle, toward a Cesium atom in order to split it. The potential difference across the plates is 50,000V. With what speed does the a particle hit the Cs atom if it starts at rest? Is this answer valid? ma= 6.6x10-27 kg qa = 2e = 3.204x10-19 C Example 2 - EXTRA A stray, stationary proton finds itself 450nm from a gold nucleus. How fast will it be travelling when it is 15mm away? Au + qp qp + + 450nm 15mm Example 3 - EXTRA A small sphere with a charge of 750mC and a mass of 25mg is located midway between two charged plates separated by 40cm with a voltage of 200V. The charge is pulled slowly upward by a string until it reaches the positive plate and is then released. a) How much work does the string do on the sphere? b) What average force does the string exert? c) With what speed does the sphere reach the negative plate?