A Positron has the same mass, but opposite charge to an electron. A Positron and electron are orbiting around each other separated by 1μm, in a stable circular orbit about their centre of mass, as a result of electrostatic attraction. Calculate the period
State Coulomb's law:F=(1/4πE0 )(qQ/d2)Since the distance separating the charges is twice the radius of the orbit relabel d to 2r and the charges are equal and opposite:F= -(1/16πƐ0 )(q/r)2Notice that this is simple circular motion so we can use the force to relate these two concepts in an equation (here we can ignore the negative since it is present in the previous equation by convention to show that the force is attractive, in circular motion an inwards force is considered positive):mw2r = (1/16πƐ0 )(q/r)2w = sqrt(1/mr3πƐ0 )(q/4)Knowing that T = 2π/w, obtain:T= sqrt(mr3 πƐ0)*(8π/q)Put all the numbers in on a calculator to get the final answer:2.8 x 10-10s (2 s.f.)
JB
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